<%BANNER%>

Laboratory rip current circulation using video-tracked lagrangian drifters

University of Florida Institutional Repository
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LABORATORY RIP CURRENT CIRCULATION USING VIDEO-TRACKED LAGRANGIAN DRIFTERS By DAVID A. THOMAS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORI DA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2003

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This thesis is dedicated to my mother and father.

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iii ACKNOWLEDGMENTS This research was funded by the University of Florida. The author would like to thank Andrew B. Kennedy for providing the fi nancial assistance, academic guidance, and raw data for this research. The author would also like to thank the other committee members, Robert J. Thieke and Robert G. Dean, for all their help and insight.

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iv TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT......................................................................................................................x ii CHAPTER 1 INTRODUCTION........................................................................................................1 Problem Statement and Objective................................................................................1 Background: Rip Current Literature Review................................................................5 Physical Description of Rip Currents....................................................................6 Impact of Rip Currents..........................................................................................9 Forcing Mechanism.............................................................................................11 Unsteady Behavior of Rip Currents....................................................................14 Summary.....................................................................................................................15 Outline of Thesis.........................................................................................................16 2 EXPERIMENTAL SETUP........................................................................................18 Physical Model...........................................................................................................18 Test Conditions...........................................................................................................20 Data Collection...........................................................................................................21 Experimental and Data Collection Error....................................................................25 3 RESULTS AND ANALYSIS.....................................................................................27 General Rip Current Behavior....................................................................................28 Mean Velocity............................................................................................................34 Fluctuating Velocity...................................................................................................40 Unsteady Rip Current Flow........................................................................................42 Vorticity...................................................................................................................... 46 Continuity...................................................................................................................47 Velocity Distribution..................................................................................................49 Velocity Validation (VDT vs. Current Meters)..........................................................51

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v 4 CONCLUSIONS........................................................................................................56 APPENDIX A RIP CURRENT FEATURES (TEST 5).....................................................................61 B DRIFTER TRAJECTORIES AND VELOCITY (TEST 12).....................................64 C DRIFTER TRAJECTORIES FOR THE LONG TESTS............................................66 D MEAN VELOCITY....................................................................................................71 E FLUCTUATING VELOCITY...................................................................................76 F RIP CURRENT INSTABILITY.................................................................................84 G TIME-AVERAGED VORTICITY.............................................................................89 H TIME-AVERGED, DEPTH-INTEGRATED CONTINUITY...................................94 I VELOCITY DISTRIBUTION...................................................................................99 LIST OF REFERENCES.................................................................................................104 BIOGRAPHICAL SKETCH...........................................................................................108

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vi LIST OF TABLES Table page 2-1 Transient test conditions...........................................................................................20 2-2 Long test conditions.................................................................................................21 3-1 Percentage of drifters which exited th e visible flow domain to a certain side.........32 3-2 Percentage of drifters co mpleting (X) closed circuits..............................................32 3-3 Averaged maximum drifter velocity for each of the long tests................................33 3-4 Number of velocity measurements used to obtain a mean velocity in the rip channel using VDT which was compared with mean velocities determined from current meters for the long tests in Figure 3-21..............................................55

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vii LIST OF FIGURES Figure page 1-1 Schematic sketch of a rip current system ..................................................................2 1-2 Three scenarios for rip current formation ..................................................................6 1-3 Swim parallel to shore past the break er line to escape a rip current system............11 2-1 Plan view and cross-section of the experimental wave basin .................................19 2-2 Unevenly spaced bathymetry contour of basin with visible flow domain and ADV locations..........................................................................................................22 2-3 Buoyant disc used as Lagrangian drifters................................................................23 2-4 Original and rectified view of the visible flow domain...........................................24 3-1 Drifter positions and velocity at t=41 s after the wave-maker startup (Test 1)........28 3-2 Drifter trajectories within 22.5s time in tervals / drifter posit ions plotted every 7.5 s and corresponding velocity vector every 15s (Test 1).....................................29 3-3 Generation of a small vortex on the corn er bar, and the transport of a coupled drifter pair offshore as part of a larger overall circ ulation (Test 2)..........................30 3-4 Drifter trajectories and correspond ing velocity time series (Test 12)......................31 3-5 Drifter paths; 2 minute time intervals (Test 16).......................................................33 3-6 Mean Velocity / Test 12 / H= 4.32cm, T= 1s, groupy waves (32); high water.......34 3-7 Mean Velocity / Test 14 / H= 4.62cm, T= 1s, groupy waves (32); low water........35 3-8 Mean Velocity / Test 13 / H= 4.28cm, T= 1s, monochromatic waves; high water.........................................................................................................................3 6 3-9 Mean Velocity / Test 16 / H= 6.18cm, T= 1s, monochromatic waves; high water.........................................................................................................................3 7 3-10 Cross shore component of velocity along the rip channel centerline versus the cross shore location for the Long tests.....................................................................38

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viii 3-11 Test 16 / One minute averages of velocity within the field of view........................41 3-12 Mean Velocity / Test 16 / Obtained by averaging one-minute mean velocities; compared to the previous Figure 3-9........................................................................42 3-13 Test 16 / Alongshore (y) migration of the maximum one-minute average of total velocity through time for three cross shore bands offshore of the rip channel.....................................................................................................................43 3-14 Test 16 / One minute averages of velocity along three cross shore bands...............44 3-15 Test 16 / Time-averaged vorticity............................................................................47 3-16 Test 16 / Time-averaged, de pth-integrated continuity ............................................48 3-17 Location of four comput ational domains within the field of view used to obtain PDFs of drifter velo cities for the long tests...................................................50 3-18 PDFs of drifter velocity components at four locations shown in Figure 3-17 (Test 16)...................................................................................................................50 3-19 Current meter and VDT window locations used to make comparisons within the rip channel for both the transient and long tests.................................................52 3-20 Comparison of instantaneous velocity between VDT and current meters within the rip channel for the transient tests........................................................................53 3-21 Comparison of mean velocity between VDT and current meters within the rip channel for the long tests..........................................................................................54 A-1 Onshore flow over the bar due to waves / Drifter positions and velocity at t = 12 s after the wave-maker startup (Test 5)..........................................................61 A-2 Feeder currents convergi ng from either side of th e rip channel / Drifter positions and velocity at t = 22 s (Test 5)................................................................62 A-3 Offshore directed current through the rip neck / Drifte r positions and velocity at t = 32 s (Test5)......................................................................................................62 A-4 Expanding rip head offshore / Drifter positions and velocity at t = 53 s (Test 5).....................................................................................................................63 B-1 Drifter trajectories and correspond ing velocity time series (Test 12)......................64 B-2 Drifter trajectories and correspond ing velocity time series (Test 12)......................65 B-3 Drifter trajectories and correspond ing velocity time series (Test 12)......................65 C-1 Test 12 / Every drifter path for the entire run length; 2 minute time intervals........66

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ix C-2 Test 13.................................................................................................................... ..67 C-3 Test 14.................................................................................................................... ..67 C-4 Test 15.................................................................................................................... ..68 C-5 Test 16.................................................................................................................... ..68 C-6 Test 19.................................................................................................................... ..69 C-7 Test 20.................................................................................................................... ..69 C-8 Test 21.................................................................................................................... ..70 D-1 Test 12 / Mean Velocity / H= 4.32cm, T= 1s, groupy waves (32); high water........71 D-2 Test 13 / Mean Velocity / H= 4.28cm, T= 1s, monochromatic waves; high water.........................................................................................................................7 2 D-3 Test 14 / Mean Velocity / H= 4.62cm, T= 1s, groupy waves (32); low water.........72 D-4 Test 15 / Mean Velocity / H= 4.83cm, T= 1s, monochromatic waves; low water.........................................................................................................................7 3 D-5 Test 16 / Mean Velocity / H= 6.18cm, T= 1s, monochromatic waves; high water.........................................................................................................................7 3 D-6 Test 19 / Mean Velocity / H= 5.22cm, T= 1.33s, monochromatic waves; low water.........................................................................................................................7 4 D-7 Test 20 / Mean Velocity / H= 3.69cm, T= 1s, groupy waves (64); high water........74 D-8 Test 21 / Mean Velocity / H= 3.97cm, T= 2.67s, monochromatic waves; high water.........................................................................................................................7 5 E-1 Test 12 / 1 minute averages of ve locity within the field of view.............................76 E-2 Test 13.................................................................................................................... ..77 E-3 Test 14.................................................................................................................... ..78 E-4 Test 15 (Only tests 15 and 16 include th e effects of the wave-maker startup)........79 E-5 Test 16 (Only tests 15 and 16 include th e effects of the wave-maker startup)........80 E-6 Test 19.................................................................................................................... ..81 E-7 Test 20.................................................................................................................... ..82

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x E-8 Test 21.................................................................................................................... ..83 F-1 Test 12 / Alongshore (y) migration of the maximum one-minute average of total velocity through time for three cross shore bands offshore of the rip channel.....................................................................................................................84 F-2 Test 13.................................................................................................................... ..85 F-3 Test 14.................................................................................................................... ..85 F-4 Test 15.................................................................................................................... ..86 F-5 Test 16.................................................................................................................... ..86 F-6 Test 19.................................................................................................................... ..87 F-7 Test 20.................................................................................................................... ..87 F-8 Test 21.................................................................................................................... ..88 G-1 Test 12.................................................................................................................... ..89 G-2 Test 13.................................................................................................................... ..90 G-3 Test 14.................................................................................................................... ..90 G-4 Test 15.................................................................................................................... ..91 G-5 Test 16.................................................................................................................... ..91 G-6 Test 19.................................................................................................................... ..92 G-7 Test 20.................................................................................................................... ..92 G-8 Test 21.................................................................................................................... ..93 H-1 Test 12 / Time-averaged, de pth-integrated continuity.............................................94 H-2 Test 13.................................................................................................................... ..95 H-3 Test 14.................................................................................................................... ..95 H-4 Test 15.................................................................................................................... ..96 H-5 Test 16.................................................................................................................... ..96 H-6 Test 19.................................................................................................................... ..97 H-7 Test 20.................................................................................................................... ..97

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xi H-8 Test 21.................................................................................................................... ..98 I-1 Locartion of four computational domains within the field of view used to obtain PDFs of drifter velo cities for the long tests...................................................99 I-2 Test 12 / PDFs of drif ter velocity components at four locations shown in Figure I-1 ...........................................................................................................100 I-3 Test 13.................................................................................................................... 100 I-4 Test 14.................................................................................................................... 101 I-5 Test 15.................................................................................................................... 101 I-6 Test 16.................................................................................................................... 102 I-7 Test 19.................................................................................................................... 102 I-8 Test 20.................................................................................................................... 103 I-9 Test 21.................................................................................................................... 103

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xii Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science LABORATORY RIP CURRENT CIRCULATION USING VIDEO-TRACKED LAGRANGIAN DRIFTERS By David A. Thomas August 2003 Chair: Andrew B. Kennedy Major Department: Civil and Coastal Engineering A laboratory rip current system with a l ongshore bar and channel bathymetry at the Center for Applied Coastal Research (Uni versity of Delaware) was analyzed by the method of Video Drifter Track ing (VDT). Steady and unsteady processes of the rip current were studied using vi deo-tracked Lagrangian drifte rs for a range of wave and water level conditions. Drifter coverage and run lengths are sufficient to resolve both averaged and fluctuating quantities over the fi eld of view including m ean velocity (1 to 18 min. averages), velocity distributions at specified locations, and time-averaged vorticity. Results show strong quantitative and qualitative dependence on wave and water level conditions. Some of the tests s how classic symmetric circulation cells, while others exhibit rips with a st rong bias in one direction, even with shore normal waves. Trajectories and velocity of individual drifters were analy zed to determine general rip current features and circulati on patterns. Circulation was found to be unsteady on scales generally spanning several orders of magnitude in space and time. Results also include

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xiii insight into the mechanisms of rip current instability. To validate the method of VDT, the velocities obtained from the drifters were compared to current meters located in the rip channel and continuity was anal yzed throughout the visible domain. The laboratory is an ideal setting due to th e temporal and spatia l unsteadiness of rip currents. Field instruments are also ve ry expensive and subjected to a harsher environment, thus requiring a greater amount of maintenance. Until recently, laboratory rip current circulation has been analyzed by pl acing a series of curre nt meters throughout the flow domain. The financial cost of these me ters inhibits the abil ity to obtain a desired resolution of quantities throughout the complete rip current system. One advantage of VDT is that additional laborator y drifters are far less expensive than more current meters or field drifters if a finer reso lution of quantities is required. A comprehensive map of rip current flow will improve understanding of the nearshore circulation pattern; and is needed for further advances in predicting sediment transport and the overall shape of the coast line, which is a major issue for the growing number of coastal landowners. Many areas of the world, including Florida, also depend on the tourism generated from their beaches and rip currents pose a serious threat to ocean bathers because of their st rong, seaward directed flows.

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1 CHAPTER 1 INTRODUCTION Problem Statement and Objective The nearshore ocean is a complex region, influencing much of society. Many shorelines are heavily populated, making the coastal waters a potentially dangerous place for humans due to large waves and strong rip currents. Nears hore circulation and currents play an important role in beach erosion and the overall movement of coastal sediments. Structures such as inlets, groins piers, and harbors also interact with the coastal hydrodynamics, driving the research for predicting and quantifying nearshore processes. Fluid motion in the nearshore is influenced by many factors and is highly unsteady. The breaking of wind generated waves can indu ce such phenomena as surf beat, edge waves, storm surge, undertow, longshore curren ts, and rip currents; which all combine to create a very dynamic system. The intera ction of nonlinear waves with a varying shoreline and bathymetry further complicates the issue of nears hore hydrodynamics. The wave-induced currents interact with the near shore morphology, creating features such as beach cusps, spits, tidal shoals, and rip channels. Our study concentrated on rip current dynamics for a barred beach with rip channels. Rip currents are a seaward flow (u sually perpendicular to the shoreline) that “rip” through the waves and have been observe d to extend past the su rfzone (Shepard et al. 1941, Schmidt et al. 2001). Figure 1-1 shows a sketch of a rip current system. These seaward moving currents are responsible for much of the water exchanged between the

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2 offshore and nearshore coastal regions (S hepard et al. 1941, Shepard and Inman 1950, Bowen 1969, Bowen and Inman 1969). Rip curren ts are prevalent in the coastal waters and subsequently have a large impact on nears hore circulation, thus the entire sediment budget near the shoreline (Shepard et al. 1941, Shepard and Inman 1950, McKenzie 1958). The impact of rip currents on human so ciety is covered in fu rther detail in the literature review sectio n of this chapter. Figure 1.1: Schematic sketch of a rip cu rrent system (from National Oceanic and Atmospheric Administration (NOAA)) For our study, rip currents were generated in an experimental wave basin because creating a large data set of field rip currents under different wave conditions would be extremely difficult due to their relatively short life and tendency to migrate in the longshore direction. Despite the qualitative know ledge of the importan ce of rip currents in nearshore circulation, a comprehensive data set of nearshore circulation in the presence of rip currents is not well doc umented. Since field rip currents are often transient, they tend to elude investigators intent on measur ing them with stationary instruments;

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3 although quantitative measurements do ex ist (Sonu 1972, Bowmann et al. 1988, Brander and Short 2000). However, due to the large sc ales of rip circulati on systems and difficult nature of rip observations, field studies have as yet been unable to obtain a comprehensive map of currents in rip system s under a range of wave conditions. Instead most field studies have concentrated on th e morphologic evolution of the beach in the presence of rip currents, and measured curre nt data are generally sparse and limited to very near the rip current. It is clear that a comprehensive rip current data set will improve understanding of the overall hydrodynamics in a rip system; and is needed in order to make further advances in predicting sediment transport characteristics. In contrast to field resear ch, the controlled environmen t of the laboratory is ideal for studying rip current systems; but the extent of laboratory data involving rip currents on longshore varying bathymetry is lim ited (Hamm 1992, Oh and Dean 1996, Haller et al. 1997, Dronen et al. 1999, Haller and Dalrymple 1999, Haller and Dalrymple 2001, Haller et al. 2001, Dronen et al 2002, Haas and Svendsen 2002). Haller et al. (2001) were the first to provide a comprehensive map of nearshore waves and currents in a laboratory setting with the use of current meters. Until recently, with the exception of Dronen et al. (2002), laboratory rip current circulation was analyzed by placing a seri es of current meters throughout the flow domain. Acoustic Doppler Velocimeters (ADV’ s) and other current meters are desirable if a continuous time series of the flow velo city at a specific location is needed; but to observe the entire flow fi eld, a large quantity of inst ruments would be required. However, researchers are usually restricted to a limited number of current meters due to the financial cost. An overabundance of meters could also possibly change the flow field,

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4 altering the true measurements of velocit y. Another method used in attempting to quantify nearshore circulation patterns is Par ticle Image Velocimetry (PIV) which tracks a large number of small part icles within a specified window size by comparing two images separated by a known time step. This technique works well in the field where turbulent bubbles exist due to breaking waves. Holland et al. (2001) used PIV to quantify the horizontal flow structure in the swash zone. Scripps Institute of Oceanography has also applied direct drifter tracking by Global Positioning Syst em (GPS) to field research of nearshore circulation pattern s involving rip currents (Schmidt et al. 2001). However, a small number of these Lagrangian field drifte rs exist due to the fi nancial cost, greatly limiting the amount of available coverage. In our study, numerous video recordings of laboratory rip currents with Lagrangian drifters were made under different conditions. Tables 2-1 and 2-2 show the water level, wave height, wave period, and group charac teristics for each test. Shore normal waves were used for every test in this study. The absence of turbulent bubbles from strong wave breaking found in the field has resulted in the use of individual drifters. A numerical description for the complete rip current circulation will be obtained by tracking a dense population of these indi vidual drifters from the digiti zed video recordings. This method will be called Video Drifter Tracking (VDT). Several advantages arise from VDT with one being that additional laboratory drifters are far less expensive than more field drifters or curr ent meters. The video recordings were transferred to the computer, tracked and analyzed using several MatLab pr ograms. A more complete description of the data collection procedure and the expe rimental wave basin and setup will be presented in Chapter 2.

PAGE 18

5 Using the approach of VDT, this study focu sed the general circulation patterns and quantities found throughout a laboratory rip current system for a longshore bar and channel bathymetry. General circulation behavi ors of rip currents examined in this study include the overall flow structur e and individual drifter trajec tories. The drifter coverage and run lengths are sufficient to resolve mo st averaged and many fluctuating quantities over the field of view containing the rip sy stem. Therefore, the quantities can be examined in particular regions of interest (such as the eddies, feeder currents, and rip head). The abundant drifter coverage and rela tively fine resolution of quantities in this study were possible due to the low cost of th e video-tracked laborat ory drifters. Mean quantities such as velocity, vorticity, and continuity th roughout the rip system are presented for many of the tests. Fluctuating ve locities were also analyzed to give some insight into the unsteady properties of rip cu rrent instabilities, such as vortex shedding and low frequency oscillations. Unavoidable ga ps in particle coverage have hindered the ability to obtain continuous quantities at a given location, th erefore fluctuating quantities are limited to one-minute averages. This tem poral resolution was found to be adequate in determining higher frequency rip current motions The data analysis and results for this study are covered in more detail in Chapter 3. Background: Rip Current Literature Review Since the 1930s, coastal scie ntists have observed the ex istence of rip currents in nearshore waters. Today, even most beachgoers know of the presence and dangers of rip currents. Lifeguards and other coastal rescue personnel are specifica lly trained for this environmental phenomenon. A considerable amount of research has been devoted to rip currents, but the difficulty of field measurem ents (due to their temporal and spatial unsteadiness) has caused many observations to be only qualitative. Previous literature

PAGE 19

6 concerning rip currents are reviewed in th is chapter to discuss: 1) the physical characteristics of rip currents, 2) the impact of rip currents to society, 3) the forcing mechanism behind rip current circulation, and 4) the unsteady behavior of rip currents. Physical Description of Rip Currents Rip currents are narrow lanes of water that move seaward through the surf zone and extend past the breaker line (Shepard et al. 1941 ). These currents have been observed on a wide range of beach types but are partic ularly common on beaches that are dominated by a longshore bar cut by rip channels, shown by the top picture in Figure 1-2. The rip channels can result from hard bottom canyons or a channel cut through the sand bar. Figure 1-2: Three scenarios for rip current formation include: Top) longshore bar with rip channels, Middle) deflected longshore current due to seaward protrusion in the bathymetry, and Bottom) deflected longshore current due to structure. (from Sanders 2002) Another mechanism for rip current form ation is when longshore currents are directed offshore by a protrusion in the bat hymetry or a headland (Sheppard and Inman

PAGE 20

7 1950). Rip currents may also occur at specif ic locations due to the interaction with coastal structure such as piers, groins, or jetties (Shepard and Inman 1950, Wind and Vreugdenhil 1985). Figure 1-2 shows three pos sible scenarios for rip current formation described above. This study focuses on the fi rst scenario, rip currents controlled by a longshore bar with channels. During the first part of the century, th e distinction between rip currents and undertow was examined. The return flow required by the landward movement of water led to the idea that water returns beneath the surface. Davis (1925) first challenged the popular idea of undertow that was said to pull bathers beneath the surface, and a considerable discussion of the subject en sued. Shepard (1936) called attention to evidence that swimmers were being dragged seaw ard in relatively narrow belts of water. These lanes of agitated water extending out at right angles to the beach were well known to lifeguards and experienced swimmers but es caped the notice of scientists for the early part of the century. They were known as “r ip tides” or “sea pulses”, but the name “rip current” was deemed more appropriate. Shepard et al. (1941) gave a description of the qualitat ive features found in a rip current system. These authors used visual observations of rip currents off the coast of Scripps, California to describe three main f eatures: the feeder currents, rip neck, and rip head. Figure 1-1 gives a visual description of these rip curr ent features. Feeder currents move along the shore from either side of the rip channel with one of these currents usually being dominant. These feeder curr ents can produce channels a few feet deep parallel and close to shore. The two currents converge and extend out in what is known as the neck, where the water rushes thr ough the breakers in a narrow lane. A shore

PAGE 21

8 normal channel in the sand can usually be found along the path of the neck, which indicates that the flow extends through the entire water colu mn. Seaward of the rip neck the rip current flow separates from the bottom and is mostly confined to surface movement (Shepard et al. 1941). Beyond th e breakers the rip current widens and dissipates, this is known as the rip head. The size and strength of rip currents ar e highly dependent on the ambient wave conditions. Shepard et al. ( 1941) observed that the size and geometric configuration of rip currents off the coast of Southern Californi a were related to the wave height. The rip currents observed by the authors extended out from a few hundred to about 2,500 feet from the shore and vary from narrow belts 50 to 100 feet across in the feeders and neck to as much as 500 feet or more in the heads. McKenzie (1958), citi ng observations made on the beaches of New South Wales, Australia, no ted that rip currents are generally absent under very low wave conditions. Rip currents were also found to be more numerous and somewhat larger under light to moderate sw ell. Shepard and Inman (1950) directly related the magnitude of flow velocities associ ated with rip currents to the height of the incident waves. An increase in wave height resulted in stronger rip currents and the response was relatively instantaneous. This relationship has important consequences for the nearshore sediment budget and beach profile equilibrium, since variations in current strength will significantly affect the erosional power of rips. Flow velocity in the rip neck has been found to be as great as 5 miles an hour (Lascody 1998). However, this flow rate is very unsteady, being greatly checked or even stopped by advancing wave fronts.

PAGE 22

9 Another factor that modulates the strength of rip currents with a bar and rip channel morphology is the tide. Severa l field observations have shown the influence of tides on rip currents. Cooke (1970) conducted a study on Redondo Beach, California and noted that stationary rip channels were common and well-defined ri p currents were only present during falling or low tide. The prevalence of rip currents during falling tides was also noted by McKenzie (1958) and wa s attributed to the concentra tion of current flow within the rip channels resulting in larger velocities in the ri p neck. Sonu (1972) observed modulations in rip current inte nsity with tidal level during field experiments conducted at Seagrove Beach, Florida. A lower tidal leve l was also thought to be significant due to stronger wave breaking, which would increase the amount of moment um transfer to the surf zone, thus resulting in st ronger rip currents. Brander (1999) and Brander and Short (2001) conducted field experime nts along the beaches of New South Wales, Australia to investigate low-energy rip current systems. Rip flows reached maximum velocities during low tide and minimum velocities duri ng high tide. Dronen et al. (2002) conducted experiments in a wave basin with a bar and half of a rip channel. A series of test runs were performed with varying wave height a nd water level and reveal ed that rip current velocity increased with increasing wave height and decreasing water level. Impact of Rip Currents Rip currents modify the nearshore wave fi eld along with the entire surf zone circulation (Shepard et al. 1941, Shepard a nd Inman 1950, many others). Therefore, rip currents are a crucial factor in determining the distribution of sediment and a general shape of the coastal region (Shepard et al 1941, McKenzie 1958, many others). This is a growing concern due to the in creasing number of people resi ding near the coast. Rip

PAGE 23

10 currents also play a role in the sorting of b each sediment across the profile (Shepard et al. 1941). Rip currents are a considerable source of danger to bathers (Shepard et al. 1941, Chandramohan et al. 1997, Short and Hogan 1993, Lascody 1998). Since 1989, an average of 19 persons have died each year as a result of rip current s in Florida (Lascody 1997). Therefore, rip currents, on average, result in more deaths in Florida than hurricanes, tropical storms, tornadoes, seve re thunderstorms and lightning combined. Victims are usually tourists who are unfamiliar with the da ngers of the ocean. Many areas of the world, including Florida, depend on their beaches for tourism and rip currents pose a serious threat to ocean bathers due to their strong, seaward directed flows. Most rescues from the surf along the coast of southe rn California are made in these rip currents (Shepard et al. 1941). Short and Hogan ( 1993) have devised a method to determine a relative level of beach safety due to the presence of rip currents. Tidal, bathymetric and incident wave conditions for the beaches of New South Wales, Australia were considered for the study. A person may find himself or herself in tr ouble either by slipping into a feeder channel, which may be very near the shore, and being swept out into the neck or by jumping through breakers in the zone next to the rip current neck and being pulled gradually toward the neck (Shepard et al. 1941). The main channel is generally beyond the bather’s depth. The seaward-moving curr ent found in the rip neck may prevent all but a very good swimmer from progressing land ward. The most efficient way to escape a rip current is to be pushed offshore by the rip neck. Once in the rip head past the breaker line, swim parallel to the s hore until out of the rip system and then back toward land.

PAGE 24

11 This method of escaping a rip current is visua lly depicted in Figure 1-3. If caught in the rip circulation again, try the other side because it may have a weaker flow strength. The worst thing someone can do is try to swim la ndward within the seaward moving rip neck. People usually get tired doing this, creati ng a very dangerous situation. Several indications are associated with the presence of a rip current that can be observed by everyday beachgoers including: 1) a darker water color due to the suspension of fine sediments, 2) waves breaking further offshore on either side of the rip neck, 3) foam or object moving steadily offshore in the rip neck, and 4) an offshore plume of turbid water past the sand bar, which is the rip head (Sheppard et al. 1941). Figure 1-3: Swim parallel to shore past the breaker line to escape a rip current system (from N.C. Sea Grant 2003) Forcing Mechanism The most direct mechanism for driving nearshore currents is the momentum transfer from breaking surface gravity waves to the nearshore flow. Longshore currents are generated from waves breaking oblique ly to the shoreline (Longuet-Higgins 1970a, Longuet-Higgins 1970b). Longshore periodic vari ations in the incide nt wave field can

PAGE 25

12 also force coherent circulation cells. Thes e cells are generally de fined as broad regions of shoreward flow separated by narrow regions of offshore-directed flow. If these narrow regions of offshore flow are sufficiently st rong they would appear as rip currents. Shepard et al. (1941) and Sonu (1972) observe d cell circulation to be most prevalent during shore-normal waves and a meanderi ng longshore current was dominant during oblique wave incidence. Nearshore cond itions usually involve a combination of longshore currents and cell circulation occurring simultaneously (Komar 1976). Up until the 1960’s researchers had attribut ed rip currents to the seaward return flow due to the mass-transport of water over the bar from ocean waves. The understanding behind the governing forces driv ing rip currents was greatly enhanced when Longuet-Higgins and Stewart (1964) introd uced the concept of radiation stress and described the change in mean sea level resu lting from waves that encounter a sloping bottom. Radiation stress is the excess flow of momentum due to the presence of waves. This stress induces a gradient in the mean wa ter level that balances the gradient of the radiation stress. The cross shore component of the radiation stress due to the breaking waves causes an increase in mean sea level (s et-up) to occur shoreward of the breakerline and a decrease of mean sea level (set -down) occurs at the break point. The maximum set-up occurs at the shore. Bowen (1969) confirmed that a large wave height would cause a greater set-up than lower waves if they break continuously from the break point to the beach. This occurs because the set-up is proportional to the wave height and higher waves break at a deeper depth, initiating the sea-surface gradient at a position that is further from shore.

PAGE 26

13 A longshore variation of breaking wave he ight, topographically controlled by the periodic bar and trough bathymetry, will cause a variation in wave set-up along the shore (Bowen 1969, Dalrymple 1978, Haller et al. 199 7). These longshore variations in the incident wave field may also arise on an in itially longshore uniform beach due to a wide range of causes including edge waves (Bow en and Inman 1969), the superposition of wave trains (Dalrymple 1975, Fowler and Da lrymple 1990), or surf zone instabilities (Dalrymple and Lozano 1978, Falques et al. 199 9). The longshore variation in set-up produces a pressure gradient in the longshore. Feeder currents devel op and flow parallel to shore from zones of high set-up to zones of lower water level. The areas of high set-up are located shoreward of the bars and areas of lower wate r level are found shoreward of the rip channels. As stated before, these feed er currents come from either side of the rip channel, converge at the base of the ri p and move seaward through the rip neck. Laboratory experiments, conducted by Haller et al. (2001) using the same experimental wave basin as presented in th is study, confirmed that wave heights were actually higher in the rip ch annel than over the bar. Ho wever, the waves in the rip channel would break very close to shore si gnificantly reducing the induced set-up around the bar. Therefore, the longs hore variation of set-up was st ill highest shoreward of the bar and lowest in the rip channel. The longs hore pressure gradient between the shore and the bar still drives flow toward the rip cha nnels where they converge. The larger wave height in the channel is due to the inte raction between the incident waves and the offshore rip current. Chen et al. (1999) also used the experi mental wave basin found in this study to examine Boussinesq modeling of a rip curren t system. A time domain numerical model

PAGE 27

14 based on the fully nonlinear extended Boussinesq equations (Wei et al. 1995) was created to investigate surface wave transformation and breaking-induced nearshore currents. Agreement was found between the numerical model results and the laboratory measurements of Haller et al. (1997), incl uding longshore and cr oss-shore velocity components. The model results revealed the temporal and spatial variability of waveinduced nearshore circulation and the instab ility of rip currents, which is also in agreement with the physical experi ments of Haller et al. (1997). Unsteady Behavior of Rip Currents The magnitude of rip current flow is highly unsteady and has been observed to pulse on the time scale of wave groups (S onu 1972). Brander and Short (2001) observed pulsations in the rip flow at a freque ncy of 0.0078 Hz (128s), which resulted in fluctuations of +/0.4 meters per second. No wave measurements were taken during the experiment and the forcing mechanism for th e modulations in mean flow or pulsations were not investigated. MacMah an et al. (2003) participated in the RIPEX experiment in Monterey, CA and concluded th at rip current pulsations o ccurred on infragravity time scales (0.004-0.04 Hz). The pulsations were attributed to cross-shore infragravity motions of long waves, which increase shorew ard and with increasi ng wave height. As mentioned before, the periodic pulsing found in the rip channel may be better analyzed with the use of current meters due to the ability to gather measurements at a particular location over a cont inuos time series. Field observations of rip currents indicat e that they can exhibit long period oscillations in their offshore-directed flow (Sonu 1972). These oscillations have generally been attributed to the presence of wave groups or low-frequency wave motions, such as surf beat. However, a mechanism fo r the instability of ri p current flow hasn’t

PAGE 28

15 been fully resolved. Haller and Dalrymple (2001) performed a theo retical analysis and concluded that these low frequency rip cu rrent oscillations can be modeled by jet instability mechanisms. These low frequenc y or large period osci llations were also noticed throughout this laborat ory study involving rip curren ts generated on a barred beach with periodic channels. Summary Rip currents have been an important topic for coastal researchers for most of the century. As stated before, much of the literature prior to the 1960s concerning rip currents was highly qualitative. In this time, most observations of rip currents were based on their physical characteristics, behavioral tendencies and interaction with the surrounding coastal hydrodynamics and sediment budget. These observations laid much of the groundwork for future research by desc ribing the physical stru cture of rip currents and possible driving forces. The large volume of water transported by these rip currents influence the nearshore circulation pattern, t hus the overall coastal sediment transport. As well as being of geological importance, rip currents pose a seri ous threat to public safety. The three main factors, documented in the literature, affecting rip current presence and strength are as follows: 1) wave he ight, 2) wave direction, and 3) tidal level. Unsteady properties of rip current flow incl ude modulations in the current strength known as “pulses” and unstable oscillations. Rip currents are intriguing due to thei r unsteady presence and tendencies to seemingly just appear or migrate down the coas t. It is clear from the review that the difficulty in field measurements due to th e temporal and spatia l unsteadiness of rip currents has resulted in a lack of quantitative data. This unst eady presence of rip currents in the field has led to the advantage of laborat ory analysis. Field instruments are also far

PAGE 29

16 more expensive and subjected to a harsher environment, thus requiring a greater amount of maintenance. It was also concluded that something besides a fixed array of current meters was needed to analyze the entire flow field of a laboratory rip current system. Many unanswered topics still exist pertaining to the physic al flow of rip currents including: 1) the detailed circulation pattern of a rip current system, 2) the different length scales of circulation that exist, 3) a comprehensive velocity map of the entire rip system, and 4) the unsteady properties of ri p currents, involving current pulsation and unstable oscillations. The more that is known about this coastal phenomenon the better humans will be able to adapt to the dynamic nearshore region. The work presented in this thesis will help further the understanding into the physical flow characteristics of rip currents for a periodically ba rred bathymetry under various wave conditions. In this study, the method of VDT enables a high resolution analysis of a complete labor atory rip current system wit hout the financial cost of numerous current meters. Outline of Thesis The remainder of this thesis is organi zed as follows: Chapter 2 discusses the physical model and data collection procedure us ed to obtain the filtered, rectified drifter positions from the video recordings. The va rious wave and water level conditions for each test will also be given. The experi mental instruments and procedure used to videotape the rip currents with Lagrangian drifters will be covered. Finally, this chapter will examine possible experiment al and data collection errors. Chapter 3 gives the details into how the f iltered, rectified drifter positions obtained from the rip current video were analyzed. Th e quantitative and quali tative results from the various laboratory rip currents will be presented for each set of test conditions. The

PAGE 30

17 variability in rip current circul ation due to the alte ring of certain conditions such as wave height, wave period, group characteristics and water level will be analyzed and compared to past research. The measurement errors encountered in the analysis will also be addressed. The drifter velocities obtained us ing VDT will then be compared to those recorded from current meters placed at specific locations in the rip channel. Chapter 4 summarizes the results and conclu sions derived from the analysis portion of this thesis. The benefits from the method of VDT, versus a plethora of current meters or direct drifter tracking in th e field, will be reiterated. S uggestions for future research will also be given.

PAGE 31

18 CHAPTER 2 EXPERIMENTAL SETUP Physical Model The Directional Wave Basin at the Center for Applied Coastal Research of the University of Delaware was used to create rip current systems under various wave and water level conditions. Figure 2-1 shows a pl anform and cross sectional view of the wave basin. The wave basin is approximat ely 17.2 m in length and 18.2 m in width. The three-dimensional “snake” wave-maker at one end consists of 34 flap-type paddles. For a more complete description of the wave-m aker see Haller and Dalrymple (1999). The fixed beach profile consists of a steep (1:5) toe located between 1.5 m and 3 m from the wave-maker with a milder (1:30) sloping se ction extending from the toe to the shore of the basin opposite the wave-maker. The bar system consist of three sections in the longshore direction including: one main se ction approximately 7.2 m and two smaller sections approximately 3.66 m. In order to ensure that the sidewa lls were located along lines of symmetry, the longest section was cen tered in the middle of the tank and the two smaller sections were placed against the sidewa lls. This left two gaps of approximately 1.82 m wide, located at and of the basin width, that served as rip channels. The edges of the bars on each side of the rip channels were r ounded off in order to create a smooth transition. The seaward and shoreward e dges of the bar sections were located at approximately x = 11.1 m and x = 12.3 m respectiv ely (Figure 2-2). Th e crest of the bar sections were located at approximately x = 12 m with a height of 6 cm above their seaward edge. For a more complete descrip tion of the wave basi n and its construction

PAGE 32

19 see Haller and Dalrymple (1999). Other studie s in which this particular wave basin was used include: Haller et al. (1997), Haller and Dalrymple (1999), Haller and Dalrymple (2001), Haller et al. (2001), and Haas and Svendsen (2002). Figure 2-1: (a) Plan view and (b) cross-sec tion of the experimental wave basin (from Haller et al. 2001) The experimental setup was not designe d to mimic a particular field beach, however it is important to note that the bar and trough geometry is a reasonable approximation of beach types found in the fi eld. Depending on the still water level, the ratio of rip current spacing to surfzone width varied between 3.1 and 4.0 during these experiments. This falls within the range of 1.5 to 8 based on field observations by Huntley and Short (1992). Another ratio of in terest is rip channel width to rip current spacing, which was fixed at 1/5. This also co mpares favorably with field observations by Aagaard et al. (1997) and Br ander and Short (2000). Finally if we consider the experiments as an undistorted Froude model of field conditions with a length scale ratio of 1/16, then the experimental conditions correspond to a rip spacing of 145 m, rip

PAGE 33

20 channel width of 29 m, depth over the bar of .43-.76m, offshore wave heights of .6-1 m, wave periods of 4-10.7 s, and mean rip neck velocities of .5-.9 m/s Test Conditions The tests can be divided into two categories: transient tests and long tests. Tables 2-1 and 2-2 present the wave and water leve l conditions for the tr ansient tests and long tests respectively. The video recordings of th e transient tests begin with no wave forcing and then some time later the wave-maker generates one wave group consisting of 32 or 64 waves which propagates toward shore. The transient tests then continue some time after the single wave group with no wave forc ing. The total durati on of these tests are approximately 5 minutes. Only monochromatic waves were used for the transient tests. The three sets of transient test conditions we re repeated three times each, creating nine separate runs. The video recordings of the long tests, with the exception of tests 15 and 16, commence some time after the wave-maker startup and the wave forcing continues throughout the entire test. Tests 15 and 16 be gin with no wave forcing and then very shortly after the wave-maker is activated, which continues until the termination of the test. The long tests are approximately 18.2 mi nutes long. Some of the long tests used monochromatic waves, wh ile others used bichromatic or groupy waves. Table 2-1: Transien t test conditions Test # Cross shore shoreline position (m) Depth over the bar (cm) Hrms (cm) T(s) Number of regular waves Number of drifters tracked 1-3 14.9 4.73 4.2 1 32 55, 67, 52 4-5, 9 14.9 4.73 6.3 1 32 62, 72, 76 6-8 14.9 4.73 4.2 1 64 81, 68, 82

PAGE 34

21 Table 2-2: Long test conditions Test # Cross shore shoreline position (m) Depth over the bar (cm) Hrms (cm) T(s) Number of waves in repeating group Number of drifters tracked 12 14.9 4.73 4.32 1 32, (a1/a2=2) 239 13 14.9 4.73 4.28 1 M 293 14 14.3 2.67 4.62 1 32, (a1/a2=2) 204 15 14.3 2.67 4.83 1 M 241 16 14.9 4.73 6.18 1 M 356 19 14.3 2.67 5.22 1.33 M 158 20 14.9 4.73 3.69 1 64, (a1/a2=2) 310 21 14.9 4.73 3.97 2.67 M 221 (M) indicates regular or monochromatic waves A wave gage, located at (x, y) = (6, 16.2)m, was used to measure a time series of water surface elevations duri ng the experiments. The root mean square of the wave height for each test was determined from th e water surface elevation records. Only shore normal waves were used for this study, which eliminates the concern of reflection from the sidewalls. The water depth in the basi n was measured by a depth gage located near the wave paddles, which is described with greate r detail in Haller et al. (2001). As stated before this was a fixed bed model, theref ore the bathymetry of the basin remained constant throughout the entire study. Data Collection Video recordings of a rip current system with floating Lagrangian drifters were made for the test conditions listed in Ta bles 2-1 and 2-2. Figure 2-2 shows the approximate field of view, which extends fr om y = 9.2 m to y = 18.2 m in the longshore and from x = 7 m to slightly past the shorelin e, at about x = 15.5 m, in the cross shore. This visible domain contains the rip current system genera ted by the bar gap centered at

PAGE 35

22 the basin width. Three 2-D ADV’s, shown in Figure 2-2, were used to obtain a time series of current velocities in the visible rip channel with a sampling frequency of 10 Hz. The three ADV’s were at a cross shore loca tion of x = 11.82 m and longshore locations of y = 13.52 m, y = 13.72 m, and y = 13.92 m. Th e velocities obtained by these current meters are later compared to drifter velocitie s determined from the method of VDT. For more detail into the experimental procedur e including the video recordings and various gages, contact Andrew B. Kennedy at the Univer sity of Florida, Department of Civil and Coastal Engineering. 0 2 4 6 8 10 12 14 16 1 8 0 2 4 6 8 10 12 14 16 ADVsField of view Wavemaker Shorelinex (m)y (m) Figure 2-2: Unevenly spaced bathymetry cont our of the wave basin with visible flow domain and ADV locations The author was a part of this research fr om this point forward. The focus of this thesis is on the analysis of the video da ta containing the rip current systems with Lagrangian drifters. Figure 2-3 shows a photo of the 4 inch buoyant discs used as drifters. The video recordings were digitized into jpeg files at a frequency of 30 Hz using Dazzle DVC II video capture card with a pixel resolution of 352 x 240. MatLab

PAGE 36

23 programs were used to perform the remainder of the analysis. The Lagrangian drifters were tracked at a frequency of 2 Hz and 3 Hz for the transient tests and long tests respectively, which is adequate to resolve high frequency motions found in currents. The drifter coverage is sufficient to resolve most averaged and many fluctuating quantities. The number of drifters tracked for each run is presented in Tables 2-1 and 2-2. The abundant coverage was possible due to the low cost of the video-tracked laboratory drifters. Field tracking techniques, such as kinematic GPS, involve expensive instrumentation, which limits the number of availa ble drifters and inhib its coverage of the overall rip system (Schmidt et al. 2001). Figure 2-3: Buoyant disc, 4 inches in diameter, used as Lagrangian drifters A considerable amount of time was spent individually and manually tracking each drifter for every test. The tracking program pr edicted the movement of the desired drifter in the next frame, but the estimated position of the drifter often needed to be manually corrected. This position correc tion was a result of three scenarios: 1) if the drifter was close to another drifter the tr acking program would jump over to the undesired drifter, 2) if the drifter was in a light patch reflected from above the tracking program would usually

PAGE 37

24 mispredict the drifters position in the follo wing frame, or 3) if the drifter was well offshore, at about x = 7 m, the tracking pr ogram had problems correctly predicting the true drifter position in the next frame. Th is required correction of the drifter position prevented the tracking program from being fully automated. Figure 2-4: Original and rectified field of view Since the video recording was taken at an oblique angle, the drifter positions saved in image coordinates were rectified into Cart esian still water level coordinates, correcting for light refraction through the vertical wate r column. Ground control points, separated by 1 m in both the cross shore and longshore, were used as known fixed points. These fixed ground points can be seen in Figure 24. Holland et al. (1997) utilized this rectification procedure for th e quantification of physical processes using video imagery from nearshore oceanographic field studies. The drifter positions were then low-pass filtered with a cut-off frequency of .25 Hz and .3 Hz, for the transient tests and the long tests respectively, ensuring that any moti ons below 4 s and 3.3 s were smoothed out. This eliminates the effect of the wave moti on from the saved drifte r positions because the

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25 wave periods used for these experiments rang e from 1 s to 2.67 s. Now the saved drifter positions are representative of the current mo tions induced by the rip current system. The quantitative and qualitative results obtained from these rectified and filtered drifter positions can be found in Chapter 3. Experimental and Data Collection Error Deviations from true rip current proce sses found in the field arise due to the limitations of the laboratory environment. Th ese possible sources of error or deviations from real life include the neighboring side wall, immovable hard bottom, designed bar shape, and lack of other coastal currents. The relatively short run lengths of these experiments are of concern due to the long time scale motions of rip current systems. The 1 s wave period used for all these expe riments, except test 19 and 21, is also somewhat small. This is representative of only a 4 s wave period in the field, using a Froude length scale ratio of 1/16. Ocean surface gravity waves found in the field generally exhibit a higher peri od. The depth over the bar, which scales up to between .43-.76 m using a Froude length scale ratio of 1/16, also seems somewhat low when compared to the field. Finally, the width of the rip channel, which scales up to approximately 29 m using the same scaling ratio of 1/16, seems so mewhat wide when compared to field observations. Possible error due to the data collection porti on of this thesis is also noted. Human error becomes an issue while semi-manually tr acking the Lagrangian drifters. This was examined by digitizing the same video reco rding of test 13 twice and tracking them separately. When the mean velocities th roughout the rip system were compared the results showed a negligible difference. The rectification procedure may also be a possible source of error, but th is was not quantified for this thesis. However, a visual

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26 examination of the fixed point throughout the flow domain concludes that the rectification procedure has pr oduced believable results (Figur e 2-4). The author feels that all of these possible sour ces of error or deviations from the field are small enough to show confidence in the results.

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27 CHAPTER 3 RESULTS AND ANALYSIS This chapter discusses the results from a laboratory rip current system using videotracked Lagrangian drifters. General rip current behavior s are analyzed using both the transient (1-9) and long (12-21) test categories discussed in Chapter 2. However, only the long test group are used to resolve aver aged and fluctuating quantities throughout the visible flow domain due to the experime ntal run length (~18 minutes) and drifter coverage. The number of drifters tracked for each test is shown in Tables 2-1 and 2-2. The computational steps used to obtain the fi ltered, rectified drifter positions from the digitized video recordings of the rip current system were described in the data collection portion of Chapter 2. The first order forwar d difference formula, shown in Equation 3-1, was used to calculate the components of dr ifter velocity from the corrected drifter positions (x, y) and known time step ( t) of 0.5 s and 0.33 s for the transient tests and the long tests respectively. The cross shore and longshore components of velocity are u and v respectively. t x x uj j j 1 t y y vj j j 1 (3-1) The results obtained from the rectified, filtered drifter positions and velocities are presented in this chapter. As stated be fore, the Froude length scaling ratio between model and prototype is approximately 1/16, wh ich creates a 1/4 time scale ratio. This

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28 means that flow velocities in the field co rrespond to around four tim es greater than found in our laboratory study. General Rip Current Behavior The main physical flow features of a rip current describe d by Shepard et al. (1941) are the feeder currents, rip neck, and rip head. Figure 3-1 s hows the formation of a strong current in the rip neck with a “sna pshot” of drifter positions and corresponding velocity vectors imposed on an averaged, rec tified view of the visible flow domain. 10 cm/sx (m) offshore =>y (m) 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure 3-1: Drifter positions and velocity at t=41 s after the wave-maker startup (Test 1) Appendix A gives additional examples of ri p current features found during the flow evolution for transient test 5 using the same plot-type as in Figure 3-1. The finest temporal resolution between these plots wa s 0.5 s and 0.33 s for the transient tests and long tests respectively, which was dictated by th e drifter tracking rate of 2 Hz and 3 Hz. However, a larger time step, such as 2 s, wa s adequate to resolve the rip current motions.

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29 (a)x (m) offshore => 10 12 14 16 18 7 8 9 10 11 12 13 14 15 (b) 10 12 14 16 1 8 7 8 9 10 11 12 13 14 15 (c)x (m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 (d) y (m) 10 12 14 16 1 8 7 8 9 10 11 12 13 14 15 Figure 3-2: Drifter trajectories within 22.5s time intervals / dr ifter positions plotted every 7.5 s and corresponding velocity vector ever y 15s; (a) 0s to 22.5s, (b) 22.5s to 45s, (c) 45s to 67.5s, (d) 67.5s to 90s (Test 1) A plot of all the drifter traj ectories and their velocities for test 1 is presented in Figure 3-2. This figure was divi ded into four equal time inte rvals of 22.5 s, starting with no wave forcing, in order to limit the confusi on of overlapping all th e drifter paths for the entire test. Figures 3-1 a nd 3-2 both show the resulting pu lse in the rip neck from a single wave group and the startup of symmetric eddies on either side of the rip channel. Schmidt et al. (2001) observed eddy-like trajecto ries and velocities fo r drifters within a cell circulation pattern of a ri p current system using direct drifter tracking by kinematic GPS. Shepard et al. (1941) and Sonu (1972) have also observed cell circulation in the nearshore zone.

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30 y (m)x (m) 11 11.5 12 12.5 13 13.5 9.5 10 10.5 11 11.5 12 12.5 y (m)x (m) 11 11.5 12 12.5 13 13.5 9.5 10 10.5 11 11.5 12 12.5 Figure 3-3: Generation of a sma ll vortex on the corner bar, a nd the transport of a coupled drifter pair offshore as part of a larger overall circulation; Solid line & (o) are the trajectory and positions for one of the coupled drifters; Dotted line & (x) are the trajectory and positions for the other coupled drifter (Test 2) Many different scales of rotational moti on were observed throughout the various tests, ranging from small scal e vortices of D = O(20cm) to basin-scale circulation with D = O(20m). Figure 3-3 shows cl early the generation of a sm all vortex on the bar corner, and its transport offshore as part of a larger overall circulation in test 2. Such vorticity generation by differential wave breaking was predicted by Peregrine (1998), but has not been observed previously. Every transient and most long tests exhibited these small vortices when drifters passed over the bar corner while bei ng ejected offshore by the rip neck. Extremely large scale circulation patt erns were difficult to resolve due to the limited field of view. Video recordings with a much larger field of view were created and are currently being analyzed. Individual drifter trajectories were examined using the rectified, filtered drifter positions and a time series of velocity components. Figure 3-4 shows two drifter trajectories or paths found in test 12 ( H= 4.32cm, T= 1s, groupy waves (32); high water). The starting and stopping point for each drifte r trajectory can be determined from the

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31 time series of velocity components. Appe ndix B contains three figures of six other individual drifter paths and corresponding ve locity time series found in test 12. These individual drifter trajectories do not represent all of the drifter paths in test 12. The path followed by a drifter depends on several factors, such as the initial position of the drifter within the flow domain and the unst eady state of the rip current flow. (a)x(m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 (b)x(m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 500 550 600 650 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) 700 800 900 100 0 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) Figure 3-4: Drifter trajectori es and corresponding velocity time series / Cross shore velocity => Dashed line Longshore velocity => Dash-Dot line Total velocity => Solid line (Test 12) An analysis of every drifter for each long test was performed to determine qualitative and quantitative details about thei r overall trajectories. The percentage of individual drifters, which exited the rip current system to a pa rticular side of the visible domain and completed (X) closed circuits, wa s determined for the long tests and can be seen in Tables 3-1 and 3-2 respectively. Table 3-3 shows the averaged maximum drifter

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32 velocity for each of the long tests. As stat ed before, the number of drifters tracked for each long test can be found in Table 2-2. Table 3-1: Percentage of drifters which exited the visible flow domain to a certain side Test # Left Top Shoreline Other 12 20 23 38 19 13 32 8 45 15 14 7 47 33 13 15 5 55 30 10 16 12 26 48 14 19 0 69 20 11 20 15 21 49 15 21 26 26 33 15 Other includes particles that were either in the visible flow domain when the tracking was ended, couldn't been seen against the right wall, or not tracked long enough to be f iltered Table 3-2: Percentage of drifters completing (X) closed circuits Test # 0 1 2 3+ Other 12 76.6 11.3 2.5 1.7 7.9 13 68.3 11.3 4.4 4.1 11.9 14 59.8 18.6 9.3 7.4 4.9 15 71.0 14.9 5.4 5.8 2.9 16 67.1 16.9 6.7 5.3 3.9 19 77.2 12.0 3.8 1.3 5.7 20 71.9 17.1 4.8 2.6 3.5 21 76.5 11.8 2.7 8.1 0.9 Other includes particles that were not tracked long enough to be filtered Closed circuits have a minimum ax is diameter greater than 15 cm

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33 Table 3-3: Averaged maximum drifter velocity for each of the long tests Test # Average maximum particle velocity within field of view (cm/s) Average time particle was tracked (s) 12 19.25 98 13 19.55 110 14 24.62 121 15 24.35 120 16 24.86 96 19 27.58 73 20 18.76 119 21 20.84 114 *Both quantities include particles that were in the flow domain when the tracking ended Figure 3-5 shows a plot of all the drifter tr ajectories for test 16. This figure was divided into nine equal time intervals of 2 minutes, starting with no wave forcing, in order to limit the confusion of overlapping all the drifter paths for the entire test. (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (b) 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 1 8 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 1 8 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 1 8 8 10 12 14 Figure 3-5: Drifter paths; 2 mi nute time intervals (Test 16)

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34 Remember, only tests 15 and 16 include th e effects of the wave-maker startup within the long test category. The direction of the offshore-flowing rip neck seems to be quite dependent on the particular eddy patterns. The instability in rip current flow will be discussed later in this chapte r. Appendix C has the same pl ot-type as in Figure 3-5 for every long test. Mean Velocity Mean fluid velocity throughout the field of view containing the rip current system was determined for the long tests. Figure 3-6 shows this plot-type for test 12, where basic rip current features such as eddy circul ation, feeder currents and a resulting rip neck can be noticed. Shoreward flow over the bar due to breaking waves a nd a decrease in rip neck strength offshore can also be seen in these figures. Test 12: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-6: Mean Velocity / Test 12 / H= 4.32cm, T= 1s, groupy waves (32); high water

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35 Appendix D contains the same plot-type for every long test. A spatial resolution of 0.5 m, used for all the averaged quantities presented in this study, was chosen based on the desired details of the rip current flow a nd the available drifter coverage. The first 5 minutes of tests 15 and 16 are excluded to elim inate the effects of the wave-maker startup on the mean flow velocity and other aver aged quantities pres ented in this study. Results in this study show a strong qu alitative and quantitative dependence on wave and water level conditions. A lower wa ter level produced str onger flow velocities within the rip current, which was most evident in the neck. This relationship can be seen from a comparison of mean velocity in Fi gure 3-6 (test 12) and Figure 3-7 (test 14), where only the water level differs. Field obser vations of stronger ri ps during lower tides have been made by McKenzie 1958, Cooke 1970, Sonu 1972, Brander 1999, Brander and Short 2001, and others. Test 14: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-7: Mean Velocity / Test 14 / H= 4.62c m, T= 1s, groupy waves (32); low water

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36 As mentioned above, the rip current flows we re also directly related to the wave height. A stronger flow in the rip neck can be noticed by comparing Figure 3-8 (test 13) and Figure 3-9 (test 16), where only the wave he ight differs. Rip cu rrent strengthing due to larger wave heights has been documented fo r more than five decades (Shepard et al. 1941, Shepard and Inman 1950, McKenzie 1958, and others). Dronen et al. (2002) also revealed that laboratory rip current velocity increased with increas ing wave height and decreasing water level. In th is study, an increase in rip cu rrent strength due to a lower water level and larger wave height can also be concluded from Table 3-3 of the averaged maximum drifter velocity for the long tests. Some of the long tests show classic symmetric circulation patterns as in Figure 3-7 (test 14), while others exhibit rips with a strong bias in one direction, shown in Figure 3-8 (test 13), even with shore normal waves. Test 13: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-8: Mean Velocity / Test 13 / H= 4.28cm, T= 1s, monochromatic waves; high water

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37 Test 16: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-9: Mean Velocity / Test 16 / H= 6.18cm, T= 1s, monochromatic waves; high water It is obvious from the figures of mean velo city that the flow strength decreases as it moves offshore of the channel through the rip neck. This d ecrease in flow velocity is more easily seen in Figure 3-10 of the cro ss shore component of mean velocity along the rip channel centerline versus th e cross shore location. The pe ak strength within the rip channel along its centerline and offshore ex tent of the rip neck varied considerably between the long tests. As a reminder, the offshore and shoreward edges of the bar are located at x = 11.1 m and x = 12.3 m respectively. A reversal of flow onshore at around x = 13 m can also be observed in these figures, for all of the long tests, which arises from waves breaking close to shore in the rip channel and a rela ted area of strong vorticity between the bar and the shoreline. Vorticity around the ri p channel will be analyzed in further detail later in this chapter.

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38 8 9 10 11 12 13 14 1 5 25 20 15 10 5 0 5 10 15 (a)U (cm/s)Cross Shore location x(m) (a) (a) (a) 8 9 10 11 12 13 14 15 25 20 15 10 5 0 5 10 15 (b)U (cm/s)Cross Shore location x(m) (b) (b) (b) Figure 3-10: Cross shore component of velo city along the rip channel centerline versus the cross shore location: Solid line (a) Test 12 (b) Test 16; Dashed line (a) Test 13 (b) Test 19; Dash-Dot line (a) Test 14 (b) Test 20; Dotted line (a) Test 15 (b) Test 21

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39 Sources of error. The unavoidable lack in drifte r coverage may cause quantities such as mean velocity, at a particular locati on to be biased. An expression for the true mean velocity was obtain by taking the time aver age of the product of velocity and drifter concentration. The velocity and drifter concen tration were both separated into mean and fluctuating components. ) )( ( c c u u uc ) )( ( ) )( ( c u c u uc c c u c uc u (3-2) In the third line of Equation 3-2, u is the true mean velocity and the first term on the right hand side is the apparent mean velocity, which is measured by the method of VDT presented in this study. This apparent mean velocity may differ from the true mean velocity, u, due to the effects of th e second term on the right ha nd side of Equation 3-2. If u and c are correlated than two separate scen arios could alter the apparent mean velocity, causing it to differ from the true mean velocity, which include: 1) if there is a greater concentration of drifters during high velocities then VDT will tend to over predict the true mean velocity within a particular co mputational bin and 2) if there is a greater concentration of drifters during low veloci ties then VDT will tend to under predict the true mean velocity within a particular computational bin. It is possible that u and c are not correlated in which case there would be no bias or the two scenarios may nearly cancel each other out. The consequence of this bias on the true fluid velocities of the rip current system can not be determined. At least 20 drifter velocity measurements, within

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40 each 0.5 m bin, were required or else no mean velocity was determined for that particular bin. However, most of the computational bins had enough drifter coverage to collect hundreds or even thousands of velocity measurements. The quantities offshore of x = 7 m are less accu rate due to the difficulty of tracking. The mean velocities presented in this secti on also neglect the effects of Stokes drift caused by the incident waves. Stokes drift has the largest effect on the rip current system within the rip neck by impeding its offshore mo vement. Therefore, if Stokes drift were taken into account the true mean fluid velocity within the ri p neck would be expected to be slightly larger than presen ted in this study. In the velo city validation section of this chapter, when the velocity in the rip ch annel is compared between VDT and current meters, Stokes drift will be taken in to account using linear wave theory. Fluctuating Velocity Next, the change in velocity within the rip current system was analyzed by separating the long tests into 18 equal time intervals of one minute. Figure 3-11 shows the one-minute averages of tota l velocity throughout the fiel d of view containing the rip current system for test 16. Again, the spatia l resolution was chosen to be .5 m due to the desired flow details and availa ble drifter coverage. At least eight velocity measurements were required for each .5 m bin, per one minute time interval, to obtain these fluctuating velocities. A finer temporal or spatial reso lution was not feasible with the available drifter coverage. Appendix E contains the same plot-type for all the long tests. Tests 15 and 16 include the effects of the wave-maker startup on the fluctuating flow velocity. Fluctuating velocity within the visible domain w ill be discussed in more detail in the next section about unsteady rip current flow.

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41 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure 3-11: Test 16 / 1 minute averages of velocity; Only tests 15 and 16 include the effects of the wave-maker startup for th e long tests; legend at the bottom right represents 10 cm/s

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42 In hopes of eliminating any bias of slow or fast moving drifters, described in the mean velocity section of this chapter, the one-minute mean velocities were averaged to obtain mean velocities for each long test. These results were compared to the mean velocities obtained by considering the entire run length and no appr eciable difference was noticed throughout the field of view, which can be noticed by comparing Figures 3-9 and 3-12 for test 16. 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-12: Mean Velocity; Obtained by averaging one-minute mean velocities (Test 16) Unsteady Rip Current Flow Rip current circulation is uns teady on scales spanning se veral orders of magnitude in space and time. In our study, modulations in rip current strength within the neck known as rip current “pulsing” can be observed from the figures of fluctuating velocity. A time series analysis of discrete drifter ve locities in the rip channel (not shown) has concluded that this unsteady pulsing occurs on the order of wave groups. In the field,

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43 these “pulses” have also been observed to occur on the order of wave groups (Sonu 1972, and Brander and Short 2001). 10 11 12 13 14 15 16 17 1 8 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure 3-13: Test 16 / Alongshore (y) migration of the maximu m one-minute average of Total velocity through time for three cro ss shore bands located between: 1) x = 9m to 9.5m Dotted line ; 2) x = 9.5m to 10m Dashed line ; and 3) x = 10m to 10.5m Solid line / Vertical Dotted lines indicate the longshore limits of the rip channel Low frequency oscillations in rip current fl ow for a barred beach with periodic rip channels were also observed in our study. As mentioned in the li terature review, field researchers have documented the existence of these unstable, long pe riod oscillations in rip current flow (Sonu 1972). In an attempt to analyze this unstable oscillation, Figure 3-13 plots the longshore migration of the maxi mum total velocity fo r three cross shore bands in test 16. Figure 3-14 shows the the three cross shore bands located offshore of the bar and channel system between: 1) x = 9m to 9.5m, 2) x = 9.5m to 10m, and 3) x =

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44 10m to 10.5m. In Figure 3-14, the fluid velo city was averaged every one minute in half meter bins along the three cross shore bands. The data points in Figure 3-13 correspond to the longshore location of the maximum total velocity along each particular cross shore band within the one minute time steps. As a reminder, the offshore and shoreward edge of the bar are approximately located at x = 11.1 m and x = 12.3 m respectively and the longshore limits of the rip channel are a pproximately at y = 12.8 m and y = 14.6 m. (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure 3-14: Test 16 / One minute averages of velocity along three cross shore bands between: 1) x = 9m to 9.5m; 2) x = 9.5m to 10m; and 3) x = 10m to 10.5m

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45 Figure 3-13 seems to show that test 16 has an oscillation period of 3 to 4 minutes. The same plot-type of the other long tests, located in Appendix F, agree with this relatively small oscillation time scale of test 16. This is complicated by the presence of other oscillation patterns, with longer time scal es, superimposed on each other. Each test was 18 minutes in duration, which is not l ong enough to resolve a complete longer time scale oscillation. Several larg e time scale oscillation peaks were noticed, but a complete period could not be determined, which can be noticed in test 13 found in Appendix F. Test 21, also found in Appendix F, was the on ly test where a long period oscillation of approximately 14 minutes could be distinguished with some confidence. The plots of all the drifte r streaks (Appendix C) and fluctuating velocity (Appendix E) for the long tests support the oscillation pa tterns that were observe d in the figures of the longshore migration of maximum total ve locity, located in A ppendix F. This can been seen for test 16 by comparing Figures 3-5 (Drifter streak s), 3-11(fluctuating velocity), 3-13 (longshore migration of ma ximum velocity), and 3-14 (fluctuating velocity along cross shore bands). No co rrelation could be made between the test conditions and the oscill ation periods observed. The plots of all the drifte r streaks and fluctuating velocity also give some qualitative insight into the instability mechan ism of rip currents. It is apparent, from these figures, that the direction of the offshore-directed flow in the rip neck is in some way associated with the shedding of one of the two oppositely spi nning vortices found on either side of the rip channel. This process can be most clearly seen for test 21 from the figures of drifter streaks (Appe ndix C) and fluctuating veloc ity throughout th e rip system (Appendix E). If the right vortex, with respec t to the shore, moves offshore the rip tends

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46 to be directed to the left a nd vice-versa. An increase in feeder current strength, on the same side as the vortex shedding, was also observed in some cases. Limitations of instability analysis. A consequence of having a record length of only 18 minutes, is that an oscillation widt h in the longshore at specific cross shore locations could not be determined with confid ence. Therefore, determining a growth rate for the unstable oscillation could not be comp leted. An oscillation width in the rip channel couldn’t be found either, therefore the oscillation period of the rip current using jet instability mechanism could not be determined. To achieve a finer temporal resolution, th an 1 minute, more drifter coverage would be needed to ensure enough measurements in the desired time step. The author doesn’t think this presents a problem because instabilit ies in rip current osci llations are associated with time scales generally larger than 1 minute. Vorticity Time-averaged vorticity ( ), calculated from Equation 3-3, was determined throughout the field of view containing the rip current sy stem for the long tests. dy u d dx v d (3-3) The terms dv/dx and du/dy in Equation 3-3 were calculated using the second-order central difference formula. As stated before, a spatial resolution of 0.5 m was used due to the available drifter coverage. Figure 3-15 s hows an example of time-averaged vorticity throughout a rip current system for test 16. Remember, the first 5 minutes of tests 15 and 16 are excluded to eliminate the effects of th e wave-maker startup on averaged quantities. Appendix G contains the pl ots of time-averaged vorticity for every long test.

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47 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-15: Test 16 / Time-averaged vor ticity; contour = 0.1/s; Positive => Dashed line Negative => Dash-Dot line and Zero => Solid line Oppositely spinning vortices on either side of the rip channel can be seen in Figure 3-14 for test 16, and all of the other long tests. These vortices or e ddies are also present in the figures of mean veloci ty (Appendix D). Shoreward of each vortex on either side of the rip channel exist another vortex circulati on, which is spinning opposite to it. This configuration of four separate ly spinning vortices is in agreement with the results from the numerical model analysis by Chen et al. (1999) of the same experimental setup as presented in this study. Continuity The depth-integrated continuity equati on, shown in Equation 3-4, was timeaveraged to obtain Equation 3-5. The velo city profile through the water column was

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48 assumed to be depth uniform and changes in depth ( h ) due to fluctuating waters levels were neglected. 0 ) ( ) ( dy hv d dx hu d dt d (3-4) 0 ) ( ) ( dy v h d dx u h d (3-5) If mass is shown to be conserved by satisfyi ng Equation 3-5 then de pth uniform flow can be considered a valid assumption. As stated before, computational bins of 0.5 m were used due to the available drifter coverage The left hand side of Equation 3-5 was calculated throughout the visible domain in an attempt to validate the mean velocity within the rip current system. Figure 3-16 shows an example of time-averaged, depthintegrated continuity throughout a rip current system for test 16. Appendix H contains this same plot-type for every long test. x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure 3-16: Test 16 / Time-averaged, depth-in tegrated continuity / contour = 0.005 m/s; Positive => Dashed line Negative => Dash-Dot line and Zero => Solid line

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49 Figure 3-16 shows a large posit ive area within the rip ne ck, which means the depthintegrated, time-averaged continuity equation, shown in Equation 3-5, is not satisfied. Therefore, more fluid is appa rently exiting than entering the computational bins located in the rip neck. In actua lity, mass is being conserved throughout the visible domain because the still water leve l (SWL) remains constant. This discrepancy in the conservation of mass flux may have resulted from assuming depth uniform flow and the effects of Stokes drift. St okes drift due to incident wave s has the largest effect on rip current flow by impeding the offshore direct ed neck, which is where the continuity equation is not satisfied. For future resear ch, wave heights could be determined from a wave model, such as REF/DIF, to calculate a value for Stokes drift throughout the visible domain. Test 16 produced the least favorab le results from the long test category. Velocity Distribution Probability density functions (PDFs) were created for each of the long tests in order to analyze the distribu tion of the longshore and cross s hore components of velocity at four locations in the visible domain. The four computational do mains throughout the rip system used to obtain the PDFs are shown in Figure 3-17. Figure 3-18 shows the plottype described above for test 16. Appendix I contains this same pl ot-type for every long test. The mean and standard deviation of th e velocity distribution for the components (u, v) can be seen in these PDF figures at the four specified locations. The number of velocity measurements used to create the PDFs is also noted in the figures. Equation 3-5 was used to calculate the st andard deviation of the velo city component distributions. 2) ( 1 1X X Ni (3-5)

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50 y(m)x(m) => offshore (a) (b) (c) (d) 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure 3-17: Four computational domains used to obtain PDFs for the long tests: (a) x = 11.6m to 12m, y = 13.42m to 14.02m (Rip channel) (b) x = 8.4m to 8.8m, y = 13.42m to 14.02m (Directly offshore of the rip channel) (c) x = 8.4m to 8.8m, y = 11.4m to 12m (Offshore of the left bar referenced from shore) (d) x = 12.4m to 12.8m, y = 11.4m to 12m (Directly behind the left bar) 40 20 0 20 0 0.05 0.1 0.15 Mean u=10.89 v=1.61 StDev u=10.62 v=10.57 # of meas. 1000Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=9.32 v=1.45 StDev u=3.42 v=2.27 # of meas. 146Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.91 v=3.11 StDev u=3.78 v=1.78 # of meas. 203Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=7.08 v=4.99 StDev u=5.51 v=4.88 # of meas. 373Velocity (cm/s)Probability / (cm/s)(d) Figure 3-18: PDF at four locat ions shown in Figure 3.17 / Cross shore velocity (u) => Solid line Longshore velocity (v) => Dashed line (Test 16)

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51 The PDFs of the longshore and cross s hore components of velocity for the long tests show a wide distribution and the unst eadiness of rip current flow at various locations, especially within the rip channel. This can be noticed from the large standard deviation of Figure 3-18 (a), wh ich represents the rip channe l. Also notice from Figure 3-18 (a) that the longshore ve locity in the channel has a mean of approximately zero, which is consistent with the cross shore flow a ssociated with the rip neck in the channel. The cross shore component of velocity in th e rip neck, shown in Figure 3-18 (a), has a mean of -10.89 cm/s directed offshore. Th e three other locations, shown in Figure 3-17 (b,c,d), used to create a PDF of veloc ity components also show a relatively wide distribution, which can be conc luded from Figure 3-18 (b,c,d). The analysis of velocity distribution for test 16 is similar for many of the other long tests, found in Appendix I, with some specific distinctions depending on the unsteady rip current behavior and test conditions. The method of VDT allows this analysis of velocity distribution to be performed anywhere in the field of view, without the trouble of moving current meters and running the test again. Mean circulation depends, to a large extent, on momentum mixing by large-scale turbulent Reynolds stresses. Direct estimat es of these Reynolds stresses (not shown) have also been obtained over the visible domai n, and are to form the basis of future studies. This will be quite important for es timating new turbulent closures in future models. Velocity Validation (VDT vs. Current Meters) A comparison was made of instantaneous ve locities within the rip channel obtained from an array of current meters and the method of VDT for the transient tests (Figure 3-20). The VDT window was 10 cm x 50 cm, extending 5 cm from the current

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52 meter group in both the longshore and cross shore direction. This is more easily seen in Figure 3-19. Figure 3-19 also displays the lo cation of the three current meters within the rip channel. 13 13.5 14 14.5 11 11.5 12 12.5 x (m) offshore =>y (m)Current Meters and VDT window located in the Rip Channel Figure 3-19: Current meter and VDT window loca tions used to make comparisons within the rip channel for both the transient and long tests / ADV 1 (y=13.52m, x=11.8m); ADV 2 (y=13.72 m, x=11.8m); ADV 3 (y=13.92m, x=11.8m) / VDT window (y=13.47m to 13.97m, x=11.75m to 11.85m) In Figure 3-20, each of the three test conditions was run one time and the three current meters or ADVs were averaged to obtain the solid line. The discrete points represent the velocities determined using VDT from three separate runs for each of the three test conditions. The drifter velocities were corrected for Stokes surface drift, which is designated by the sym bol (x) in Figure 3-20.

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53 20 0 20 40 60 80 100 40 30 20 10 0 10 U (cm/s)(a) 20 0 20 40 60 80 100 40 30 20 10 0 10 U (cm/s)(b) 20 0 20 40 60 80 100 40 30 20 10 0 10 U (cm/s)Time (s) (c) Figure 3-20: Comparison of instantaneous ve locity between VDT and Current Meters within the rip channel for the transien t tests / (-) Averaged current meter velocities; (.) VDT velocities befo re Stokes drift co rrection from window encompassing Current Meter array; (x) VDT drifter velocities after Stokes drift correction / (a) Tests 1-3 (b) Tests 4-5, 9 (c) Tests 6-8 After correction for Stokes drift, agreement between current meter and drifter velocities is good, except at th e time of peak current during large waves, which can be noticed in Figure 3.20 (b). The remaining di screpancies are attributed to the difference between small-amplitude theories and the finite wave heights in the rip channel. All the transient tests show similar behavior in th at velocities increase st rongly after the first wave arrival. A peak current is then achieved, which is followed by a decline in strength. Also note that Figure 3.20 (a) and Figure 3.20 (c) show almost identical peak currents despite the difference in wave group duration.

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54 A comparison was also made of mean velo cities within the rip channel obtained from both an array of current meters and the method of VDT for the long tests. Table 3-4 shows the number of discrete drifter veloci ty measurements used to obtain the mean velocity in the rip channel for the method of VDT. The current meter and VDT window locations within the rip channel, shown in Figure 3-19, are the same as the comparison made for the transient tests. In Figure 3-21 (a), the mean cross shore component of velocity obtained from VDT for the long te sts was corrected for Stokes drift, which decreased the root mean square (RMS) of th e error from 6.81 cm/s to 3.30 cm/s. The RMS of the error for the longshore component of velocity was 1.84 cm/s. This shows adequate agreement between the mean veloci ties obtained from the current meters and the method of VDT for the long tests. 25 20 15 10 5 0 25 20 15 10 5 0 Current Meter (cm/s)VDT (cm/s)(a) 10 5 0 5 10 10 5 0 5 10 Current Meter (cm/s)VDT (cm/s)(b) Figure 3-21: Comparison of mean velocity be tween VDT and Current Meters within the rip channel for the long tests / (o) Be fore Stokes drift correction to VDT measurements; (x) After Stokes drift co rrection to VDT measurements / (a) Cross shore velocity; (b) Longshore velocity

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55 Table 3-4: Number of drifter ve locity measurements used to ob tain a mean velocity in the rip channel using VDT which was compared with mean velocities determined from current meters for the long tests (Figure 3-21) Test # # of drifter ve locity measurements 12 119 13 155 14 119 15 173 16 338 19 72 20 118 21 93

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56 CHAPTER 4 CONCLUSIONS A laboratory rip current system with a l ongshore bar and channel bathymetry at the Center for Applied Coastal Research (Uni versity of Delaware) was analyzed by the method of Video Drifter Track ing (VDT). Steady and unste ady rip current processes were studied using video-tracke d Lagrangian drifters for a range of wave and water level conditions, which are given in Tables 2.1 a nd 2.2. The tests are divided into two categories: transient tests and long tests, with specific parameters discussed in Chapter 2. The drifter coverage and r un lengths are sufficient to obtain both averaged and fluctuating quantities over the visible flow domain including: 1) Mean velocity (1 to 18 min. averages), 2) Velocity distributions at specified locations, and 3) Time-averaged vorticity. A spatial resolution of 0.5 m, used for all the averaged quantities presented in this study, was chosen based on the desired details of the rip current flow and the available drifter coverage. Rip current flow features, observed in the field by Shepard et al. (1941), such as feeder currents, rip neck, and rip head were al l seen in this laboratory study. Symmetric eddies on either side of the rip channel were also noticed in many cases here and have been documented in the field by Shephard et al. (1941), Sonu (1972) and Schmidt et al. (2001). These oppositely spinning circulation ce lls on either side of the rip channel can be seen either from the figures of mean velo city, time-averaged vorti city, or snapshots of drifter positions with corres ponding velocity vectors.

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57 The plots of time-averaged vorticity also show another eddy ci rculation shoreward of each vortex on either side of the rip channel, which is spinning opposite to it. This configuration of four separate ly spinning vortices is in agreement with the results from the numerical model analysis by Chen et al. ( 1999) with the same experimental setup as presented in this study. The reversal of fl ow onshore in the rip channel behind the bar, noticed in this study, can be attributed to these vortices located between the bar and the shoreline. Many different length scales of rotati onal motion were observed throughout the various tests, ranging from sma ll scale vortices of D = O(20cm) to basin-scale circulation with D = O(20m). The generation of a ve ry small vortex on the bar corner, and its transport offshore as part of a larger overall circulation was observed in Figure 3.3. Such vorticity generation by differential wave br eaking was predicted by Peregrine (1998), but has not been observed previously. Every tr ansient and most long tests exhibited these small vortices when drifters passed over th e bar corner while being ejected offshore by the rip neck. Extremely large scale circulat ion patterns were difficult to resolve due to the limited field of view. Video recordings w ith a much larger field of view were created and are currently being analyzed. The trajectories and velocity of individual drifters were also analyzed to show the various scales of circulation found in a rip current system. In this study, rip current strength was shown to increase with higher waves and a lower water level, which was concluded by the plots of mean velocity and Table 3.3 of the averaged maximum drifter velocity for the long tests. This relationship between rip current strength and wave height and water level conditions is in agreement with field observations made by McKenzie 1958, C ooke 1970, Sonu 1972, Brander 1999, Brander

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58 and Short 2001, Shepard et al. 1941, Shep ard and Inman 1950, McKenzie 1958, Dronen et al. (2002) and others. The pl ots of mean velocity also show that some of the long tests exhibit classic symmetric circ ulation cells, while other rips have a strong bias in one direction, even with shore normal waves. Th e lack of drifter coverage may have caused quantities to be biased, however this effect on the true mean velocity was not determined. However, the drifter coverage was usually enough to collect hundreds or even thousands of velocity measurements within each half meter bin. Rip current circulation was found to be unsteady on scales spanning several orders of magnitude in time as well as space. Most of the long tests showed an unstable oscillation period of approximately 3 to 4 mi nutes in the offshore direct flow. Field researchers have documented the existence of these unstable, long pe riod oscillations in rip currents (Sonu 1972). This is furthe r complicated by the presence of other oscillations patterns, with longer time scal es, superimposed on each other. Throughout the 18 minute run length for the long tests se veral isolated large time scale oscillation peaks were noticed. However, in many cases this run length was not long enough to resolve the period of a complete longer time scale oscillation. Test 21, found in Appendix F, was the only test where a long period oscillation of approximately 14 minutes could be distinguished with some co nfidence. The finest temporal resolution that could be determined was one minute, which is adequate for any high frequency motions of rip current instability. Th e PDFs of the longshore and cross shore components of velocity within the field of view for the long tests also show a wide distribution and the unsteadiness of rip curr ent flow, especially within the channel.

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59 Results for this study also include insight into the in stability mechanism of rip currents. From the figures of all the drifte r paths within two-minute intervals (Appendix C) and one-minute averages of velocity (Appendi x E), it is apparent that the direction of the offshore flow in the rip neck is in some way associated with the shedding of one of the two oppositely spinning vortices found on either side of the rip channel. If the right vortex, with respect to the shore, moves offshor e the rip tends to be directed to the left and vice-versa. This unstable processes is most easily seen in Test 21. An increase in feeder current strength, on the same side as the vortex shedding, was also observed in some cases. In an attempt to validate the method of VD T, the drifter velocities obtained were compared to current meters located in the rip channel and continuity was analyzed throughout the visible domain. After correc tion for Stokes drift, agreement between current meter and drifter velocities in the rip channel was good for both the transient tests (Figure 3.20) and long tests (Figure 3.21). Some of the figures showing continuity for the long tests have a large pos itive area within the rip n eck, which means the depthintegrated, time-averaged continuity equation is not satisfied. This discrepancy in the conservation of mass flux may have resulted from assuming depth uniform flow and the effects of Stokes drift. Stokes drift due to incident waves has the largest effect on rip current flow by impeding the offshore direct ed neck, which is where the continuity equation is not satisfied. For future resear ch, wave heights could be determined from a wave model, such as REF/DIF, to calculate a value for Stokes drift throughout the visible domain. Other future studies may involve the analysis of mome ntum mixing by largescale turbulent Reynolds stress es. Direct estimates of these Reynolds stresses (not

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60 shown) have been obtained over the visible domain. This will be quite important for estimating new turbulent closures in future models. It is evident that a comprehensive map of rip current flow will aid in the improved understanding of the nearshore ci rculation pattern and is needed in order to make further advances in predicting sediment transport and the overall shape of the coastline, which is a major issue for the growing number of co astal landowners. Many areas of the world, including Florida, also depend on the tour ism generated from their beaches and rip currents pose a serious threat to ocean bathers due to their strong, seaward directed flows. The method of VDT has proved to be quite be neficial for the analysis of a complete laboratory rip current system. The financial cost of current meters has inhibited the ability to obtain a desired spatial resolution of quantities within a complete rip current system, which shown by this study, can be achieved by the use of VDT due to the low cost of video-tracked laboratory drifters.

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61 APPENDIX A RIP CURRENT FEATURES (TEST 5) 10 cm/sx (m) offshore =>y (m) 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure A-1: Onshore flow over the bar due to waves / Drifter positions and velocity at t = 12 s after the wave-maker startup (Test 5)

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62 10 cm/sx (m) offshore =>y (m) 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure A-2: Feeder currents c onverging from either side of the rip cha nnel / Drifter positions and velocity at t = 22 s (Test 5) 10 cm/sx (m) offshore =>y (m) 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure A-3: Offshore directed cu rrent through the rip neck / Dr ifter positions and velocity at t = 32 s (Test 5)

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63 10 cm/sx (m) offshore =>y (m) 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 cm/s 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure A-4: Expanding rip head offshore / Drifter positions a nd velocity at t = 53 s (Test 5)

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64 APPENDIX B DRIFTER TRAJECTORIES AND VELOCITY (TEST 12) (a)x(m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 (b)x(m) offshore =>y (m) 10 12 14 16 1 8 7 8 9 10 11 12 13 14 15 50 100 150 200 250 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) 200 220 240 260 280 300 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) Figure B-1: Drifter trajectori es and corresponding velocity time series / Cross shore velocity => Dashed line Longshore velocity => Dash-Dot line Total velocity => Solid line (Test 12)

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65 (a)x(m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 (b)x(m) offshore =>y (m) 10 12 14 16 1 8 7 8 9 10 11 12 13 14 15 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) 800 850 900 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) Figure B-2: Refer to Figure B-1 (a)x(m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 (b)x(m) offshore =>y (m) 10 12 14 16 18 7 8 9 10 11 12 13 14 15 600 700 800 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) 750 800 850 900 950 0 0.2 0.4 0.6 0.8 1 1.2 velocity (m/s)time (s) Figure B-3: Refer to Figure B-1

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66 APPENDIX C DRIFTER TRAJECTORIES FOR THE LONG TESTS (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (b) 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 1 8 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 1 8 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 1 8 8 10 12 14 Figure C-1: Test 12 / Drifter pa ths; 2 minute time intervals

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67 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 1 8 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 1 8 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 1 8 8 10 12 14 Figure C-2: Test 13 / Drifter paths; 2 minute time intervals (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 18 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 18 8 10 12 14 Figure C-3: Test 14 / Drifter paths; 2 minute time intervals

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68 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 1 8 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 1 8 8 10 12 14 Figure C-4: Test 15 / Drifter pa ths; 2 minute time intervals (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (b) 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 18 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 18 8 10 12 14 Figure C-5: Test 16 / Drifter pa ths; 2 minute time intervals

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69 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 1 8 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 1 8 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 1 8 8 10 12 14 Figure C-6: Test 19 / Drifter paths; 2 minute time intervals (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (b) 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 18 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 18 8 10 12 14 Figure C-7: Test 20 / Drifter pa ths; 2 minute time intervals

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70 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 x(m) offshore => (c) 10 12 14 16 1 8 8 10 12 14 x(m) offshore => (d) 10 12 14 16 18 8 10 12 14 x(m) offshore => (e) 10 12 14 16 18 8 10 12 14 x(m) offshore => (f) 10 12 14 16 1 8 8 10 12 14 x(m) offshore =>y (m) (g) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (h) 10 12 14 16 18 8 10 12 14 x(m) offshore =>y (m) (i) 10 12 14 16 1 8 8 10 12 14 Figure C-8: Test 21 / Drifter paths; 2 minute time intervals

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71 APPENDIX D MEAN VELOCITY Test 12: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-1: Test 12 / H= 4.32cm, T= 1s, groupy waves (32); high water

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72 Test 13: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-2: Test 13 / H= 4.28cm, T= 1s, monochromatic waves; high water Test 14: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-3: Test 14 / H= 4.62cm, T= 1s, groupy waves (32); low water

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73 Test 15: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-4: Test 15 / H= 4.83cm, T= 1s, monochromatic waves; low water Test 16: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-5: Test 16 / H= 6.18cm, T= 1s, monochromatic waves; high water

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74 Test 19: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-6: Test 19 / H= 5.22cm, T= 1.33s, monochromatic waves; low water Test 20: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-7: Test 20 / H= 3.69cm, T= 1s, groupy waves (64); high water

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75 Test 21: Mean Velocities 10 cm/sx(m) offshore =>y(m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure D-8: Test 21 / H= 3.97cm, T= 2. 67s, monochromatic waves; high water

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76 APPENDIX E FLUCTUATING VELOCITY (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-1: Test 12 / 1 minute averages of velocity; Legend at the bottom right represents 10 cm/s

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77 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-2: Test 13 / 1 minute averages of velocity; Legend at the bottom right represents 10 cm/s

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78 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-3: Test 14 / 1 minute averages of velocity; Legend at the bottom right represents 10 cm/s

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79 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-4: Test 15 / 1 minute averages of veloc ity; Only tests 15 and 16 include the effects of the wave-maker startup; Le gend at the bottom right represents 10 cm/s

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80 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-5: Test 16 / 1 minute averages of veloc ity; Only tests 15 and 16 include the effects of the wave-maker startup; Le gend at the bottom right represents 10 cm/s

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81 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-6: Test 19 / 1 minute averages of velocity; Legend at the bottom right represents 10 cm/s

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82 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-7: Test 20 / 1 minute averages of velocity; Legend at the bottom right represents 10 cm/s

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83 (a)x(m) offshore => 10 12 14 16 18 8 10 12 14 (b)x(m) offshore => 10 12 14 16 18 8 10 12 14 (c)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (d)x(m) offshore => 10 12 14 16 18 8 10 12 14 (e)x(m) offshore => 10 12 14 16 18 8 10 12 14 (f)x(m) offshore => 10 12 14 16 1 8 8 10 12 14 (g)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (h)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (i)x(m) offshore =>y (m) 10 12 14 16 1 8 8 10 12 14 (j)x(m) offshore => 10 12 14 16 18 8 10 12 14 (k)x(m) offshore => 10 12 14 16 18 8 10 12 14 (l)x(m) offshore => 10 12 14 16 18 8 10 12 14 (m)x(m) offshore => 10 12 14 16 18 8 10 12 14 (n)x(m) offshore => 10 12 14 16 18 8 10 12 14 (o)x(m) offshore => 10 12 14 16 18 8 10 12 14 (p)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (q)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 (r)x(m) offshore =>y (m) 10 12 14 16 18 8 10 12 14 Figure E-8: Test 21 / 1 minute averages of velocity; Legend at the bottom right represents 10 cm/s

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84 APPENDIX F RIP CURRENT INSTABILITY 10 11 12 13 14 15 16 1 7 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-1: Test 12 / Alongshor e migration of the maximum one-minute average of total velocity through time for th ree cross shore bands locat ed between: 1) x = 9m to 9.5m Dotted line ; 2) x = 9.5m to 10m Dashed line ; and 3) x = 10m to 10.5m Solid line / Vertical Dotted lines indicate the longshore limits of the rip channel

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85 10 11 12 13 14 15 16 17 1 8 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-2: Test 13 / Refer to Figure F-1 12 12.5 13 13.5 14 14.5 15 15.5 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-3: Test 14 / Refer to Figure F-1

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86 12 12.5 13 13.5 14 14.5 15 15.5 1 6 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-4: Test 15 / Refer to Figure F-1 10 11 12 13 14 15 16 17 18 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-5: Test 16 / Refer to Figure F-1

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87 11 12 13 14 15 16 17 1 8 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F.6: Test 19 / Refer to Figure F.1 10 11 12 13 14 15 16 17 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-7: Test 20 / Refer to Figure F-1

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88 10 11 12 13 14 15 16 17 1 8 0 2 4 6 8 10 12 14 16 18 20 Time (min)Alongshore Location (m) Figure F-8: Test 21 / Refer to Figure F-1

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89 APPENDIX G TIME-AVERAGED VORTICITY y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-1: Test 12 / contour = 0.1/s; Positive => Dashed line Negative => Dash-Dot line and Zero => Solid line

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90 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-2: Test 13 / Refer to figure G-1 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-3: Test 14 / Refer to figure G-1

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91 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-4: Test 15 / Refer to figure G-1 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-5: Test 16 / Refer to figure G-1

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92 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-6: Test 19 / Re fer to figure G-1 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-7: Test 20 / Re fer to figure G-1

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93 y(m)x(m) => offshore 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure G-8: Test 21 / Re fer to figure G-1

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94 APPENDIX H TIME-AVERGED, DEPTH-IN TEGRATED CONTINUITY x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-1: Test 12 / contour = 0.005 m/s; Positive => Dashed line Negative => DashDot line and Zero => Solid line

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95 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-2: Test 13 / Refer to Figure H-1 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-3: Test 14 / Refer to Figure H-1

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96 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-4: Test 15 / Refer to Figure H-1 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-5: Test 16 / Refer to Figure H-1

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97 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-6: Test 19 / Refer to Figure H-1 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-7: Test 20 / Refer to Figure H-1

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98 x direction (m) offshore =>y direction (m) 10 11 12 13 14 15 16 17 18 8 9 10 11 12 13 14 15 Figure H-8: Test 21 / Refer to Figure H-1

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99 APPENDIX I VELOCITY DISTRIBUTION y(m)x(m) => offshore (a) (b) (c) (d) 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 13 14 15 Figure I-1: Location of four computational domains used to obtain PDFs of drifter velocity components for th e long tests:(a) x = 11.6m to 12m, y = 13.42m to 14.02m (Rip channel); (b) x = 8.4m to 8.8m, y = 13.42m to 14.02m (Directly offshore of the rip channel); (c) x = 8.4m to 8.8m, y = 11.4m to 12m (Offshore of the left bar referenced from shore); (d) x = 12.4m to 12.8m, y = 11.4m to 12m (Directly behind the left bar);

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100 40 20 0 20 0 0.05 0.1 0.15 Mean u=6.58 v=1.96 StDev u=8.61 v=6.97 # of meas. 523Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=2.14 v=1.28 StDev u=3.94 v=1.55 # of meas. 232Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=1.01 v=2.26 StDev u=3.27 v=2.14 # of meas. 562Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=7.60 v=6.75 StDev u=6.66 v=4.75 # of meas. 233Velocity (cm/s)Probability / (cm/s)(d) Figure I-2: Test 12 / PDFs of drifter velocity components at four locations shown in Figure I-1 / Cross shore velocity (u) => Solid line Longshore velocity (v) => Dashed line 40 20 0 20 0 0.05 0.1 0.15 Mean u=12.61 v=2.35 StDev u=5.94 v=9.17 # of meas. 725Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.66 v=0.19 StDev u=2.51 v=1.83 # of meas. 552Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=1.59 v=4.69 StDev u=4.09 v=1.94 # of meas. 153Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=6.01 v=7.01 StDev u=6.34 v=4.25 # of meas. 315Velocity (cm/s)Probability / (cm/s)(d) Figure I-3: Test 13 / Refer to Figure I-2

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101 40 20 0 20 0 0.05 0.1 0.15 Mean u=14.77 v=2.96 StDev u=9.48 v=8.21 # of meas. 555Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=8.76 v=0.30 StDev u=4.40 v=4.51 # of meas. 362Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=1.58 v=3.68 StDev u=3.09 v=2.10 # of meas. 355Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=5.35 v=9.43 StDev u=4.37 v=4.54 # of meas. 213Velocity (cm/s)Probability / (cm/s)(d) Figure I-4: Test 14 / Refer to Figure I-2 40 20 0 20 0 0.05 0.1 0.15 Mean u=17.10 v=0.14 StDev u=9.02 v=8.99 # of meas. 408Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=8.33 v=2.10 StDev u=6.31 v=5.33 # of meas. 265Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.80 v=1.53 StDev u=2.56 v=2.24 # of meas. 473Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=4.56 v=9.87 StDev u=2.86 v=3.53 # of meas. 143Velocity (cm/s)Probability / (cm/s)(d) Figure I-5: Test 15 / Refer to Figure I-2

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102 40 20 0 20 0 0.05 0.1 0.15 Mean u=10.89 v=1.61 StDev u=10.62 v=10.57 # of meas. 1000Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=9.32 v=1.45 StDev u=3.42 v=2.27 # of meas. 146Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.91 v=3.11 StDev u=3.78 v=1.78 # of meas. 203Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=7.08 v=4.99 StDev u=5.51 v=4.88 # of meas. 373Velocity (cm/s)Probability / (cm/s)(d) Figure I-6: Test 16 / Refer to Figure I-2 40 20 0 20 0 0.05 0.1 0.15 Mean u=9.94 v=2.58 StDev u=9.76 v=6.92 # of meas. 358Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=11.40 v=6.91 StDev u=6.48 v=4.53 # of meas. 264Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.43 v=1.61 StDev u=2.58 v=2.53 # of meas. 131Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.19 v=1.62 StDev u=1.25 v=1.53 # of meas. 37Velocity (cm/s)Probability / (cm/s)(d) Figure I-7: Test 19 / Refer to Figure I-2

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103 40 20 0 20 0 0.05 0.1 0.15 Mean u=6.90 v=0.68 StDev u=7.34 v=8.86 # of meas. 774Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=2.79 v=1.10 StDev u=4.82 v=2.53 # of meas. 311Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=0.48 v=0.05 StDev u=2.60 v=1.54 # of meas. 667Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=8.05 v=4.49 StDev u=6.30 v=4.46 # of meas. 458Velocity (cm/s)Probability / (cm/s)(d) Figure I-8: Test 20 / Refer to Figure I-2 40 20 0 20 0 0.05 0.1 0.15 Mean u=8.20 v=0.18 StDev u=6.48 v=5.19 # of meas. 519Probability / (cm/s)(a) 40 20 0 20 0 0.05 0.1 0.15 Mean u=1.76 v=3.21 StDev u=5.17 v=3.42 # of meas. 278Probability / (cm/s)(b) 40 20 0 20 0 0.05 0.1 0.15 Mean u=2.43 v=0.49 StDev u=4.67 v=4.09 # of meas. 400Velocity (cm/s)Probability / (cm/s)(c) 40 20 0 20 0 0.05 0.1 0.15 Mean u=2.56 v=9.00 StDev u=3.63 v=3.31 # of meas. 249Velocity (cm/s)Probability / (cm/s)(d) Figure I-9: Test 21 / Refer to Figure I-2

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104 LIST OF REFERENCES Aagaard, T., B. Greenwood, and J. Nielson, 1997, Mean Currents and sediment transport in a rip channel, Mar. Geol., 140, pp. 25-45. Bowen, A. J., 1969, Rip currents, 1. Theoreti cal investigations, J. Geophys. Res., 74, pp. 5467-5478. Bowen, A. J., D. I. Inman, 1969, Rip currents, 2. Laboratory and fiel d investigations, J. Geophys Res., 74(23), pp. 5479-5490. Bowman, D., D. Arad, D.S. Rosen, E. Kit, R. Goldbery, and A. Slavicz, 1988, Flow characteristics along the rip current sy stem under low-energy conditions, Mar. Geol., 79, pp. 149-167. Brander, R. W., 1999, Field observations on morphodynamic evolution of a low-energy rip current system, Mar. Geol., 157(3-4), pp. 199-217. Brander, R. W, and A. D. Short, 2000, Mo rphodynamics of a largescale rip curent at Muriwai Beach, New Zealand, Mar. Geol., 165, pp. 27-39. Brander, R. W., A. D. Short, 2001, Flow kinematics of low-en egy rip current systems, J. Coast. Res., 17(2), pp. 468-481. Chandramohan, P., V. S. Kumar, B. K. Je na, 1997, Rip current zones along the beaches in Goa, west coast of India, J. Waterway, Port, Coast., and Ocean. Eng., 123(6), pp.322-328. Chen, Q., R. A. Dalrymple, J. T. Kirby, A. B. Kennedy, and M. C. Haller, 1999, Boussinesq modeling of a rip current system, J. Geophys. Res., 104, pp. 20,61720,637. Cooke, D. O., 1970, The occurrence and geological work of rip currents off the coast of southern California, Mar. Geol., 9, pp. 173-186. Dalrymple, R. A., 1975, A mechanism for rip current generation on an open coast, J. Geophys. Res., 80(24), pp. 3485-3487. Dalrymple, R. A., 1978, Rip current s and their causes, Proc. of 16th Conf. on Coast. Eng., Vol. II, pp. 1414-1427.

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105 Dalrymple, R. A., C. J. Lozano, 1978, Wave-c urrent interaction mode ls for rip currents, J. Geophys. Res., 83, pp. 6063-6071. Davis, W. M., 1925, The Undertow, Science, Vol. LXII pp. 206-208. Dronen, N., H. Karunarathna, J. Fredsoe, B. M. Sumer, and R. Deigaard, 1999, The circulation over a longshore bar with ri p channels, Proc. Coast. Sed., pp. 576-587. Dronen, N., H. Karunarathna, J. Fredsoe, B. M. Sumer, R. Deigaard, 2002, An experimental study of rip channel flow, J. Coast. Eng., 45, pp. 223-238. Falques, A., A. Montoto, D. Vila, 1999, A note on hydrodynamic instabilities, and horizontal circulation in the surfzone, J. Geophys. Res., 104(20), pp. 605-620. Folwer, R. E., R. A. Dalrymple, 1990, Wave group forced nearshore circulation, Proc. 22nd Intl. Conf. of Coast. Eng., Delft, The Netherlands, ASCE. Haas, K. A., 2002, Laboratory measurements of the vertical structure of rip currents, J. Geophysical Research-Oceans, 107 (C5), art. no. 3047. Haller, M. C., R. A. Dalrymple, I. A. Svendsen, 1997, Rip channels and nearshore circulation, Proc. Co ast. Dyn., pp. 594-603. Haller, M. C., R. A. Dalrymple, 1999, Rip current dynamics and nearshore circulation, Center for Applied Coast. Res., Res. Rep. # CACR-99-05, pp. 1-144. Haller, M. C., R. A. Dalrymple, 2001, Rip current instabilities, J. Fluid Mech., 433, pp. 161-192. Haller, C., R. A. Dalrymple, I. A. Sve ndsen, 2001, Experimental study of nearshore dynamics on a barred beach with rip cha nnels, Submitted to J. Geophys. Res., May. Hamm, L., 1992, Directional nearshore wa ve propagation over a rip channel: an experiment, Proc. ICCE, pp. 226-239. Holland, K. T., R. A. Holman, T. C. Lippma nn, 1997, Practical use of video imagery in nearshore oceanographic field studies, J. Ocean. Eng., 22, pp. 81-91. Holland, K. T., J. A. Puleo, 2001, Quantification of swash flows using video-based particle image velocimetry, 44 (2), pp. 65-77. Huntley, D. A., A. D. Short, 1992, On the sp acing between observed rip currents, Coast. Eng., 17, pp. 211-225. Komar, P. D., 1976, Beach processes and se dimentation, Prentice Hall Inc., pp. 343-350. Lascody, R. L., 1998, East Central Florida ri p current program, Na tional Weather Digest, 22(2), pp. 25-30.

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106 Longuet-Higgins, M. S., 1970a, Longshore curren ts generated by obliquely incident sea waves, 1, J. Geophys. Res., 75, pp. 6778-6789. Longuet-Higgins, M. S., 1970b, Longshore curren ts generated by obliquely incident sea waves, 2, J. Geophys. Res., 75, pp. 6790-6801. Longuet-Higgins, M. S., R. W. Stewart, 1964, Radiation stress in water waves, a physical discussion with applications, D eep Sea Res., 11(4), pp. 529-563. MacMahan, J., A. J. H. M. Reniers, T. P. St anton, and E. B. Thorton, 2003, Infragravity motions on a complex beach, part 1: observations, Submitted to J. Geophys. Res., December. McKenzie, P., 1958, Rip current systems, J.Geol., 66, pp.103-113. N. C. Sea Grant, 2003, Rip current brochure, Available [on-line] http://www.ncsu.edu/seagrant/PDF/RipBrochure.pdf. NOAA, Rip currents….a threat to life, Available [on-line] http://205.156.54.206/er/akq/rip/ripmain.html Oh, T. M., R. G. Dean, 1996, Three-demensional hydrodynamics on a barred beach, Proc. Intl. Conf. Coast. Eng., pp. 3680-3692. Peregrine, D. H., 1998, Surf zone curren ts, Theoretical and computational fluid dynamics, 10 (1-4), pp. 295-309. Sanders, R., 2002, Rip currents at Ocean B each are a severe hazard for unwary, UC Berkeley expert warns, UC Berkeley Ca mpus News / Media Relations, Available [on-line] http://www.berkeley.edu/news/ media/releases/2002/05/23_tides.html. Schmidt, W. E., B. T. Woodward, K. S. Millikan, R. T. Guza, B. Raubenheimer, and S. Elgar, 2001, A GPS tracked surfzone dr ifter, Submitted to J-TECH, November. Shepard, F. P., 1936, Undertow, Rip Tides, or Rip Currents, Science, Vol. LXXXIV, pp. 181-182. Shepard, F. P., K. O. Emery, E. C. La F ond, 1941, Rip Currents: A process of geological importance, J. Geol., 49, pp. 337-369. Shepard F. P., D. L. Inman, 1950, Nears hore water circulation related to bottom topography and wave refraction, EO S Trans. AGU, 31(2), pp. 196-212. Short, A. D., C. L. Hogan, 1993, Rip Curre nts and beach hazards: Their impact on pubic safety and implications for coastal ma nagement, J. Coast. Res.,12, pp.197-209. Sonu, C. J., 1972, Field observation of nears hore circulation and m eandering currents, J. Geophys. Res., 77, pp. 3232-3247.

PAGE 120

107 Wei, G., J. T. Kirby, S. T. Grilli, R. Subramanya, 1995, A fully nonlinear boussinesq model for surface waves, 1. Highly nonlinea r unsteady waves, J. Fluid Mech., 294, pp. 271-299. Wind, H. G., C. B. Vreugdenhil, 1986, Rip cu rrent generation near structures, J. Fluid Mech., 171, pp. 459-476.

PAGE 121

108 BIOGRAPHICAL SKETCH The author was born on May 21, 1979 in Ke y West, Fl. Whether in California, Puerto Rico, or Florida, living on the coast ga ve the author a strong interest in the ocean and a passion for surfing. During the summe r of 1997, the author moved from Imperial Beach, CA to Gainesville, Fl to learn about the coastal processes and possible engineering solutions to the many coasta l problems witnessed over a lifetime. A bachelor’s degree in engineer ing science (2001) led to a master’s degree in coastal engineering (2003). Both degr ees were obtained from the Un iversity of Florida. Now the author is off to put his knowledge to good use in the South Pacific.


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Physical Description: Mixed Material
Creator: Thomas, David A. ( Author, Primary )
Publication Date: 2003
Copyright Date: 2003

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LABORATORY RIP CURRENT CIRCULATION
USING VIDEO-TRACKED LAGRANGIAN DRIFTERS















By

DAVID A. THOMAS


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2003

































This thesis is dedicated to my mother and father.















ACKNOWLEDGMENTS

This research was funded by the University of Florida. The author would like to

thank Andrew B. Kennedy for providing the financial assistance, academic guidance, and

raw data for this research. The author would also like to thank the other committee

members, Robert J. Thieke and Robert G. Dean, for all their help and insight.
















TABLE OF CONTENTS
page

A C K N O W L E D G M E N T S ................................................................................................. iii

LIST OF TABLES ....................................................... ............ ....... ....... vi

L IST O F F IG U R E S .... ...... ................................................ .. .. ..... .............. vii

ABSTRACT ........ .............. ............. .. ...... .......... .......... xii

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

Problem Statem ent and Objective ........................................ .......................... 1
Background: Rip Current Literature Review ..................................... .....................5
Physical Description of Rip Currents ............ ..............................................6
Im pact of R ip Currents ........................................................... ............9
Forcing M mechanism ............... .... ........ ........ .... ..... .............. .. 11
Unsteady Behavior of Rip Currents ...........................................................14
S u m m ary ...................................... .................................................. 15
O u tlin e of T h esis......................................................................................... 16

2 E X PE R IM E N TA L SE TU P ............................................................. .....................18

P h y sic a l M o d e l ..................................................................................................... 1 8
T est C conditions ..................................................................................................20
Data Collection ................................................... 21
Experim mental and Data Collection Error .............................................. ......25




M ean V elo city ................................................................34
F luctuating V velocity .......................................................................................40
Unsteady Rip Current Flow ......................................................... ............... 42
V orticity ............................................ ................ ... ... .. ...... ......... 46
C o n tin u ity .......................................................................................................4 7
V velocity D distribution ..................... .......... ...................... .... ......... ........ 49
Velocity Validation (VDT vs. Current Meters) ................ ....................................51










4 CON CLU SION S .................................. .. .......... .. .............56

APPENDIX

A RIP CURRENT FEATURES (TEST 5)...... ...................... ..............61

B DRIFTER TRAJECTORIES AND VELOCITY (TEST 12)....................................64

C DRIFTER TRAJECTORIES FOR THE LONG TESTS.........................................66

D M E A N V E L O C IT Y .............. ................................................................................7 1

E FLUCTUATING VELOCITY ...........................................................................76

F RIP CURRENT INSTABILITY.............................. ............. ............... 84

G TIM E-AVERAGED V ORTICITY .................................................. .....................89

H TIME-AVERGED, DEPTH-INTEGRATED CONTINUITY...............................94

I V ELO C ITY D ISTR IB U TIO N ........................................................ .....................99

L IST O F R E FE R E N C E S ....................................................................... .................... 104

BIOGRAPHICAL SKETCH ............................................................. ...............108





























v
















LIST OF TABLES


Table page

2-1 Transient test conditions................................................. .............................. 20

2-2 L ong test conditions ......................................... .............................21

3-1 Percentage of drifters which exited the visible flow domain to a certain side.........32

3-2 Percentage of drifters completing (X) closed circuits..............................................32

3-3 Averaged maximum drifter velocity for each of the long tests............................. 33

3-4 Number of velocity measurements used to obtain a mean velocity in the rip
channel using VDT which was compared with mean velocities determined
from current meters for the long tests in Figure 3-21 ...........................................55
















LIST OF FIGURES


Figure p

1-1 Schem atic sketch of a rip current system ...................................... ...............

1-2 Three scenarios for rip current form ation ........................................ .....................6

1-3 Swim parallel to shore past the breaker line to escape a rip current system............ 11

2-1 Plan view and cross-section of the experimental wave basin ................................19

2-2 Unevenly spaced bathymetry contour of basin with visible flow domain and
A D V locations ............ .................................................................22

2-3 Buoyant disc used as Lagrangian drifters ..................................... .................23

2-4 Original and rectified view of the visible flow domain .....................................24

3-1 Drifter positions and velocity at t=41 s after the wave-maker startup (Test 1)........28

3-2 Drifter trajectories within 22.5s time intervals / drifter positions plotted every
7.5 s and corresponding velocity vector every 15s (Test 1).....................................29

3-3 Generation of a small vortex on the corner bar, and the transport of a coupled
drifter pair offshore as part of a larger overall circulation (Test 2)........................30

3-4 Drifter trajectories and corresponding velocity time series (Test 12)...................31

3-5 Drifter paths; 2 minute time intervals (Test 16) ..................................................33

3-6 Mean Velocity / Test 12 / H= 4.32cm, T= Is, group waves (32); high water.......34

3-7 Mean Velocity / Test 14 / H= 4.62cm, T= Is, group waves (32); low water........35

3-8 Mean Velocity / Test 13 / H= 4.28cm, T= Is, monochromatic waves; high
w ate r ...................................... .................................................... 3 6

3-9 Mean Velocity / Test 16 / H= 6.18cm, T= Is, monochromatic waves; high
w after ...................................... .................................................... 3 7

3-10 Cross shore component of velocity along the rip channel centerline versus the
cross shore location for the Long tests ........................................... .................. 38









3-11 Test 16 / One minute averages of velocity within the field of view ......................41

3-12 Mean Velocity / Test 16 / Obtained by averaging one-minute mean velocities;
com pared to the previous Figure 3-9..................................... ....................... 42

3-13 Test 16 / Alongshore (y) migration of the maximum one-minute average of
total velocity through time for three cross shore bands offshore of the rip
c h a n n e l ........................................................................... 4 3

3-14 Test 16 / One minute averages of velocity along three cross shore bands ..............44

3-15 Test 16 / Tim e-averaged vorticity ........................................ ........................ 47

3-16 Test 16 / Time-averaged, depth-integrated continuity ........................................48

3-17 Location of four computational domains within the field of view used to
obtain PDFs of drifter velocities for the long tests............................................50

3-18 PDFs of drifter velocity components at four locations shown in Figure 3-17
(T e st 1 6 ) .......................................................................... 5 0

3-19 Current meter and VDT window locations used to make comparisons within
the rip channel for both the transient and long tests.............................................. 52

3-20 Comparison of instantaneous velocity between VDT and current meters within
the rip channel for the transient tests ............................ .................................... 53

3-21 Comparison of mean velocity between VDT and current meters within the rip
channel for the long tests............................................................................ .... ... 54

A-i Onshore flow over the bar due to waves / Drifter positions and velocity at
t = 12 s after the w ave-m aker startup (Test 5)............................... ..................... 61

A-2 Feeder currents converging from either side of the rip channel / Drifter
positions and velocity at t = 22 s (Test 5) ..................................... ............... ..62

A-3 Offshore directed current through the rip neck / Drifter positions and velocity
at t = 32 s (T est5) ................................................. ...................62

A-4 Expanding rip head offshore / Drifter positions and velocity at t = 53 s
(T e st 5 ) ........................................................................... 6 3

B-l Drifter trajectories and corresponding velocity time series (Test 12)...................64

B-2 Drifter trajectories and corresponding velocity time series (Test 12)...................65

B-3 Drifter trajectories and corresponding velocity time series (Test 12)...................65

C-1 Test 12 / Every drifter path for the entire run length; 2 minute time intervals ........66










C -2 T e st 13 ................................................................6 7

C -3 T e st 1 4 ......................................................................................................................6 7

C -4 T e st 1 5 ......................................................................................................................6 8

C -5 T e st 1 6 ......................................................................................................................6 8

C -6 T e st 1 9 ......................................................................................................................6 9

C -7 T e st 2 0 ......................................................................................................................6 9

C -8 T e st 2 1 ...................................................................7 0

D-i Test 12 / Mean Velocity / H= 4.32cm, T= is, group waves (32); high water........71

D-2 Test 13 / Mean Velocity / H= 4.28cm, T= is, monochromatic waves; high
w a te r ............. ......... .. ............. .. ........................................................7 2

D-3 Test 14 / Mean Velocity / H= 4.62cm, T= is, group waves (32); low water.........72

D-4 Test 15 / Mean Velocity / H= 4.83cm, T= is, monochromatic waves; low
w a te r ................................ ......................................................7 3

D-5 Test 16 / Mean Velocity / H= 6.18cm, T= is, monochromatic waves; high
w a te r ................................ ......................................................7 3

D-6 Test 19 / Mean Velocity / H= 5.22cm, T= 1.33s, monochromatic waves; low
w a te r ................................ ......................................................7 4

D-7 Test 20 / Mean Velocity / H= 3.69cm, T= is, group waves (64); high water........74

D-8 Test 21 / Mean Velocity / H= 3.97cm, T= 2.67s, monochromatic waves; high
w a te r ...................... .. ............. .. .......................................................7 5

E-1 Test 12 / 1 minute averages of velocity within the field of view .............................76

E -2 T e st 13 ................................................................7 7

E -3 T e st 1 4 ......................................................................................................................7 8

E-4 Test 15 (Only tests 15 and 16 include the effects of the wave-maker startup) ........79

E-5 Test 16 (Only tests 15 and 16 include the effects of the wave-maker startup) ........80

E -6 T e st 1 9 ...................................................................................................................... 8 1

E -7 T e st 2 0 ........... ... ............... .................................... ...........................82










E-8 Test 21 ...............................................................................83

F-l Test 12 / Alongshore (y) migration of the maximum one-minute average of
total velocity through time for three cross shore bands offshore of the rip
c h a n n e l ........................................................................... 8 4

F-2 Test 13 ..............................................................................85

F -3 T e st 14 .......................................................................... 8 5

F -4 T e st 1 5 ................................................................................................................. 8 6

F -5 T e st 1 6 ................................................................................................................. 8 6

F -6 T e st 1 9 ................................................................................................................. 8 7

F -7 T e st 2 0 .................................................................................................. ................. 8 7

F -8 T e st 2 1 .................................................................8 8

G 1 T e st 1 2 ................................................................................................................. 8 9

G -2 Test 13 ................................................................90

G -3 T e st 1 4 ................................................................................................................. 9 0

G -4 T e st 1 5 ................................................................................................................. 9 1

G -5 T e st 1 6 ................................................................................................................. 9 1

G -6 T e st 1 9 ................................................................................................................. 9 2

G -7 Test 20 ........... ......................... ..... .. ........................ 92

G -8 Test 21 ...................................................................93

H -1 Test 12 / Tim e-averaged, depth-integrated continuity ...........................................94

H -2 Test 13 ................................................................95

H -3 T e st 1 4 ................................................................................................................. 9 5

H -4 T e st 1 5 ................................................................................................................. 9 6

H -5 T e st 1 6 ................................................................................................................. 9 6

H -6 T e st 1 9 ................................................................................................................. 9 7

H -7 Test 20 ......... ..... .... ......... ..........................................97



x









H -8 T e st 2 1 ........................................................................... 9 8

I-1 Locartion of four computational domains within the field of view used to
obtain PDFs of drifter velocities for the long tests..........................................99

1-2 Test 12 / PDFs of drifter velocity components at four locations shown
in Figure I-1 .................................................100

I-3 T e st 1 3 .............................................................................1 0 0

I-4 T e st 14 ...........................................................10 1

1-5 T e st 1 5 ...........................................................10 1

1-6 T e st 16 ...........................................................10 2

I-7 T e st 19 ...........................................................10 2

I-8 T e st 2 0 ................................................................................................ ............ 1 0 3

1-9 T e st 2 1 ............................................................................................................... 1 0 3















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

LABORATORY RIP CURRENT CIRCULATION
USING VIDEO-TRACKED LAGRANGIAN DRIFTERS

By

David A. Thomas

August 2003

Chair: Andrew B. Kennedy
Major Department: Civil and Coastal Engineering

A laboratory rip current system with a longshore bar and channel bathymetry at the

Center for Applied Coastal Research (University of Delaware) was analyzed by the

method of Video Drifter Tracking (VDT). Steady and unsteady processes of the rip

current were studied using video-tracked Lagrangian drifters for a range of wave and

water level conditions. Drifter coverage and run lengths are sufficient to resolve both

averaged and fluctuating quantities over the field of view including mean velocity (1 to

18 min. averages), velocity distributions at specified locations, and time-averaged

vorticity. Results show strong quantitative and qualitative dependence on wave and

water level conditions. Some of the tests show classic symmetric circulation cells, while

others exhibit rips with a strong bias in one direction, even with shore normal waves.

Trajectories and velocity of individual drifters were analyzed to determine general rip

current features and circulation patterns. Circulation was found to be unsteady on scales

generally spanning several orders of magnitude in space and time. Results also include









insight into the mechanisms of rip current instability. To validate the method of VDT,

the velocities obtained from the drifters were compared to current meters located in the

rip channel and continuity was analyzed throughout the visible domain.

The laboratory is an ideal setting due to the temporal and spatial unsteadiness of rip

currents. Field instruments are also very expensive and subjected to a harsher

environment, thus requiring a greater amount of maintenance. Until recently, laboratory

rip current circulation has been analyzed by placing a series of current meters throughout

the flow domain. The financial cost of these meters inhibits the ability to obtain a desired

resolution of quantities throughout the complete rip current system. One advantage of

VDT is that additional laboratory drifters are far less expensive than more current meters

or field drifters if a finer resolution of quantities is required.

A comprehensive map of rip current flow will improve understanding of the

nearshore circulation pattern; and is needed for further advances in predicting sediment

transport and the overall shape of the coastline, which is a major issue for the growing

number of coastal landowners. Many areas of the world, including Florida, also depend

on the tourism generated from their beaches and rip currents pose a serious threat to

ocean bathers because of their strong, seaward directed flows.














CHAPTER 1
INTRODUCTION

Problem Statement and Objective

The nearshore ocean is a complex region, influencing much of society. Many

shorelines are heavily populated, making the coastal waters a potentially dangerous place

for humans due to large waves and strong rip currents. Nearshore circulation and

currents play an important role in beach erosion and the overall movement of coastal

sediments. Structures such as inlets, groins, piers, and harbors also interact with the

coastal hydrodynamics, driving the research for predicting and quantifying nearshore

processes.

Fluid motion in the nearshore is influenced by many factors and is highly unsteady.

The breaking of wind generated waves can induce such phenomena as surf beat, edge

waves, storm surge, undertow, longshore currents, and rip currents; which all combine to

create a very dynamic system. The interaction of nonlinear waves with a varying

shoreline and bathymetry further complicates the issue of nearshore hydrodynamics. The

wave-induced currents interact with the nearshore morphology, creating features such as

beach cusps, spits, tidal shoals, and rip channels.

Our study concentrated on rip current dynamics for a barred beach with rip

channels. Rip currents are a seaward flow (usually perpendicular to the shoreline) that

"rip" through the waves and have been observed to extend past the surfzone (Shepard et

al. 1941, Schmidt et al. 2001). Figure 1-1 shows a sketch of a rip current system. These

seaward moving currents are responsible for much of the water exchanged between the









offshore and nearshore coastal regions (Shepard et al. 1941, Shepard and Inman 1950,

Bowen 1969, Bowen and Inman 1969). Rip currents are prevalent in the coastal waters

and subsequently have a large impact on nearshore circulation, thus the entire sediment

budget near the shoreline (Shepard et al. 1941, Shepard and Inman 1950, McKenzie

1958). The impact of rip currents on human society is covered in further detail in the

literature review section of this chapter.










,', n i, p..... ..... ....









Figure 1.1: Schematic sketch of a rip current system (from National Oceanic and
Atmospheric Administration (NOAA))


For our study, rip currents were generated in an experimental wave basin because

creating a large data set of field rip currents under different wave conditions would be

extremely difficult due to their relatively short life and tendency to migrate in the

longshore direction. Despite the qualitative knowledge of the importance of rip currents

in nearshore circulation, a comprehensive data set of nearshore circulation in the presence

of rip currents is not well documented. Since field rip currents are often transient, they

tend to elude investigators intent on measuring them with stationary instruments;









although quantitative measurements do exist (Sonu 1972, Bowmann et al. 1988, Brander

and Short 2000). However, due to the large scales of rip circulation systems and difficult

nature of rip observations, field studies have as yet been unable to obtain a

comprehensive map of currents in rip systems under a range of wave conditions. Instead

most field studies have concentrated on the morphologic evolution of the beach in the

presence of rip currents, and measured current data are generally sparse and limited to

very near the rip current. It is clear that a comprehensive rip current data set will improve

understanding of the overall hydrodynamics in a rip system; and is needed in order to

make further advances in predicting sediment transport characteristics.

In contrast to field research, the controlled environment of the laboratory is ideal

for studying rip current systems; but the extent of laboratory data involving rip currents

on longshore varying bathymetry is limited (Hamm 1992, Oh and Dean 1996, Haller et

al. 1997, Dronen et al. 1999, Haller and Dalrymple 1999, Haller and Dalrymple 2001,

Haller et al. 2001, Dronen et al. 2002, Haas and Svendsen 2002). Haller et al. (2001)

were the first to provide a comprehensive map of nearshore waves and currents in a

laboratory setting with the use of current meters.

Until recently, with the exception of Dronen et al. (2002), laboratory rip current

circulation was analyzed by placing a series of current meters throughout the flow

domain. Acoustic Doppler Velocimeters (ADV's) and other current meters are desirable

if a continuous time series of the flow velocity at a specific location is needed; but to

observe the entire flow field, a large quantity of instruments would be required.

However, researchers are usually restricted to a limited number of current meters due to

the financial cost. An overabundance of meters could also possibly change the flow field,









altering the true measurements of velocity. Another method used in attempting to

quantify nearshore circulation patterns is Particle Image Velocimetry (PIV) which tracks

a large number of small particles within a specified window size by comparing two

images separated by a known time step. This technique works well in the field where

turbulent bubbles exist due to breaking waves. Holland et al. (2001) used PIV to quantify

the horizontal flow structure in the swash zone. Scripps Institute of Oceanography has

also applied direct drifter tracking by Global Positioning System (GPS) to field research

of nearshore circulation patterns involving rip currents (Schmidt et al. 2001). However, a

small number of these Lagrangian field drifters exist due to the financial cost, greatly

limiting the amount of available coverage.

In our study, numerous video recordings of laboratory rip currents with Lagrangian

drifters were made under different conditions. Tables 2-1 and 2-2 show the water level,

wave height, wave period, and group characteristics for each test. Shore normal waves

were used for every test in this study. The absence of turbulent bubbles from strong

wave breaking found in the field has resulted in the use of individual drifters. A

numerical description for the complete rip current circulation will be obtained by tracking

a dense population of these individual drifters from the digitized video recordings. This

method will be called Video Drifter Tracking (VDT). Several advantages arise from

VDT with one being that additional laboratory drifters are far less expensive than more

field drifters or current meters. The video recordings were transferred to the computer,

tracked and analyzed using several MatLab programs. A more complete description of

the data collection procedure and the experimental wave basin and setup will be

presented in Chapter 2.









Using the approach of VDT, this study focused the general circulation patterns and

quantities found throughout a laboratory rip current system for a longshore bar and

channel bathymetry. General circulation behaviors of rip currents examined in this study

include the overall flow structure and individual drifter trajectories. The drifter coverage

and run lengths are sufficient to resolve most averaged and many fluctuating quantities

over the field of view containing the rip system. Therefore, the quantities can be

examined in particular regions of interest (such as the eddies, feeder currents, and rip

head). The abundant drifter coverage and relatively fine resolution of quantities in this

study were possible due to the low cost of the video-tracked laboratory drifters. Mean

quantities such as velocity, vorticity, and continuity throughout the rip system are

presented for many of the tests. Fluctuating velocities were also analyzed to give some

insight into the unsteady properties of rip current instabilities, such as vortex shedding

and low frequency oscillations. Unavoidable gaps in particle coverage have hindered the

ability to obtain continuous quantities at a given location, therefore fluctuating quantities

are limited to one-minute averages. This temporal resolution was found to be adequate in

determining higher frequency rip current motions. The data analysis and results for this

study are covered in more detail in Chapter 3.

Background: Rip Current Literature Review

Since the 1930s, coastal scientists have observed the existence of rip currents in

nearshore waters. Today, even most beachgoers know of the presence and dangers of rip

currents. Lifeguards and other coastal rescue personnel are specifically trained for this

environmental phenomenon. A considerable amount of research has been devoted to rip

currents, but the difficulty of field measurements (due to their temporal and spatial

unsteadiness) has caused many observations to be only qualitative. Previous literature










concerning rip currents are reviewed in this chapter to discuss: 1) the physical

characteristics of rip currents, 2) the impact of rip currents to society, 3) the forcing

mechanism behind rip current circulation, and 4) the unsteady behavior of rip currents.

Physical Description of Rip Currents

Rip currents are narrow lanes of water that move seaward through the surf zone and

extend past the breaker line (Shepard et al. 1941). These currents have been observed on

a wide range of beach types but are particularly common on beaches that are dominated

by a longshore bar cut by rip channels, shown by the top picture in Figure 1-2. The rip

channels can result from hard bottom canyons or a channel cut through the sand bar.



WA"Trr; VE ;I !`- \\\ S^ACH~

RIPS
H H3H ELC LOC NECK


: : ,BEACH:::BE




RIPS





RIP
MER



BEACHI: i: i:


Figure 1-2: Three scenarios for rip current formation include: Top) longshore bar with rip
channels, Middle) deflected longshore current due to seaward protrusion in the
bathymetry, and Bottom) deflected longshore current due to structure. (from
Sanders 2002)

Another mechanism for rip current formation is when longshore currents are

directed offshore by a protrusion in the bathymetry or a headland (Sheppard and Inman









1950). Rip currents may also occur at specific locations due to the interaction with

coastal structure such as piers, groins, orjetties (Shepard and Inman 1950, Wind and

Vreugdenhil 1985). Figure 1-2 shows three possible scenarios for rip current formation

described above. This study focuses on the first scenario, rip currents controlled by a

longshore bar with channels.

During the first part of the century, the distinction between rip currents and

undertow was examined. The return flow required by the landward movement of water

led to the idea that water returns beneath the surface. Davis (1925) first challenged the

popular idea of undertow that was said to pull bathers beneath the surface, and a

considerable discussion of the subject ensued. Shepard (1936) called attention to

evidence that swimmers were being dragged seaward in relatively narrow belts of water.

These lanes of agitated water extending out at right angles to the beach were well known

to lifeguards and experienced swimmers but escaped the notice of scientists for the early

part of the century. They were known as "rip tides" or "sea pulses", but the name "rip

current" was deemed more appropriate.

Shepard et al. (1941) gave a description of the qualitative features found in a rip

current system. These authors used visual observations of rip currents off the coast of

Scripps, California to describe three main features: the feeder currents, rip neck, and rip

head. Figure 1-1 gives a visual description of these rip current features. Feeder currents

move along the shore from either side of the rip channel with one of these currents

usually being dominant. These feeder currents can produce channels a few feet deep

parallel and close to shore. The two currents converge and extend out in what is known

as the neck, where the water rushes through the breakers in a narrow lane. A shore









normal channel in the sand can usually be found along the path of the neck, which

indicates that the flow extends through the entire water column. Seaward of the rip neck

the rip current flow separates from the bottom and is mostly confined to surface

movement (Shepard et al. 1941). Beyond the breakers the rip current widens and

dissipates, this is known as the rip head.

The size and strength of rip currents are highly dependent on the ambient wave

conditions. Shepard et al. (1941) observed that the size and geometric configuration of

rip currents off the coast of Southern California were related to the wave height. The rip

currents observed by the authors extended out from a few hundred to about 2,500 feet

from the shore and vary from narrow belts 50 to 100 feet across in the feeders and neck to

as much as 500 feet or more in the heads. McKenzie (1958), citing observations made on

the beaches of New South Wales, Australia, noted that rip currents are generally absent

under very low wave conditions. Rip currents were also found to be more numerous and

somewhat larger under light to moderate swell. Shepard and Inman (1950) directly

related the magnitude of flow velocities associated with rip currents to the height of the

incident waves. An increase in wave height resulted in stronger rip currents and the

response was relatively instantaneous. This relationship has important consequences for

the nearshore sediment budget and beach profile equilibrium, since variations in current

strength will significantly affect the erosional power of rips. Flow velocity in the rip

neck has been found to be as great as 5 miles an hour (Lascody 1998). However, this

flow rate is very unsteady, being greatly checked or even stopped by advancing wave

fronts.









Another factor that modulates the strength of rip currents with a bar and rip channel

morphology is the tide. Several field observations have shown the influence of tides on

rip currents. Cooke (1970) conducted a study on Redondo Beach, California and noted

that stationary rip channels were common and well-defined rip currents were only present

during falling or low tide. The prevalence of rip currents during falling tides was also

noted by McKenzie (1958) and was attributed to the concentration of current flow within

the rip channels resulting in larger velocities in the rip neck. Sonu (1972) observed

modulations in rip current intensity with tidal level during field experiments conducted at

Seagrove Beach, Florida. A lower tidal level was also thought to be significant due to

stronger wave breaking, which would increase the amount of momentum transfer to the

surf zone, thus resulting in stronger rip currents. Brander (1999) and Brander and Short

(2001) conducted field experiments along the beaches of New South Wales, Australia to

investigate low-energy rip current systems. Rip flows reached maximum velocities

during low tide and minimum velocities during high tide. Dronen et al. (2002) conducted

experiments in a wave basin with a bar and half of a rip channel. A series of test runs

were performed with varying wave height and water level and revealed that rip current

velocity increased with increasing wave height and decreasing water level.

Impact of Rip Currents

Rip currents modify the nearshore wave field along with the entire surf zone

circulation (Shepard et al. 1941, Shepard and Inman 1950, many others). Therefore, rip

currents are a crucial factor in determining the distribution of sediment and a general

shape of the coastal region (Shepard et al. 1941, McKenzie 1958, many others). This is a

growing concern due to the increasing number of people residing near the coast. Rip









currents also play a role in the sorting of beach sediment across the profile (Shepard et al.

1941).

Rip currents are a considerable source of danger to bathers (Shepard et al. 1941,

Chandramohan et al. 1997, Short and Hogan 1993, Lascody 1998). Since 1989, an

average of 19 persons have died each year as a result of rip currents in Florida (Lascody

1997). Therefore, rip currents, on average, result in more deaths in Florida than

hurricanes, tropical storms, tornadoes, severe thunderstorms and lightning combined.

Victims are usually tourists who are unfamiliar with the dangers of the ocean. Many

areas of the world, including Florida, depend on their beaches for tourism and rip currents

pose a serious threat to ocean bathers due to their strong, seaward directed flows. Most

rescues from the surf along the coast of southern California are made in these rip currents

(Shepard et al. 1941). Short and Hogan (1993) have devised a method to determine a

relative level of beach safety due to the presence of rip currents. Tidal, bathymetric and

incident wave conditions for the beaches of New South Wales, Australia were considered

for the study.

A person may find himself or herself in trouble either by slipping into a feeder

channel, which may be very near the shore, and being swept out into the neck or by

jumping through breakers in the zone next to the rip current neck and being pulled

gradually toward the neck (Shepard et al. 1941). The main channel is generally beyond

the bather's depth. The seaward-moving current found in the rip neck may prevent all

but a very good swimmer from progressing landward. The most efficient way to escape a

rip current is to be pushed offshore by the rip neck. Once in the rip head past the breaker

line, swim parallel to the shore until out of the rip system and then back toward land.









This method of escaping a rip current is visually depicted in Figure 1-3. If caught in the

rip circulation again, try the other side because it may have a weaker flow strength. The

worst thing someone can do is try to swim landward within the seaward moving rip neck.

People usually get tired doing this, creating a very dangerous situation. Several

indications are associated with the presence of a rip current that can be observed by

everyday beachgoers including: 1) a darker water color due to the suspension of fine

sediments, 2) waves breaking further offshore on either side of the rip neck, 3) foam or

object moving steadily offshore in the rip neck, and 4) an offshore plume of turbid water

past the sand bar, which is the rip head (Sheppard et al. 1941).








*--.----t K-








Figure 1-3: Swim parallel to shore past the breaker line to escape a rip current system
(from N.C. Sea Grant 2003)


Forcing Mechanism

The most direct mechanism for driving nearshore currents is the momentum

transfer from breaking surface gravity waves to the nearshore flow. Longshore currents

are generated from waves breaking obliquely to the shoreline (Longuet-Higgins 1970a,

Longuet-Higgins 1970b). Longshore periodic variations in the incident wave field can









also force coherent circulation cells. These cells are generally defined as broad regions

of shoreward flow separated by narrow regions of offshore-directed flow. If these narrow

regions of offshore flow are sufficiently strong they would appear as rip currents.

Shepard et al. (1941) and Sonu (1972) observed cell circulation to be most prevalent

during shore-normal waves and a meandering longshore current was dominant during

oblique wave incidence. Nearshore conditions usually involve a combination of

longshore currents and cell circulation occurring simultaneously (Komar 1976).

Up until the 1960's researchers had attributed rip currents to the seaward return

flow due to the mass-transport of water over the bar from ocean waves. The

understanding behind the governing forces driving rip currents was greatly enhanced

when Longuet-Higgins and Stewart (1964) introduced the concept of radiation stress and

described the change in mean sea level resulting from waves that encounter a sloping

bottom. Radiation stress is the excess flow of momentum due to the presence of waves.

This stress induces a gradient in the mean water level that balances the gradient of the

radiation stress. The cross shore component of the radiation stress due to the breaking

waves causes an increase in mean sea level (set-up) to occur shoreward of the breaker-

line and a decrease of mean sea level (set-down) occurs at the break point. The

maximum set-up occurs at the shore. Bowen (1969) confirmed that a large wave height

would cause a greater set-up than lower waves if they break continuously from the break

point to the beach. This occurs because the set-up is proportional to the wave height and

higher waves break at a deeper depth, initiating the sea-surface gradient at a position that

is further from shore.









A longshore variation of breaking wave height, topographically controlled by the

periodic bar and trough bathymetry, will cause a variation in wave set-up along the shore

(Bowen 1969, Dalrymple 1978, Haller et al. 1997). These longshore variations in the

incident wave field may also arise on an initially longshore uniform beach due to a wide

range of causes including edge waves (Bowen and Inman 1969), the superposition of

wave trains (Dalrymple 1975, Fowler and Dalrymple 1990), or surf zone instabilities

(Dalrymple and Lozano 1978, Falques et al. 1999). The longshore variation in set-up

produces a pressure gradient in the longshore. Feeder currents develop and flow parallel

to shore from zones of high set-up to zones of lower water level. The areas of high set-up

are located shoreward of the bars and areas of lower water level are found shoreward of

the rip channels. As stated before, these feeder currents come from either side of the rip

channel, converge at the base of the rip and move seaward through the rip neck.

Laboratory experiments, conducted by Haller et al. (2001) using the same

experimental wave basin as presented in this study, confirmed that wave heights were

actually higher in the rip channel than over the bar. However, the waves in the rip

channel would break very close to shore significantly reducing the induced set-up around

the bar. Therefore, the longshore variation of set-up was still highest shoreward of the

bar and lowest in the rip channel. The longshore pressure gradient between the shore and

the bar still drives flow toward the rip channels where they converge. The larger wave

height in the channel is due to the interaction between the incident waves and the

offshore rip current.

Chen et al. (1999) also used the experimental wave basin found in this study to

examine Boussinesq modeling of a rip current system. A time domain numerical model









based on the fully nonlinear extended Boussinesq equations (Wei et al. 1995) was created

to investigate surface wave transformation and breaking-induced nearshore currents.

Agreement was found between the numerical model results and the laboratory

measurements of Haller et al. (1997), including longshore and cross-shore velocity

components. The model results revealed the temporal and spatial variability of wave-

induced nearshore circulation and the instability of rip currents, which is also in

agreement with the physical experiments of Haller et al. (1997).

Unsteady Behavior of Rip Currents

The magnitude of rip current flow is highly unsteady and has been observed to

pulse on the time scale of wave groups (Sonu 1972). Brander and Short (2001) observed

pulsations in the rip flow at a frequency of 0.0078 Hz (128s), which resulted in

fluctuations of +/- 0.4 meters per second. No wave measurements were taken during the

experiment and the forcing mechanism for the modulations in mean flow or pulsations

were not investigated. MacMahan et al. (2003) participated in the RIPEX experiment in

Monterey, CA and concluded that rip current pulsations occurred on infragravity time

scales (0.004-0.04 Hz). The pulsations were attributed to cross-shore infragravity

motions of long waves, which increase shoreward and with increasing wave height. As

mentioned before, the periodic pulsing found in the rip channel may be better analyzed

with the use of current meters due to the ability to gather measurements at a particular

location over a continues time series.

Field observations of rip currents indicate that they can exhibit long period

oscillations in their offshore-directed flow (Sonu 1972). These oscillations have

generally been attributed to the presence of wave groups or low-frequency wave motions,

such as surf beat. However, a mechanism for the instability of rip current flow hasn't









been fully resolved. Haller and Dalrymple (2001) performed a theoretical analysis and

concluded that these low frequency rip current oscillations can be modeled by jet

instability mechanisms. These low frequency or large period oscillations were also

noticed throughout this laboratory study involving rip currents generated on a barred

beach with periodic channels.

Summary

Rip currents have been an important topic for coastal researchers for most of the

century. As stated before, much of the literature prior to the 1960s concerning rip

currents was highly qualitative. In this time, most observations of rip currents were based

on their physical characteristics, behavioral tendencies and interaction with the

surrounding coastal hydrodynamics and sediment budget. These observations laid much

of the groundwork for future research by describing the physical structure of rip currents

and possible driving forces. The large volume of water transported by these rip currents

influence the nearshore circulation pattern, thus the overall coastal sediment transport.

As well as being of geological importance, rip currents pose a serious threat to public

safety. The three main factors, documented in the literature, affecting rip current

presence and strength are as follows: 1) wave height, 2) wave direction, and 3) tidal level.

Unsteady properties of rip current flow include modulations in the current strength

known as "pulses" and unstable oscillations.

Rip currents are intriguing due to their unsteady presence and tendencies to

seemingly just appear or migrate down the coast. It is clear from the review that the

difficulty in field measurements due to the temporal and spatial unsteadiness of rip

currents has resulted in a lack of quantitative data. This unsteady presence of rip currents

in the field has led to the advantage of laboratory analysis. Field instruments are also far









more expensive and subjected to a harsher environment, thus requiring a greater amount

of maintenance. It was also concluded that something besides a fixed array of current

meters was needed to analyze the entire flow field of a laboratory rip current system.

Many unanswered topics still exist pertaining to the physical flow of rip currents

including: 1) the detailed circulation pattern of a rip current system, 2) the different

length scales of circulation that exist, 3) a comprehensive velocity map of the entire rip

system, and 4) the unsteady properties of rip currents, involving current pulsation and

unstable oscillations. The more that is known about this coastal phenomenon the better

humans will be able to adapt to the dynamic nearshore region.

The work presented in this thesis will help further the understanding into the

physical flow characteristics of rip currents for a periodically barred bathymetry under

various wave conditions. In this study, the method of VDT enables a high resolution

analysis of a complete laboratory rip current system without the financial cost of

numerous current meters.

Outline of Thesis

The remainder of this thesis is organized as follows: Chapter 2 discusses the

physical model and data collection procedure used to obtain the filtered, rectified drifter

positions from the video recordings. The various wave and water level conditions for

each test will also be given. The experimental instruments and procedure used to

videotape the rip currents with Lagrangian drifters will be covered. Finally, this chapter

will examine possible experimental and data collection errors.

Chapter 3 gives the details into how the filtered, rectified drifter positions obtained

from the rip current video were analyzed. The quantitative and qualitative results from

the various laboratory rip currents will be presented for each set of test conditions. The









variability in rip current circulation due to the altering of certain conditions such as wave

height, wave period, group characteristics and water level will be analyzed and compared

to past research. The measurement errors encountered in the analysis will also be

addressed. The drifter velocities obtained using VDT will then be compared to those

recorded from current meters placed at specific locations in the rip channel.

Chapter 4 summarizes the results and conclusions derived from the analysis portion

of this thesis. The benefits from the method of VDT, versus a plethora of current meters

or direct drifter tracking in the field, will be reiterated. Suggestions for future research

will also be given.














CHAPTER 2
EXPERIMENTAL SETUP

Physical Model

The Directional Wave Basin at the Center for Applied Coastal Research of the

University of Delaware was used to create rip current systems under various wave and

water level conditions. Figure 2-1 shows a planform and cross sectional view of the

wave basin. The wave basin is approximately 17.2 m in length and 18.2 m in width. The

three-dimensional "snake" wave-maker at one end consists of 34 flap-type paddles. For a

more complete description of the wave-maker see Haller and Dalrymple (1999). The

fixed beach profile consists of a steep (1:5) toe located between 1.5 m and 3 m from the

wave-maker with a milder (1:30) sloping section extending from the toe to the shore of

the basin opposite the wave-maker. The bar system consist of three sections in the

longshore direction including: one main section approximately 7.2 m and two smaller

sections approximately 3.66 m. In order to ensure that the sidewalls were located along

lines of symmetry, the longest section was centered in the middle of the tank and the two

smaller sections were placed against the sidewalls. This left two gaps of approximately

1.82 m wide, located at 14 and 3 of the basin width, that served as rip channels. The

edges of the bars on each side of the rip channels were rounded off in order to create a

smooth transition. The seaward and shoreward edges of the bar sections were located at

approximately x = 11.1 m and x = 12.3 m respectively (Figure 2-2). The crest of the bar

sections were located at approximately x = 12 m with a height of 6 cm above their

seaward edge. For a more complete description of the wave basin and its construction










see Haller and Dalrymple (1999). Other studies in which this particular wave basin was

used include: Haller et al. (1997), Haller and Dalrymple (1999), Haller and Dalrymple

(2001), Haller et al. (2001), and Haas and Svendsen (2002).



() ------------ 2 ------------------

) .2 Toe



17 m
3.66 in 7.32 m 3.66 m


1.82m 1.82m


1:5


Figure 2-1: (a) Plan view and (b) cross-section of the experimental wave basin (from
Haller et al. 2001)


The experimental setup was not designed to mimic a particular field beach,

however it is important to note that the bar and trough geometry is a reasonable

approximation of beach types found in the field. Depending on the still water level, the

ratio of rip current spacing to surfzone width varied between 3.1 and 4.0 during these

experiments. This falls within the range of 1.5 to 8 based on field observations by

Huntley and Short (1992). Another ratio of interest is rip channel width to rip current

spacing, which was fixed at 1/5. This also compares favorably with field observations by

Aagaard et al. (1997) and Brander and Short (2000). Finally if we consider the

experiments as an undistorted Froude model of field conditions with a length scale ratio

of 1/16, then the experimental conditions correspond to a rip spacing of 145 m, rip









channel width of 29 m, depth over the bar of .43-.76m, offshore wave heights of .6-1 m,

wave periods of 4-10.7 s, and mean rip neck velocities of .5-.9 m/s.

Test Conditions

The tests can be divided into two categories: transient tests and long tests. Tables

2-1 and 2-2 present the wave and water level conditions for the transient tests and long

tests respectively. The video recordings of the transient tests begin with no wave forcing

and then some time later the wave-maker generates one wave group consisting of 32 or

64 waves which propagates toward shore. The transient tests then continue some time

after the single wave group with no wave forcing. The total duration of these tests are

approximately 5 minutes. Only monochromatic waves were used for the transient tests.

The three sets of transient test conditions were repeated three times each, creating nine

separate runs.

The video recordings of the long tests, with the exception of tests 15 and 16,

commence some time after the wave-maker startup and the wave forcing continues

throughout the entire test. Tests 15 and 16 begin with no wave forcing and then very

shortly after the wave-maker is activated, which continues until the termination of the

test. The long tests are approximately 18.2 minutes long. Some of the long tests used

monochromatic waves, while others used bichromatic or group waves.


Table 2-1: Transient test conditions
Cross shore Number of Number of
shoreline Depth over regular drifters
Test # position (m) the bar (cm) Hrms (cm) T(s) waves tracked
1-3 14.9 4.73 4.2 1 32 55, 67, 52

4-5, 9 14.9 4.73 6.3 1 32 62, 72, 76

6-8 14.9 4.73 4.2 1 64 81, 68, 82










Table 2-2: Long test conditions

Cross shore Number of Number of
shoreline Depth over waves in drifters
Test # position (m) the bar (cm) Hrms (cm) T(s) repeating group tracked
12 14.9 4.73 4.32 1 32, (al/a2=2) 239
13 14.9 4.73 4.28 1 M 293
14 14.3 2.67 4.62 1 32, (al/a2=2) 204
15 14.3 2.67 4.83 1 M 241
16 14.9 4.73 6.18 1 M 356
19 14.3 2.67 5.22 1.33 M 158
20 14.9 4.73 3.69 1 64, (al/a2=2) 310
21 14.9 4.73 3.97 2.67 M 221
* (M) indicates regular or monochromatic waves

A wave gage, located at (x, y) = (6, 16.2)m, was used to measure a time series of

water surface elevations during the experiments. The root mean square of the wave

height for each test was determined from the water surface elevation records. Only shore

normal waves were used for this study, which eliminates the concern of reflection from

the sidewalls. The water depth in the basin was measured by a depth gage located near

the wave paddles, which is described with greater detail in Haller et al. (2001). As stated

before this was a fixed bed model, therefore the bathymetry of the basin remained

constant throughout the entire study.

Data Collection

Video recordings of a rip current system with floating Lagrangian drifters were

made for the test conditions listed in Tables 2-1 and 2-2. Figure 2-2 shows the

approximate field of view, which extends from y = 9.2 m to y = 18.2 m in the longshore

and from x = 7 m to slightly past the shoreline, at about x = 15.5 m, in the cross shore.

This visible domain contains the rip current system generated by the bar gap centered at











34 the basin width. Three 2-D ADV's, shown in Figure 2-2, were used to obtain a time

series of current velocities in the visible rip channel with a sampling frequency of 10 Hz.

The three ADV's were at a cross shore location of x = 11.82 m and longshore locations of

y = 13.52 m, y = 13.72 m, and y = 13.92 m. The velocities obtained by these current

meters are later compared to drifter velocities determined from the method of VDT. For

more detail into the experimental procedure including the video recordings and various

gages, contact Andrew B. Kennedy at the University of Florida, Department of Civil and

Coastal Engineering.



Wavemaker
2

4

6


-E 8 Field of view
10

12

14 ()

16
0 2 4 6 8 10 12 14 16 18
y (m)

Figure 2-2: Unevenly spaced bathymetry contour of the wave basin with visible flow
domain and ADV locations



The author was a part of this research from this point forward. The focus of this

thesis is on the analysis of the video data containing the rip current systems with

Lagrangian drifters. Figure 2-3 shows a photo of the 4 inch buoyant discs used as

drifters. The video recordings were digitized into jpeg files at a frequency of 30 Hz using

Dazzle DVC II video capture card with a pixel resolution of 352 x 240. MatLab









programs were used to perform the remainder of the analysis. The Lagrangian drifters

were tracked at a frequency of 2 Hz and 3 Hz for the transient tests and long tests

respectively, which is adequate to resolve high frequency motions found in currents. The

drifter coverage is sufficient to resolve most averaged and many fluctuating quantities.

The number of drifters tracked for each run is presented in Tables 2-1 and 2-2. The

abundant coverage was possible due to the low cost of the video-tracked laboratory

drifters. Field tracking techniques, such as kinematic GPS, involve expensive

instrumentation, which limits the number of available drifters and inhibits coverage of the

overall rip system (Schmidt et al. 2001).
















Figure 2-3: Buoyant disc, 4 inches in diameter, used as Lagrangian drifters


A considerable amount of time was spent individually and manually tracking each

drifter for every test. The tracking program predicted the movement of the desired drifter

in the next frame, but the estimated position of the drifter often needed to be manually

corrected. This position correction was a result of three scenarios: 1) if the drifter was

close to another drifter the tracking program would jump over to the undesired drifter, 2)

if the drifter was in a light patch reflected from above the tracking program would usually









mispredict the drifters position in the following frame, or 3) if the drifter was well

offshore, at about x = 7 m, the tracking program had problems correctly predicting the

true drifter position in the next frame. This required correction of the drifter position

prevented the tracking program from being fully automated.


















Figure 2-4: Original and rectified field of view


Since the video recording was taken at an oblique angle, the drifter positions saved

in image coordinates were rectified into Cartesian still water level coordinates, correcting

for light refraction through the vertical water column. Ground control points, separated

by 1 m in both the cross shore and longshore, were used as known fixed points. These

fixed ground points can be seen in Figure 2-4. Holland et al. (1997) utilized this

rectification procedure for the quantification of physical processes using video imagery

from nearshore oceanographic field studies. The drifter positions were then low-pass

filtered with a cut-off frequency of .25 Hz and .3 Hz, for the transient tests and the long

tests respectively, ensuring that any motions below 4 s and 3.3 s were smoothed out.

This eliminates the effect of the wave motion from the saved drifter positions because the









wave periods used for these experiments range from 1 s to 2.67 s. Now the saved drifter

positions are representative of the current motions induced by the rip current system. The

quantitative and qualitative results obtained from these rectified and filtered drifter

positions can be found in Chapter 3.

Experimental and Data Collection Error

Deviations from true rip current processes found in the field arise due to the

limitations of the laboratory environment. These possible sources of error or deviations

from real life include the neighboring sidewall, immovable hard bottom, designed bar

shape, and lack of other coastal currents. The relatively short run lengths of these

experiments are of concern due to the long time scale motions of rip current systems.

The 1 s wave period used for all these experiments, except test 19 and 21, is also

somewhat small. This is representative of only a 4 s wave period in the field, using a

Froude length scale ratio of 1/16. Ocean surface gravity waves found in the field

generally exhibit a higher period. The depth over the bar, which scales up to between

.43-.76 m using a Froude length scale ratio of 1/16, also seems somewhat low when

compared to the field. Finally, the width of the rip channel, which scales up to

approximately 29 m using the same scaling ratio of 1/16, seems somewhat wide when

compared to field observations.

Possible error due to the data collection portion of this thesis is also noted. Human

error becomes an issue while semi-manually tracking the Lagrangian drifters. This was

examined by digitizing the same video recording of test 13 twice and tracking them

separately. When the mean velocities throughout the rip system were compared the

results showed a negligible difference. The rectification procedure may also be a

possible source of error, but this was not quantified for this thesis. However, a visual






26


examination of the fixed point throughout the flow domain concludes that the

rectification procedure has produced believable results (Figure 2-4). The author feels

that all of these possible sources of error or deviations from the field are small enough to

show confidence in the results.














CHAPTER 3
RESULTS AND ANALYSIS

This chapter discusses the results from a laboratory rip current system using video-

tracked Lagrangian drifters. General rip current behaviors are analyzed using both the

transient (1-9) and long (12-21) test categories discussed in Chapter 2. However, only

the long test group are used to resolve averaged and fluctuating quantities throughout the

visible flow domain due to the experimental run length (-18 minutes) and drifter

coverage. The number of drifters tracked for each test is shown in Tables 2-1 and 2-2.

The computational steps used to obtain the filtered, rectified drifter positions from the

digitized video recordings of the rip current system were described in the data collection

portion of Chapter 2. The first order forward difference formula, shown in Equation 3-1,

was used to calculate the components of drifter velocity from the corrected drifter

positions (x, y) and known time step (At) of 0.5 s and 0.33 s for the transient tests and the

long tests respectively. The cross shore and longshore components of velocity are u and

v respectively.



X+ j y+ (3-1)
u j VJ= (3-1)
At At

The results obtained from the rectified, filtered drifter positions and velocities are

presented in this chapter. As stated before, the Froude length scaling ratio between

model and prototype is approximately 1/16, which creates a 1/4 time scale ratio. This










means that flow velocities in the field correspond to around four times greater than found

in our laboratory study.

General Rip Current Behavior

The main physical flow features of a rip current described by Shepard et al.

(1941) are the feeder currents, rip neck, and rip head. Figure 3-1 shows the formation of

a strong current in the rip neck with a "snapshot" of drifter positions and corresponding

velocity vectors imposed on an averaged, rectified view of the visible flow domain.











10
-
11






14


10 11 12 13 14 15 16 17 18
y(m)

Figure 3-1: Drifter positions and velocity at t=41 s after the wave-maker startup (Test 1)


Appendix A gives additional examples of rip current features found during the flow

evolution for transient test 5 using the same plot-type as in Figure 3-1. The finest

temporal resolution between these plots was 0.5 s and 0.33 s for the transient tests and

long tests respectively, which was dictated by the drifter tracking rate of 2 Hz and 3 Hz.

However, a larger time step, such as 2 s, was adequate to resolve the rip current motions.










(a) (b)
7 7
8 8
9 9
10 10

o 7 7 11




15 15
10 12 14 16 18 10 12 14 16 18


(c) (d)
7 7
8 8
A 9 9






15 15

10 12 14 16 18 10 12 14 16 18
y (m) y (m)

Figure 3-2: Drifter trajectories within 22.5s time intervals / drifter positions plotted every
7.5 s and corresponding velocity vector every 15s; (a) Os to 22.5s, (b) 22.5s to
45s, (c) 45s to 67.5s, (d) 67.5s to 90s (Test 1)



A plot of all the drifter trajectories and their velocities for test 1 is presented in

Figure 3-2. This figure was divided into four equal time intervals of 22.5 s, starting with

no wave forcing, in order to limit the confusion of overlapping all the drifter paths for the

entire test. Figures 3-1 and 3-2 both show the resulting pulse in the rip neck from a

single wave group and the startup of symmetric eddies on either side of the rip channel.

Schmidt et al. (2001) observed eddy-like trajectories and velocities for drifters within a

cell circulation pattern of a rip current system using direct drifter tracking by kinematic

GPS. Shepard et al. (1941) and Sonu (1972) have also observed cell circulation in the

nearshore zone.












""' h "i' I

:14-


11.5 11.5

12 12

12.5 12.5
11 11.5 12 12.5 13 13.5 11 11.5 12 12.5 13 13.5
y(m) y (m)

Figure 3-3: Generation of a small vortex on the corer bar, and the transport of a coupled
drifter pair offshore as part of a larger overall circulation; Solid line & (o) are
the trajectory and positions for one of the coupled drifters; Dotted line & (x)
are the trajectory and positions for the other coupled drifter (Test 2)


Many different scales of rotational motion were observed throughout the various

tests, ranging from small scale vortices ofD = 0(20cm) to basin-scale circulation with D

= O(20m). Figure 3-3 shows clearly the generation of a small vortex on the bar corner,

and its transport offshore as part of a larger overall circulation in test 2. Such vorticity

generation by differential wave breaking was predicted by Peregrine (1998), but has not

been observed previously. Every transient and most long tests exhibited these small

vortices when drifters passed over the bar corer while being ejected offshore by the rip

neck. Extremely large scale circulation patterns were difficult to resolve due to the

limited field of view. Video recordings with a much larger field of view were created

and are currently being analyzed.

Individual drifter trajectories were examined using the rectified, filtered drifter

positions and a time series of velocity components. Figure 3-4 shows two drifter

trajectories or paths found in test 12 ( H= 4.32cm, T= is, group waves (32); high water).

The starting and stopping point for each drifter trajectory can be determined from the


9.5


9.5~""












time series of velocity components. Appendix B contains three figures of six other


individual drifter paths and corresponding velocity time series found in test 12. These


individual drifter trajectories do not represent all of the drifter paths in test 12. The path


followed by a drifter depends on several factors, such as the initial position of the drifter


within the flow domain and the unsteady state of the rip current flow.



(a) (b)
7 7
8 8
9 9
10 10
o11 o11

E12 E12
13 13
14 14
15 15


10 12 14
y(m)


16 18


10 12 14
y(m)


1.2

1

E0.8

S0.6
0
> 0.4

0.2
n "O


1.2


P \
E0.8

S0.6

> 0.4

0.2
C -^^ 1, ,


500 550 600 650 700 800 900 1000
time (s) time (s)


Figure 3-4: Drifter trajectories and corresponding velocity time series / Cross shore
velocity => Dashed line, Longshore velocity => Dash-Dot line, Total velocity
=> Solid line (Test 12)



An analysis of every drifter for each long test was performed to determine


qualitative and quantitative details about their overall trajectories. The percentage of


individual drifters, which exited the rip current system to a particular side of the visible


domain and completed (X) closed circuits, was determined for the long tests and can be


seen in Tables 3-1 and 3-2 respectively. Table 3-3 shows the averaged maximum drifter


16 18


r
/V









velocity for each of the long tests. As stated before, the number of drifters tracked for

each long test can be found in Table 2-2.


Table 3-1: Percentage of drifters which exited the visible flow domain to a certain side

Test # Left Top Shoreline Other
12 20 23 38 19

13 32 8 45 15

14 7 47 33 13

15 5 55 30 10

16 12 26 48 14

19 0 69 20 11

20 15 21 49 15

21 26 26 33 15
* Other includes particles that were either in the visible.flow domain when the tracking
was ended, couldn't been seen against the right wall, or not tracked long enough to be
filtered


Table 3-2: Percentage of drifters completing (X) closed circuits

Test # 0 1 2 3+ Other
12 76.6 11.3 2.5 1.7 7.9

13 68.3 11.3 4.4 4.1 11.9

14 59.8 18.6 9.3 7.4 4.9

15 71.0 14.9 5.4 5.8 2.9

16 67.1 16.9 6.7 5.3 3.9

19 77.2 12.0 3.8 1.3 5.7

20 71.9 17.1 4.8 2.6 3.5

21 76.5 11.8 2.7 8.1 0.9
Other includes particles that were not tracked long enough to be filtered

Closed circuits have a minimum axis diameter greater than 15 cm












Table 3-3: Averaged maximum drifter velocity for each of the long tests

Average maximum particle Average time particle
Test # velocity within field of view (cm/s) was tracked (s)
12 19.25 98

13 19.55 110

14 24.62 121

15 24.35 120

16 24.86 96

19 27.58 73

20 18.76 119

21 20.84 114
*Both quantities include particles that were in the flow domain when the tracking
ended


Figure 3-5 shows a plot of all the drifter trajectories for test 16. This figure was


divided into nine equal time intervals of 2 minutes, starting with no wave forcing, in


order to limit the confusion of overlapping all the drifter paths for the entire test.


IU IZ 14 IB 10l
(d)


IU IZ 14 IB 10l
(e)


10 12 14 16 18 10 12 14 16 18
(a) (h)


10

n12

14
10 12 14 16 18
y (m)


10 12 14 16 18
y (m)


y (m)


Figure 3-5: Drifter paths; 2 minute time intervals (Test 16)










Remember, only tests 15 and 16 include the effects of the wave-maker startup

within the long test category. The direction of the offshore-flowing rip neck seems to be

quite dependent on the particular eddy patterns. The instability in rip current flow will be

discussed later in this chapter. Appendix C has the same plot-type as in Figure 3-5 for

every long test.

Mean Velocity

Mean fluid velocity throughout the field of view containing the rip current system

was determined for the long tests. Figure 3-6 shows this plot-type for test 12, where

basic rip current features such as eddy circulation, feeder currents and a resulting rip neck

can be noticed. Shoreward flow over the bar due to breaking waves and a decrease in rip

neck strength offshore can also be seen in these figures.


Test 12 Mean Velocities






10





E12


13


14


15
10 11 12 13 14 15 16 17 18
y(m)

Figure 3-6: Mean Velocity / Test 12 / H= 4.32cm, T= Is, group waves (32); high water










Appendix D contains the same plot-type for every long test. A spatial resolution of

0.5 m, used for all the averaged quantities presented in this study, was chosen based on

the desired details of the rip current flow and the available drifter coverage. The first 5

minutes of tests 15 and 16 are excluded to eliminate the effects of the wave-maker startup

on the mean flow velocity and other averaged quantities presented in this study.

Results in this study show a strong qualitative and quantitative dependence on

wave and water level conditions. A lower water level produced stronger flow velocities

within the rip current, which was most evident in the neck. This relationship can be seen

from a comparison of mean velocity in Figure 3-6 (test 12) and Figure 3-7 (test 14),

where only the water level differs. Field observations of stronger rips during lower tides

have been made by McKenzie 1958, Cooke 1970, Sonu 1972, Brander 1999, Brander and

Short 2001, and others.


Test 14 Mean Velocities
8


9


10





S12
Xc


10 11 12 13 14 1b 16 1/ 18
y(m)

Figure 3-7: Mean Velocity / Test 14 / H= 4.62cm, T= Is, group waves (32); low water










As mentioned above, the rip current flows were also directly related to the wave

height. A stronger flow in the rip neck can be noticed by comparing Figure 3-8 (test 13)

and Figure 3-9 (test 16), where only the wave height differs. Rip current strengthing due

to larger wave heights has been documented for more than five decades (Shepard et al.

1941, Shepard and Inman 1950, McKenzie 1958, and others). Dronen et al. (2002) also

revealed that laboratory rip current velocity increased with increasing wave height and

decreasing water level. In this study, an increase in rip current strength due to a lower

water level and larger wave height can also be concluded from Table 3-3 of the averaged

maximum drifter velocity for the long tests. Some of the long tests show classic

symmetric circulation patterns as in Figure 3-7 (test 14), while others exhibit rips with a

strong bias in one direction, shown in Figure 3-8 (test 13), even with shore normal waves.


Test 13 Mean Velocities






10


11





13


14


15
10 11 12 13 14 15 16 17 18
y(m)

Figure 3-8: Mean Velocity / Test 13 / H= 4.28cm, T= Is, monochromatic waves; high
water










Test 16 Mean Velocities






10


'11





13


14


15
10 11 12 13 14 15 16 17 18
y(m)

Figure 3-9: Mean Velocity / Test 16 /H= 6.18cm, T= Is, monochromatic waves; high
water



It is obvious from the figures of mean velocity that the flow strength decreases as it

moves offshore of the channel through the rip neck. This decrease in flow velocity is

more easily seen in Figure 3-10 of the cross shore component of mean velocity along the

rip channel centerline versus the cross shore location. The peak strength within the rip

channel along its centerline and offshore extent of the rip neck varied considerably

between the long tests. As a reminder, the offshore and shoreward edges of the bar are

located at x = 11.1 m and x = 12.3 m respectively. A reversal of flow onshore at around

x = 13 m can also be observed in these figures, for all of the long tests, which arises from

waves breaking close to shore in the rip channel and a related area of strong vorticity

between the bar and the shoreline. Vorticity around the rip channel will be analyzed in

further detail later in this chapter.































-10 /.
S\ / /


-15 -



-20-



-25
8 9 10 11 12 13 14 15
Cross Shore location x(m)


15

(b)
10- /









-------------------
E -5 "



-10 -

\ /

-15 /



-20- /


-25
8 9 10 11 12 13 14 15
Cross Shore location x(m)


Figure 3-10: Cross shore component of velocity along the rip channel centerline versus
the cross shore location: Solid line (a) Test 12 (b) Test 16; Dashed line (a)
Test 13 (b) Test 19; Dash-Dot line (a) Test 14 (b) Test 20; Dotted line (a) Test
15 (b) Test 21









Sources of error. The unavoidable lack in drifter coverage may cause quantities

such as mean velocity, at a particular location to be biased. An expression for the true

mean velocity was obtain by taking the time average of the product of velocity and drifter

concentration. The velocity and drifter concentration were both separated into mean and

fluctuating components.


uc = (u +')(c + c')

uc = (u)(c) + (u')(c')


u = -f (3-2)


In the third line of Equation 3-2, u is the true mean velocity and the first term on

the right hand side is the apparent mean velocity, which is measured by the method of

VDT presented in this study. This apparent mean velocity may differ from the true mean

velocity, u, due to the effects of the second term on the right hand side of Equation 3-2.

If u' and c' are correlated than two separate scenarios could alter the apparent mean

velocity, causing it to differ from the true mean velocity, which include: 1) if there is a

greater concentration of drifters during high velocities then VDT will tend to over predict

the true mean velocity within a particular computational bin and 2) if there is a greater

concentration of drifters during low velocities then VDT will tend to under predict the

true mean velocity within a particular computational bin. It is possible that u' and c' are

not correlated in which case there would be no bias or the two scenarios may nearly

cancel each other out. The consequence of this bias on the true fluid velocities of the rip

current system can not be determined. At least 20 drifter velocity measurements, within









each 0.5 m bin, were required or else no mean velocity was determined for that particular

bin. However, most of the computational bins had enough drifter coverage to collect

hundreds or even thousands of velocity measurements.

The quantities offshore of x = 7 m are less accurate due to the difficulty of tracking.

The mean velocities presented in this section also neglect the effects of Stokes drift

caused by the incident waves. Stokes drift has the largest effect on the rip current system

within the rip neck by impeding its offshore movement. Therefore, if Stokes drift were

taken into account the true mean fluid velocity within the rip neck would be expected to

be slightly larger than presented in this study. In the velocity validation section of this

chapter, when the velocity in the rip channel is compared between VDT and current

meters, Stokes drift will be taken into account using linear wave theory.

Fluctuating Velocity

Next, the change in velocity within the rip current system was analyzed by

separating the long tests into 18 equal time intervals of one minute. Figure 3-11 shows

the one-minute averages of total velocity throughout the field of view containing the rip

current system for test 16. Again, the spatial resolution was chosen to be .5 m due to the

desired flow details and available drifter coverage. At least eight velocity measurements

were required for each .5 m bin, per one minute time interval, to obtain these fluctuating

velocities. A finer temporal or spatial resolution was not feasible with the available

drifter coverage. Appendix E contains the same plot-type for all the long tests. Tests 15

and 16 include the effects of the wave-maker startup on the fluctuating flow velocity.

Fluctuating velocity within the visible domain will be discussed in more detail in the next

section about unsteady rip current flow.















10

12



10 12 14 16 18
(e)


0 0 12
1212

14 14

10 12 14 16 18 10 12 14 16 18
(g) (h)


10 110
/ /
7' 12 612

14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) y (m)


(j) (k) (I)


C10
Eo o1



14 14
10 12 14 16 18 10 12 14 16 18
(m) (n)


10 12 14 16 18
(o)


B10

S12

"14

10 12 14 16 18
(p)
8

210

S12

'14


10 12 14 16 18
(a)


10 12 14 16 18
(r)


10 12 14 16 18 10 12 14 16 18
y (m) y (m)


12 14 16 18
y(m)


Figure 3-11: Test 16 / 1 minute averages of velocity; Only tests 15 and 16 include the
effects of the wave-maker startup for the long tests; legend at the bottom right
represents 10 cm/s










In hopes of eliminating any bias of slow or fast moving drifters, described in the

mean velocity section of this chapter, the one-minute mean velocities were averaged to

obtain mean velocities for each long test. These results were compared to the mean

velocities obtained by considering the entire run length and no appreciable difference was

noticed throughout the field of view, which can be noticed by comparing Figures 3-9 and

3-12 for test 16.











11





14


10 11 12 13 14 15 16 17 18
y(m)

Figure 3-12: Mean Velocity; Obtained by averaging one-minute mean velocities
(Test 16)


Unsteady Rip Current Flow

Rip current circulation is unsteady on scales spanning several orders of magnitude

in space and time. In our study, modulations in rip current strength within the neck

known as rip current "pulsing" can be observed from the figures of fluctuating velocity.

A time series analysis of discrete drifter velocities in the rip channel (not shown) has

concluded that this unsteady pulsing occurs on the order of wave groups. In the field,







43


these "pulses" have also been observed to occur on the order of wave groups (Sonu 1972,


and Brander and Short 2001).



20

18

-A
16 -

14-

12 -

E
10
E
8-

6-

4-

2-


10 11 12 13 14 15 16 17 18
Alongshore Location (m)

Figure 3-13: Test 16 / Alongshore (y) migration of the maximum one-minute average of
Total velocity through time for three cross shore bands located between: 1) x
= 9m to 9.5m Dotted line; 2) x = 9.5m to 10m Dashed line; and 3) x = 10m
to 10.5m Solid line / Vertical Dotted lines indicate the longshore limits of the
rip channel



Low frequency oscillations in rip current flow for a barred beach with periodic rip


channels were also observed in our study. As mentioned in the literature review, field


researchers have documented the existence of these unstable, long period oscillations in


rip current flow (Sonu 1972). In an attempt to analyze this unstable oscillation, Figure


3-13 plots the longshore migration of the maximum total velocity for three cross shore


bands in test 16. Figure 3-14 shows the the three cross shore bands located offshore of


the bar and channel system between: 1) x = 9m to 9.5m, 2) x = 9.5m to 10m, and 3) x =








44



10m to 10.5m. In Figure 3-14, the fluid velocity was averaged every one minute in half


meter bins along the three cross shore bands. The data points in Figure 3-13 correspond


to the longshore location of the maximum total velocity along each particular cross shore


band within the one minute time steps. As a reminder, the offshore and shoreward edge


of the bar are approximately located at x = 11.1 m and x = 12.3 m respectively and the


longshore limits of the rip channel are approximately at y = 12.8 m and y = 14.6 m.



(a) (b) (c)
8 8 8




14 14 14
10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8




10 14 14
10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (I)






10 12 14 16 18 10 12 14 16 18 10 12 14 16 18









10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (n) (m)
8 8 8
10 10 10












Figure 3-14: Test 16 / One minute averages of velocity along three cross shore bands
10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (n)

10 10 10



10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(P) (q) (r)











between: 1) x = 9m to 9.5m; 2) x = 9.5m to 10m; and 3) x = 10m to 10.5m









Figure 3-13 seems to show that test 16 has an oscillation period of 3 to 4 minutes.

The same plot-type of the other long tests, located in Appendix F, agree with this

relatively small oscillation time scale of test 16. This is complicated by the presence of

other oscillation patterns, with longer time scales, superimposed on each other. Each test

was 18 minutes in duration, which is not long enough to resolve a complete longer time

scale oscillation. Several large time scale oscillation peaks were noticed, but a complete

period could not be determined, which can be noticed in test 13 found in Appendix F.

Test 21, also found in Appendix F, was the only test where a long period oscillation of

approximately 14 minutes could be distinguished with some confidence.

The plots of all the drifter streaks (Appendix C) and fluctuating velocity (Appendix

E) for the long tests support the oscillation patterns that were observed in the figures of

the longshore migration of maximum total velocity, located in Appendix F. This can

been seen for test 16 by comparing Figures 3-5 (Drifter streaks), 3-11 (fluctuating

velocity), 3-13 longshoree migration of maximum velocity), and 3-14 (fluctuating

velocity along cross shore bands). No correlation could be made between the test

conditions and the oscillation periods observed.

The plots of all the drifter streaks and fluctuating velocity also give some

qualitative insight into the instability mechanism of rip currents. It is apparent, from

these figures, that the direction of the offshore-directed flow in the rip neck is in some

way associated with the shedding of one of the two oppositely spinning vortices found on

either side of the rip channel. This process can be most clearly seen for test 21 from the

figures of drifter streaks (Appendix C) and fluctuating velocity throughout the rip system

(Appendix E). If the right vortex, with respect to the shore, moves offshore the rip tends









to be directed to the left and vice-versa. An increase in feeder current strength, on the

same side as the vortex shedding, was also observed in some cases.

Limitations of instability analysis. A consequence of having a record length of

only 18 minutes, is that an oscillation width in the longshore at specific cross shore

locations could not be determined with confidence. Therefore, determining a growth rate

for the unstable oscillation could not be completed. An oscillation width in the rip

channel couldn't be found either, therefore the oscillation period of the rip current using

jet instability mechanism could not be determined.

To achieve a finer temporal resolution, than 1 minute, more drifter coverage would

be needed to ensure enough measurements in the desired time step. The author doesn't

think this presents a problem because instabilities in rip current oscillations are associated

with time scales generally larger than 1 minute.

Vorticity

Time-averaged vorticity (co), calculated from Equation 3-3, was determined

throughout the field of view containing the rip current system for the long tests.


dv du
0) = (3-3)
dx dy

The terms dv/dx and du/dy in Equation 3-3 were calculated using the second-order

central difference formula. As stated before, a spatial resolution of 0.5 m was used due to

the available drifter coverage. Figure 3-15 shows an example of time-averaged vorticity

throughout a rip current system for test 16. Remember, the first 5 minutes of tests 15 and

16 are excluded to eliminate the effects of the wave-maker startup on averaged quantities.

Appendix G contains the plots of time-averaged vorticity for every long test.














9


10


o11

A




13


14


15
10 11 12 13 14 15 16 17 18
y(m)

Figure 3-15: Test 16 / Time-averaged vorticity; contour = 0. /s; Positive =>Dashed line,
Negative =>Dash-Dot line, and Zero =>Solid line



Oppositely spinning vortices on either side of the rip channel can be seen in Figure

3-14 for test 16, and all of the other long tests. These vortices or eddies are also present

in the figures of mean velocity (Appendix D). Shoreward of each vortex on either side of

the rip channel exist another vortex circulation, which is spinning opposite to it. This

configuration of four separately spinning vortices is in agreement with the results from

the numerical model analysis by Chen et al. (1999) of the same experimental setup as

presented in this study.

Continuity

The depth-integrated continuity equation, shown in Equation 3-4, was time-

averaged to obtain Equation 3-5. The velocity profile through the water column was










assumed to be depth uniform and changes in depth (h) due to fluctuating waters levels

were neglected.



dr d(hu) d(hv)
+ + = 0 (3-4)
dt dx dy


d(hu) d(hv)
+ =0 (3-5)
x dy

If mass is shown to be conserved by satisfying Equation 3-5 then depth uniform flow can

be considered a valid assumption. As stated before, computational bins of 0.5 m were

used due to the available drifter coverage. The left hand side of Equation 3-5 was

calculated throughout the visible domain in an attempt to validate the mean velocity

within the rip current system. Figure 3-16 shows an example of time-averaged, depth-

integrated continuity throughout a rip current system for test 16. Appendix H contains

this same plot-type for every long test.








10

11






14


15
10 11 12 13 14 15 16 17 18
y direction (m)

Figure 3-16: Test 16 / Time-averaged, depth-integrated continuity / contour = 0.005 m/s;
Positive =>Dashed line, Negative =>Dash-Dot line, and Zero =>Solid line










Figure 3-16 shows a large positive area within the rip neck, which means the depth-

integrated, time-averaged continuity equation, shown in Equation 3-5, is not satisfied.

Therefore, more fluid is apparently exiting than entering the computational bins located

in the rip neck. In actuality, mass is being conserved throughout the visible domain

because the still water level (SWL) remains constant. This discrepancy in the

conservation of mass flux may have resulted from assuming depth uniform flow and the

effects of Stokes drift. Stokes drift due to incident waves has the largest effect on rip

current flow by impeding the offshore directed neck, which is where the continuity

equation is not satisfied. For future research, wave heights could be determined from a

wave model, such as REF/DIF, to calculate a value for Stokes drift throughout the visible

domain. Test 16 produced the least favorable results from the long test category.

Velocity Distribution

Probability density functions (PDFs) were created for each of the long tests in order

to analyze the distribution of the longshore and cross shore components of velocity at

four locations in the visible domain. The four computational domains throughout the rip

system used to obtain the PDFs are shown in Figure 3-17. Figure 3-18 shows the plot-

type described above for test 16. Appendix I contains this same plot-type for every long

test. The mean and standard deviation of the velocity distribution for the components (u,

v) can be seen in these PDF figures at the four specified locations. The number of

velocity measurements used to create the PDFs is also noted in the figures. Equation 3-5

was used to calculate the standard deviation of the velocity component distributions.



S= (X, X)2 (3-5)











































10 11 12 13 14
y(m)


15 16 17 18


Figure 3-17: Four computational domains used to obtain PDFs for the long tests: (a) x =

11.6m to 12m, y = 13.42m to 14.02m (Rip channel) (b) x = 8.4m to 8.8m, y =

13.42m to 14.02m (Directly offshore of the rip channel) (c) x = 8.4m to 8.8m,

y = 11.4m to 12m (Offshore of the left bar referenced from shore) (d) x =

12.4m to 12.8m, y = 11.4m to 12m (Directly behind the left bar)


0 15 Mean u=-1089v=-1 61
StDev u=10 62v=10 57
#ofmeas 1000
E
' 01


0 0
o 005
_


0 15 Mean u=-932 v=1 45
StDev u=3 42 v=2 27
#ofmeas 146


E0 05
0_


-40 -20 0 20


0 15 Mean u=-0 91 v=-3 11'
StDev u=378v=1 78
# of meas 203

o 01


2 005



-40 -20 0 20
Velocity (cm/s)


015 Mean u=7 08 v=4 99
StDev u=5 51 v=488
# of meas 373


S0 05


0-
-40 -20 0 20
Velocity (cm/s)


Figure 3-18: PDF at four locations shown in Figure 3.17 / Cross shore velocity (u) =>

Solid line, Longshore velocity (v) => Dashed line (Test 16)


-40 -20









The PDFs of the longshore and cross shore components of velocity for the long

tests show a wide distribution and the unsteadiness of rip current flow at various

locations, especially within the rip channel. This can be noticed from the large standard

deviation of Figure 3-18 (a), which represents the rip channel. Also notice from Figure

3-18 (a) that the longshore velocity in the channel has a mean of approximately zero,

which is consistent with the cross shore flow associated with the rip neck in the channel.

The cross shore component of velocity in the rip neck, shown in Figure 3-18 (a), has a

mean of -10.89 cm/s directed offshore. The three other locations, shown in Figure 3-17

(b,c,d), used to create a PDF of velocity components also show a relatively wide

distribution, which can be concluded from Figure 3-18 (b,c,d). The analysis of velocity

distribution for test 16 is similar for many of the other long tests, found in Appendix I,

with some specific distinctions depending on the unsteady rip current behavior and test

conditions. The method of VDT allows this analysis of velocity distribution to be

performed anywhere in the field of view, without the trouble of moving current meters

and running the test again.

Mean circulation depends, to a large extent, on momentum mixing by large-scale

turbulent Reynolds stresses. Direct estimates of these Reynolds stresses (not shown)

have also been obtained over the visible domain, and are to form the basis of future

studies. This will be quite important for estimating new turbulent closures in future

models.

Velocity Validation (VDT vs. Current Meters)

A comparison was made of instantaneous velocities within the rip channel obtained

from an array of current meters and the method of VDT for the transient tests

(Figure 3-20). The VDT window was 10 cm x 50 cm, extending 5 cm from the current










meter group in both the longshore and cross shore direction. This is more easily seen in

Figure 3-19. Figure 3-19 also displays the location of the three current meters within the

rip channel.



Current Meters and VDT window located in the Rip Channel


A
II 11.5
o
-r
t
0

E
x


0 i


y (m)

Figure 3-19: Current meter and VDT window locations used to make comparisons within
the rip channel for both the transient and long tests / ADV 1 (y=13.52m,
x=11.8m); ADV 2 (y=13.72 m, x=11.8m); ADV 3 (y=13.92m, x=11.8m)/
VDT window (y=13.47m to 13.97m, x= 1.75m to 11.85m)


In Figure 3-20, each of the three test conditions was run one time and the three

current meters or ADVs were averaged to obtain the solid line. The discrete points

represent the velocities determined using VDT from three separate runs for each of the

three test conditions. The drifter velocities were corrected for Stokes surface drift, which

is designated by the symbol (x) in Figure 3-20.






















0
-10
E
-20
-30
-30


-20 0 20 40 60 80 100

10


E- -10 "

-30 (C)

-40
-20 0 20 40 60 80 100
Time (s)

Figure 3-20: Comparison of instantaneous velocity between VDT and Current Meters
within the rip channel for the transient tests / (-) Averaged current meter
velocities; (.) VDT velocities before Stokes drift correction from window
encompassing Current Meter array; (x) VDT drifter velocities after Stokes
drift correction / (a) Tests 1-3 (b) Tests 4-5, 9 (c) Tests 6-8


After correction for Stokes drift, agreement between current meter and drifter

velocities is good, except at the time of peak current during large waves, which can be

noticed in Figure 3.20 (b). The remaining discrepancies are attributed to the difference

between small-amplitude theories and the finite wave heights in the rip channel. All the

transient tests show similar behavior in that velocities increase strongly after the first

wave arrival. A peak current is then achieved, which is followed by a decline in strength.

Also note that Figure 3.20 (a) and Figure 3.20 (c) show almost identical peak currents

despite the difference in wave group duration.










A comparison was also made of mean velocities within the rip channel obtained

from both an array of current meters and the method of VDT for the long tests. Table 3-4

shows the number of discrete drifter velocity measurements used to obtain the mean

velocity in the rip channel for the method of VDT. The current meter and VDT window

locations within the rip channel, shown in Figure 3-19, are the same as the comparison

made for the transient tests. In Figure 3-21 (a), the mean cross shore component of

velocity obtained from VDT for the long tests was corrected for Stokes drift, which

decreased the root mean square (RMS) of the error from 6.81 cm/s to 3.30 cm/s. The

RMS of the error for the longshore component of velocity was 1.84 cm/s. This shows

adequate agreement between the mean velocities obtained from the current meters and

the method of VDT for the long tests.


0 10
(a) (b)
-50
o 5-
0 0
-10 9 o0
E 0 E
x 7
o -15 o O

x -5
-20 x

-25 -10
-25 -20 -15 -10 -5 0 -10 -5 0 5 10
Current Meter (cm/s) Current Meter (cm/s)

Figure 3-21: Comparison of mean velocity between VDT and Current Meters within the
rip channel for the long tests / (o) Before Stokes drift correction to VDT
measurements; (x) After Stokes drift correction to VDT measurements / (a)
Cross shore velocity; (b) Longshore velocity












Table 3-4: Number of drifter velocity measurements used to obtain a mean velocity in the
rip channel using VDT which was compared with mean velocities
determined from current meters for the long tests (Figure 3-21)

Test # # of drifter velocity measurements
12 119
13 155
14 119
15 173
16 338
19 72
20 118














CHAPTER 4
CONCLUSIONS

A laboratory rip current system with a longshore bar and channel bathymetry at the

Center for Applied Coastal Research (University of Delaware) was analyzed by the

method of Video Drifter Tracking (VDT). Steady and unsteady rip current processes

were studied using video-tracked Lagrangian drifters for a range of wave and water level

conditions, which are given in Tables 2.1 and 2.2. The tests are divided into two

categories: transient tests and long tests, with specific parameters discussed in Chapter 2.

The drifter coverage and run lengths are sufficient to obtain both averaged and

fluctuating quantities over the visible flow domain including: 1) Mean velocity (1 to 18

min. averages), 2) Velocity distributions at specified locations, and 3) Time-averaged

vorticity. A spatial resolution of 0.5 m, used for all the averaged quantities presented in

this study, was chosen based on the desired details of the rip current flow and the

available drifter coverage.

Rip current flow features, observed in the field by Shepard et al. (1941), such as

feeder currents, rip neck, and rip head were all seen in this laboratory study. Symmetric

eddies on either side of the rip channel were also noticed in many cases here and have

been documented in the field by Shephard et al. (1941), Sonu (1972) and Schmidt et al.

(2001). These oppositely spinning circulation cells on either side of the rip channel can

be seen either from the figures of mean velocity, time-averaged vorticity, or snapshots of

drifter positions with corresponding velocity vectors.









The plots of time-averaged vorticity also show another eddy circulation shoreward

of each vortex on either side of the rip channel, which is spinning opposite to it. This

configuration of four separately spinning vortices is in agreement with the results from

the numerical model analysis by Chen et al. (1999) with the same experimental setup as

presented in this study. The reversal of flow onshore in the rip channel behind the bar,

noticed in this study, can be attributed to these vortices located between the bar and the

shoreline.

Many different length scales of rotational motion were observed throughout the

various tests, ranging from small scale vortices ofD = 0(20cm) to basin-scale circulation

with D = 0(20m). The generation of a very small vortex on the bar corner, and its

transport offshore as part of a larger overall circulation was observed in Figure 3.3. Such

vorticity generation by differential wave breaking was predicted by Peregrine (1998), but

has not been observed previously. Every transient and most long tests exhibited these

small vortices when drifters passed over the bar corer while being ejected offshore by

the rip neck. Extremely large scale circulation patterns were difficult to resolve due to

the limited field of view. Video recordings with a much larger field of view were created

and are currently being analyzed. The trajectories and velocity of individual drifters were

also analyzed to show the various scales of circulation found in a rip current system.

In this study, rip current strength was shown to increase with higher waves and a

lower water level, which was concluded by the plots of mean velocity and Table 3.3 of

the averaged maximum drifter velocity for the long tests. This relationship between rip

current strength and wave height and water level conditions is in agreement with field

observations made by McKenzie 1958, Cooke 1970, Sonu 1972, Brander 1999, Brander









and Short 2001, Shepard et al. 1941, Shepard and Inman 1950, McKenzie 1958, Dronen

et al. (2002) and others. The plots of mean velocity also show that some of the long tests

exhibit classic symmetric circulation cells, while other rips have a strong bias in one

direction, even with shore normal waves. The lack of drifter coverage may have caused

quantities to be biased, however this effect on the true mean velocity was not determined.

However, the drifter coverage was usually enough to collect hundreds or even thousands

of velocity measurements within each half meter bin.

Rip current circulation was found to be unsteady on scales spanning several orders

of magnitude in time as well as space. Most of the long tests showed an unstable

oscillation period of approximately 3 to 4 minutes in the offshore direct flow. Field

researchers have documented the existence of these unstable, long period oscillations in

rip currents (Sonu 1972). This is further complicated by the presence of other

oscillations patterns, with longer time scales, superimposed on each other. Throughout

the 18 minute run length for the long tests several isolated large time scale oscillation

peaks were noticed. However, in many cases this run length was not long enough to

resolve the period of a complete longer time scale oscillation. Test 21, found in

Appendix F, was the only test where a long period oscillation of approximately 14

minutes could be distinguished with some confidence. The finest temporal resolution

that could be determined was one minute, which is adequate for any high frequency

motions of rip current instability. The PDFs of the longshore and cross shore

components of velocity within the field of view for the long tests also show a wide

distribution and the unsteadiness of rip current flow, especially within the channel.









Results for this study also include insight into the instability mechanism of rip

currents. From the figures of all the drifter paths within two-minute intervals (Appendix

C) and one-minute averages of velocity (Appendix E), it is apparent that the direction of

the offshore flow in the rip neck is in some way associated with the shedding of one of

the two oppositely spinning vortices found on either side of the rip channel. If the right

vortex, with respect to the shore, moves offshore the rip tends to be directed to the left

and vice-versa. This unstable processes is most easily seen in Test 21. An increase in

feeder current strength, on the same side as the vortex shedding, was also observed in

some cases.

In an attempt to validate the method of VDT, the drifter velocities obtained were

compared to current meters located in the rip channel and continuity was analyzed

throughout the visible domain. After correction for Stokes drift, agreement between

current meter and drifter velocities in the rip channel was good for both the transient tests

(Figure 3.20) and long tests (Figure 3.21). Some of the figures showing continuity for the

long tests have a large positive area within the rip neck, which means the depth-

integrated, time-averaged continuity equation is not satisfied. This discrepancy in the

conservation of mass flux may have resulted from assuming depth uniform flow and the

effects of Stokes drift. Stokes drift due to incident waves has the largest effect on rip

current flow by impeding the offshore directed neck, which is where the continuity

equation is not satisfied. For future research, wave heights could be determined from a

wave model, such as REF/DIF, to calculate a value for Stokes drift throughout the visible

domain. Other future studies may involve the analysis of momentum mixing by large-

scale turbulent Reynolds stresses. Direct estimates of these Reynolds stresses (not









shown) have been obtained over the visible domain. This will be quite important for

estimating new turbulent closures in future models.

It is evident that a comprehensive map of rip current flow will aid in the improved

understanding of the nearshore circulation pattern and is needed in order to make further

advances in predicting sediment transport and the overall shape of the coastline, which is

a major issue for the growing number of coastal landowners. Many areas of the world,

including Florida, also depend on the tourism generated from their beaches and rip

currents pose a serious threat to ocean bathers due to their strong, seaward directed flows.

The method of VDT has proved to be quite beneficial for the analysis of a complete

laboratory rip current system. The financial cost of current meters has inhibited the

ability to obtain a desired spatial resolution of quantities within a complete rip current

system, which shown by this study, can be achieved by the use of VDT due to the low

cost of video-tracked laboratory drifters.


















APPENDIX A
RIP CURRENT FEATURES (TEST 5)


I U I I 1 10 I
y(m)


Figure A-i: Onshore flow over the bar due to waves / Drifter positions and velocity at t
12 s after the wave-maker startup (Test 5)


I U I U I 10



































IU I I I1 10 1'4 1) 10 11 10
y(m)


Figure A-2: Feeder currents converging from either side of the rip channel / Drifter
positions and velocity at t = 22 s (Test 5)


10 11 12 13 14
y(m)


Figure A-3: Offshore directed current through the rip neck /
at t = 32 s (Test 5)


15 16 17 18


Drifter positions and velocity






































Figure A-4: Expanding rip head
(Test 5)


15 16 17 18


offshore / Drifter positions and velocity at t = 53 s


10 11 12 13 14
y(m)



















APPENDIX B
DRIFTER TRAJECTORIES AND VELOCITY (TEST 12)


10 12 14
y (m)


16 18


10 12 14
y (m)


16 18


1.2

1

S0.8

0.6

>0.4

0.2


50 100 150 200 250
time (s)


0o N-- -------
200 220 240 260 280 300
time (s)


Figure B-1: Drifter trajectories and corresponding velocity time series / Cross shore
velocity => Dashed line, Longshore velocity => Dash-Dot line, Total velocity
=> Solid line (Test 12)




























10 12 14 16 18
y (m)


10 20 30 40 50
time (s)


10
S11
E 12
13
14
15





1.2

1

2 0.8

0.6

> 0.4

0.2

0


10 12 14 16 18
y (m)


800 850
time (s)


IU IZ 14 1b IB1
y (m)


1.2

1

E 0.8

0.6
(D


600 700
time (s)


800


IU 1Z 14 b1 IB
y (m)
















750 800 850 900 950
time (s)
time (s)


Figure B-3: Refer to Figure B-1


10
S11
E 12
13
14
15





1.2

1

2 0.8

0.6


0
> 0.4

0.2

0


Figure B-2: Refer to Figure B-1


















APPENDIX C
DRIFTER TRAJECTORIES FOR THE LONG TESTS


10 12 14 16 18
(a)


10 12 14 16 18
(h)


y(m) y(m)


Figure C-1: Test 12 / Drifter paths; 2 minute time intervals








67



(a) (b) (c)
8 8 8

10 10 10

012 012 12

X14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

210 10 10

012 012 012

x14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

S10 10 10

012 012 012

x 14 x 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y (m) y (m) y (m)


Figure C-2: Test 13 / Drifter paths; 2 minute time intervals



(a) (b) (c)
8 8 8

10 111 1 10 10

o12 o12 012
E
x14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (i)
8 8 8

210 010 10

012 012 12

14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

10 010 10

012 12 12

x 14 x 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) y(m)


Figure C-3: Test 14 / Drifter paths; 2 minute time intervals








68



(a) (b) (c)


10 1010

o12 12 12

S14 4 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)









(g) (h) (i)
8 8 8

210 210 210





12 12 12

1x 114 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y (m) y (m) y (m)


Figure C-4: Test 15 / Drifter paths; 2 minute time intervals



(a) (b) (c)
8 8 8









210 10 2 10

S12 12 2 12
14 "14 X 14









10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (C)
8 8 8

10 10 10





12 12 12


Q14 14 Q 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8






10 10 t 10t





o 12 o 12 o 12
x 14 x 14 x 14






10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) y(m)
y W) y W) y W


Figure C-5: Test 16 / Drifter paths; 2 minute time intervals








69



(a) (b) (c)
8 8 8

S10 10 10

12 012 12

X14 x 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

10 10 10

12 12 12

"14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

10 10 10

12 12 0o12

X14 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) y (m)


Figure C-6: Test 19 / Drifter paths; 2 minute time intervals



(a) (b) (c)
8 8 8

10 10 10

o12 o12 o12

x14 X 14 B 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

10 10 10

o12 12 12

"14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

10 10 10

0o 12 12
E E E
x x 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y (m) y (m) y (m)


Figure C-7: Test 20 / Drifter paths; 2 minute time intervals








70




(a) (b) (c)
8 8 8

o10 10 ~10

12 12 12

14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) ()
8 8 8

10 W10 10

12 12 12

14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

210 10 210

12 12 12

x 14 x 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y (m) y (m) y (m)


Figure C-8: Test 21 / Drifter paths; 2 minute time intervals

















APPENDIX D
MEAN VELOCITY

Test 12: Mean Velocities


IU I I IL 113 14 10 10 1/ 10


Figure D-l: Test 12 / H= 4.32cm, T-


Is, group waves (3 2); high water







72


Test 13: Mean Velocities


Figure D-2:


10 11 12 13 14 15 16 17
y(m)

Test 13 / H= 4.28cm, T= is, monochromatic waves; high water


Test 14: Mean Velocities


Figure D-3:


IU I I IL 1 14 1 10 II
y(m)

Test 14 / H= 4.62cm, T= is, group waves (32); low water








73



Test 15: Mean Velocities


10 11 12 13 14 15 16 17
y(m)


Figure D-4: Test 15 / H= 4.83cm, T= Is, monochromatic waves; low water



Test 16: Mean Velocities


IU I I I Z 1 14 1 1D 1
y(m)


Figure D-5: Test 16 / H= 6.18cm, T= Is, monochromatic waves; high water


10








74



Test 19: Mean Velocities


A
2 11
0e


12



13



14



15
10 11 12



Figure D-6: Test 19 / H= 5.22cm, T:




8



9



10


A




12



13



14



15


1 5 14 10 10 I 10
y(m)


1.33s, monochromatic waves; low water


Test 20: Mean Velocities


10 11 12 13 14 15 16 17
y(m)


Figure D-7: Test 20 / H= 3.69cm, T= Is, group waves (64); high water









75



Test 21: Mean Velocities
8



9



10


A
a 11
0



12



13



14



15
10 11 12 13 14 15 16 17 18
y(m)


Figure D-8: Test 21 / H= 3.97cm, T= 2.67s, monochromatic waves; high water




















APPENDIX E
FLUCTUATING VELOCITY

(a) (b) (c)


10 12 14 16 18 10 10
1212 14112 14 6 18 12 1

14 14 E 14




10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (M)










8 8 8
12 0112 o 1 12 1



14 14 14





10 12 14 16 18 10 12 14 16 18 10 12 14 16 18


(g) (k) (I)
8 8 8








10 10 10
12 212
14 14 14
















10 12 14 16 18 10 12 14 16 18 10 12 14 16 18













y (m) y (m) y (m)


Figure E-l: Test 12 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s
10 cm/s























10 12 14 16 18
(d)


10 12 14 16 18
(e)


10 12 14 16 18
(f)


10 210
e e
012 12 '

141 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)


10 12 14 16 18
y (m)


10 12 14 16 18
(m)


10 12 14 16 18
y (m)


10 12 14 16 18
(n)


10 12 14 16 18
y (m)


(I)


10 12 14 16 18
(o)


10 12 14 16 18 10 12 14 16 18
(P) (q)


10 12 14 16 18 10 12 14 16 18
y (m) y (m)


Figure E-2: Test 13 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s























10 12 14 16 18
(d)


10 12 14 16 18
(e)


10 12 14 16 18
(f)


10 12 14 16 18 10 12 14 16 18
(g) (h)


10 12 14 16 18
y(m)


10 12 14 16 18
(m)


10 12 14 16 18
y (m)


10 12 14 16 18
(n)


10 12 14 16 18
y (m)


10 12 14 16 18
(o)


10 12 14 16 18 10 12 14 16 18
(P) (q)


10 12 14 16 18 10 12 14 16 18
y (m) y (m)


10 12 14 16 18
y (m)


Figure E-3: Test 14 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s








79



(a) (b) (c)
8 8 8

10 10 10

o12 41 12 12

x14 x14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

1010 10

12 12 12

14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

210 o10 210

0 12 1 12 1 12

x14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) y (m)


(j) (k) (I)
8 8 8

10 10 10



S12 o 12 6 1 12
14 C 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (n) (o)
8 8 8

10 o10 ,10

o12 12 12
14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (m) (r)
8 8 8

10 10 10

o 12 o 12 o 12

x14 x 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18



Figure E-4: Test 15 / 1 minute averages of velocity; Only tests 15 and 16 include the
effects of the wave-maker startup; Legend at the bottom right represents 10
cm/s








80



(a) (b) (c)
8 8 8
A A
10 10 10

12 12 12

Q14 14 x 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

10 111 110 10

12 12 12

Q14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (I)
8 8 8

10 10 10

o -
12 12 12

x14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18



(j) (k) (1)
8 8 8

1010 10

S12 12 4 12

14 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (n) (o)
8 8 8

10 10 10

o12 12 12

x14 x 14 14

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (q) (r)
8 8 8

210 10 1100 w

12 012 / 12

x14 X 14 14
10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) y(m)


Figure E-5: Test 16 / 1 minute averages of velocity; Only tests 15 and 16 include the
effects of the wave-maker startup; Legend at the bottom right represents 10
cm/s























10 12 14 16 18
(d)


10 12 14 16 18
(e)


10 12 14 16 18
(f)


10 12 14 16 18
(9)









10 12 14 16 18
y(m)


10 12 14 16 18
(m)


10 12 14 16 18
(P)


10 12 14 16 18
y(m)


210




14

10 12 14 16 18 10 12 14 16 18
(h) (i)


10 12 14 16 18
y (m)


10

12

14

10 12 14 16 18
(n)
8

10

12

14

10 12 14 16 18
(q)


10

0 12

S14

10 12 14 16 18
y (m)


10 12 14 16 18
y (m)


10 12 14 16 18
(o)


10 12 14 16 18
y (m)


Figure E-6: Test 19 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s























10 12 14 16 18
(d)


10 12 14 16 18
(e)


10 12 14 16 18
(f)


10 12 14 16 18 10 12 14 16 18
(g) (h)


10 12 14 16 18
y(m)


10 12 14 16 18
y (m)


10 12 14 16 18
(m)


10 12 14 16 18
(n)


10 12 14 16 18
(o)


10 12 14 16 18 10 12 14 16 18
(P) (q)


10 12 14 16 18 10 12 14 16 18
y (m) y (m)


10 12 14 16 18
y (m)


Figure E-7: Test 20 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s























10 12 14 16 18
(d)


10 12 14 16 18
(e)


10 12 14 16 18
(f)


10 12 14 16 18 10 12 14 16 18
(g) (h)


10 12 14 16 18
y(m)


10 12 14 16 18
(m)


10 12 14 16 18
y (m)


10 12 14 16 18
(n)


10 12 14 16 18
y (m)


10 12 14 16 18
(o)


10 12 14 16 18 10 12 14 16 18
(P) (q)


10 12 14 16 18 10 12 14 16 18
y (m) y (m)


10 12 14 16 18
y (m)


Figure E-8: Test 21 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s



















APPENDIX F
RIP CURRENT INSTABILITY


20


18


16


14


12


I-
10
E

8-


6-


4-


2-


0-
10


11 12 13 14 15 16 17
Alongshore Location (m)


Figure F-l: Test 12 / Alongshore migration of the maximum one-minute average of total
velocity through time for three cross shore bands located between: 1) x = 9m
to 9.5m Dotted line; 2) x = 9.5m to 10m Dashed line; and 3) x = 10m to
10.5m Solid line / Vertical Dotted lines indicate the longshore limits of the rip
channel









85



20


18


16

x


-.
12


10 -
E ""

8-


6


4


2


0-
10 11 12 13 14 15 16 17 18
Alongshore Location (m)


Figure F-2: Test 13 / Refer to Figure F-l




20


18


16


14-


12


10 1
E

8


6-


4
~ ~ "-A.._^--



2


0
12 12.5 13 13.5 14 14.5 15 15.5
Alongshore Location (m)


Figure F-3: Test 14 / Refer to Figure F-l




















16-


12.5 13 13.5 14 14.5
Alongshore Location (m)


X- '


Figure F-4: Test 15 / Refer to Figure F-l


11 12 13 14 15
Alongshore Location (m)


16 17 18


Figure F-5: Test 16 / Refer to Figure F-l


X.

.x. A
A tI


7n,


15 15.5 16





























10-














0 A
2 A


11 12 13 14 15
Alongshore Location (m)


Figure F.6: Test 19 / Refer to Figure F. 1


^ ~ ^ ^ / --







x
X .







A-X
IIx





10 1 2 1 1


10 11 12 13 14
Alongshore Location (m)


Figure F-7: Test 20 / Refer to Figure F-l


15 16 17