Laboratory rip current circulation using video-tracked lagrangian drifters

UFL/COEL-2003/005

LABORATORY RIP CURRENT CIRCULATION USING
VIDEO-TRACKED LAGRANGIAN DRIFTERS

by

David A. Thomas

Thesis

2003

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 a ry ............................................................................................................... 1 5
O outline of T hesis .................................................................................................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.

.... ....

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;
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.

RIPS
I ''F *, SM ~ ~

. . . .. BEAC H

j I :: :BEACH

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).

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

19

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).

( el) n _18 .2 i
(()---------------- S2i-------
Toe

17 im
3.66 m 7.32 rn 3.66 m

1.82 in 1.82 in ,

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

iE 8Field of view
10

12 GOD

14 n

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
-

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

(a) (b)

7
8
A 9
10
S-

14

7
8
9

11

1_21
T-:

'I

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

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

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.

9.5N

*V A.. h i "' i1 J

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

. . ..... ..... .

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
11 11

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

1.2 1.2
r -* -\ I _J I -", ,

1 -'--- .J-- -- -

8
6
- ** .' - p

11 \ 1 I
E 0.8
S0.6
9'

> 0.4 / 0.4

0.2 0.2
0 ----- 0
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

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.

(a) (b) (c)

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (I)
8 8 8

10 12 14
y (m)

14 16 18
y (m)

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

Iu Io

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

S11
0

II I I I i
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

10

10 11 12 13 14 15 16 17 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

11 1 1i 1J i I
y(m)

Figure 3-8: Mean Velocity / Test 13 / H= 4.28cm, T= Is, monochromatic waves; high
water

Test 16 Mean Velocities

10

1C, 11 1 1 iL 1 i
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 -- \ / ..

-15 /

-20-

-25
8 9 10 11 12 13 14 15
Cross Shore location x(m)

15

(b)
10 -

5-
S\\'\.

-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')

- uc u'c'
u K- (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.

41

(a) (b) (c)
8 8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(9) (h) ()
8 8 8
A,1n A A

1 1

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

(j) (k) (i)
8 8 8

I E

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(p) (n) (0)

8 8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
y(m) y(m) 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
_ Z, 21
4 o 4 o 4 o

Y W Y W Y W

Fiue31:Tet1 iut vrgso vlct;Olytss1 n 1 nld h
efet fte aemkrstru o heln et; eeda hebto ih

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.

(Test 16)

Unsteady Rip Current Flow

Rip current circulation is unsteady on scales spanning several orders of magnitude
... ..... ...

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,

these "pulses" have also been observed to occur on the order of wave groups (Sonu 1972,

and Brander and Short 2001).

20 I I I

18

16 -

10
E X..
x .::: ..
8

6-

0 I I I L I I
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)

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)

0 4 6 180 6 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
8 8

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) (I)

y(m) y(W) y(m)

between: 1) x = 9m to 9.5m 2) x = 9.5m to 10m; and 3) x 10m to 1.5m

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.

10

I-
011

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.

d+ d(hu) d(hv)
+ -+ =0 (3-4)
dt dx dy

d(hu) d(hv)
+ = 0 (3-5)
a 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.

0 11

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.

I = *(X X)2 (3-5)

II I I I

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)

(a)
Mean u=-1089 v=- 61
StDev u=10 62 v=10 57
#ofmeas 1000

-40 -20 0 20

(c)
Mean u=-0 91 v=-3 111
StDev u=378 v= 78 I
# of meas 203 I

I I
I I

-40 -20 0 20
Velocity (cm/s)

0

E

20
0n

15

II

(b)
SMean u=-9 32 v=1 45
StDev u=3 42 v=2 27
# of meas 146

I \

05

0
-40 -20 0 20

0 15

E
S01

e 005
0-

(d)
Mean u=7 08 v=4 99
StDev u=5 51 v=488
# of meas 373

-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)

0 15

E
' 01
>.

0 005

0

0 15

E
S01

e 005
0

0

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
-c
t
0

E
x

10 0 01
L

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
10 -_1- ---------------------------------

E
"-20 >*
-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.

0O 10
(a) (b)
0 5-
5 0

I-
S-15 0 O

x -5
-20 -5

-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)

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)

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)

15 16 17 18

Figure A-3: Offshore directed current through the rip neck /
at t = 32 s (Test 5)

Drifter positions and velocity

y(m)

Figure A-4: Expanding rip head
(Test 5)

offshore / Drifter positions and velocity at t = 53 s

APPENDIX B
DRIFTER TRAJECTORIES AND VELOCITY (TEST 12)

10 12 14
y (m)

16 18

.8

.6

.2

0
50 100 150 200 250
time (s)

10 12 14
y (m)

16 18

1 -

.8

.6

.4 .

.2

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
y (m)

16 18

.2 /
/ \ // \

.8

.6

.4 -.

.2

0
10 20 30 40 50
time (s)

Figure B-2: Refer to Figure B-1

IU IZ 14
y (m)

Ib It1

l I/,

rA
^1'., ----- -- -! ----'-.1.,;. -
*- *" I I "'

600 700 800
time (s)

10 12 14
y (m)

I / '

-\ 7,

S I .

800 850 900
time (s)

(b)

I U 1Z 14
y (m)

;1 '\!

C. '. I .il1 *I -.. .
'- ._ii "

750 800 850
time (s)

Figure B-3: Refer to Figure B-1

16 18

Ib It

900 950

APPENDIX C
DRIFTER TRAJECTORIES FOR THE LONG TESTS

10 12 14 16 18
(a)

10 12 14 16 18
(h)

10 12 14 16 18
(i)

y(m) y(m)

Figure C-1: Test 12 / Drifter paths; 2 minute time intervals

0 I

10 12 14 16 18
(d)

10 12 14 16 18
(e)

I II

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

10 12 14 16 18
(f)

10 12 14 16 18
(i)

10 12 14 16 18
y (m)

10 12 14 16 18
y(m)

10 12 14 16 18
y (m)

Figure C-2: Test 13 / Drifter paths; 2 minute time intervals

(a) (b)

10 12 14 16 18
(d)

10 12 14 16 18
(g)

10 12 14 16 18
y (m)

10 12 14 16 18
(e)

10 12 14 16 18
(h)

10 12 14 16 18
y(m)

10 12 14 16 18
(f)

10 12 14 16 18
(i)

10 12 14 16 18
y (m)

Figure C-3: Test 14 / Drifter paths; 2 minute time intervals

10 12 14 16 18
(d)
8 8

10 12 14 16 18
(9)

10 12 14 16 18
y (m)

10 12 14 16 18
(e)

10 12 14 16 18
(h)

1.

10 12 14 16 18
y(m)

10 12 14 16 18
(f)

10 12 14 16 18
(i)

10 12 14 16 18
y (m)

Figure C-4: Test 15 / Drifter paths; 2 minute time intervals

I ..

10 12 14 16 18
(d)

10 12 14 16 18
(e)

10 12 14 16 18
(f)

,1 11

10 12 14 16 18
(g)
8

E

10 12 14 16 18
y (m)

1.

10 12 14 16 18
(h)
8

10 12 14 16 18
y(m)

Figure C-5: Test 16 / Drifter paths; 2 minute time intervals

1Ic

m

10 12 14 16 18
(d)

10 12 14 16 18
(e)

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

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

10 12 14 16 18
(f)
8

10 12 14 16 18
(i)

10 12 14 16 18
y(m)

Figure C-6: Test 19 / Drifter paths; 2 minute time intervals

10 12 14 16 18

8

10 12 14 16 18
(g)
8I

10 12 14 16 18
y(m)

10 12 14 16
(e)

10 12 14 16 18
(h)

E

10 12 14 16 18
y(m)

10 12 14 16 18
(f)
8

10 12 14 16 18
(i)

Figure C-7: Test 20 / Drifter paths; 2 minute time intervals

iIn

10 12 14 16 18 10 12 14 16 18
(d) (e)

10 12 14 16 18
(a)C

10 12 14 16 18
(f)

10 12 14 16 18
(i)

10 12 14 16 18
y(m)

10 12 14 16 18
y(m)

10 12 14 16 18
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

I1
10 11 12 13 14 15 16 17
y(m)

Figure D-2: Test 13 / H= 4.28cm, T= Is, monochromatic waves; high water

Test 14: Mean Velocities

Figure D-3:

IU II IZ 1I 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

10 11 12

Figure D-6: Test 19 / H= 5.22cm, T:

8

9

10

A

-C-

1 14 13 1 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

10

A
a{l

Figure D-8:

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

Test 21 / H= 3.97cm, T= 2.67s, monochromatic waves; high water

10 m/

APPENDIX E
FLUCTUATING VELOCITY

(a) (b) (c)

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8E 8

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

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

() (k) ()
8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (n) (o)
8 8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(p) (q) (r)

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

Figure E-1: Test 12 / 1 minute averages of velocity; Legend at the bottom right represents
10 cm/s

10 12 14 16 18 10 12 14 16 18
(d) (e)

10 12 14 16 18
(9)

10 12 14 16 18
y (m)

10 12 14 16 18
(f)

10 12 14 16 18 10 12 14 16 18
(h) (i)
8 8

I) c' I)

i01.1

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

10 12 14 16 18
(m)

10 12 14 16 18
(n)

10 12 14 16 18
(o)

,in

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
(r)

10 12 14 16 18
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 10 12 14 16 18
(d) (e)

10 12 14 16 18
(f)

A A
0n 0

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 e0I

~I

10 12 14 16 18
(p)

10 12 14 16 18
(q)

10 12 14 16 18
(r)

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

I J I-J IJ

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

-J -J In

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (I)
8 8 8

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

(j) (k) (o)
8 8 8

.10 10

E
7 e

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(M) (n) (o)
8 8 8

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

8 8 8

y(m) y(m) y(m)

Figure E-4: Test 11 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

IJ Ic IJ

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(d) (e) (f)
8 8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

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 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(m) (n) (o)
8 8 8

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(p) (q) (r)
8 8 8

I 'x

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)

4n In

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
y (m)

10 12 14 16 18
y (m)

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

10 12 14 16 18
(p)

10 12 14 16 18
(o)

,10 10

10 12 14 16 18 10 12 14 16 18
(q) (r)

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

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 10 12 14 16 18
(d) (e)

10 12 14 16 18
(f)

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)

I-

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-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 1 .. .In

10 12 14 16 18 10 12 14 16 18 10 12 14 16 18
(g) (h) (i)
8 8 8

10 12 14 16 18
y(m)

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

10 12 14 16 18 10 12 14 16 18
(q) (r)
8

Hr ]
Bi^^ri'''' i~ B^ ESr' *''
gT K-d J i I-T:..--'. J
n5 *B'

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

E
0--

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

10 11 12 13 14 15
Alongshore Location (m)

16 17 18

Figure F-2: Test 13 / Refer to Figure F-l

13.5 14
Alongshore Location (m)

Figure F-3: Test 14 / Refer to Figure F-l

2U

18

A16 -mx

10 -

Sx. .

4 -
".

2
x.
8-

'10

A:,

16-

12.5 13 13.5 14 14.5
Alongshore Location (m)

Figure F-4: Test 15 / Refer to Figure F-l

20

18
X

10 --
16-

14-
2-
10
,E "
.- . . . . . . . .
8

6

2 -

0 i
10 11 12 13 14 15
Alongshore Location (m)

Figure F-5: Test 16 / Refer to Figure F-l

15 15.5 16

16 17 18

X..""

x ..... ..... 2
I I
m
ma

mn-=

x-A-

MILLISECOND	CLASS.METHOD	MESSAGE
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0	sobekcm_database.verify_item_lookup_object
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0	sobekcm_database.verify_item_lookup_object
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0	system.web.ui.page.page_load (ufdc.page_load)
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0	html_echo_mainwriter.add_text_to_page	Reading the text from the file and echoing back to the output stream
2	html_echo_mainwriter.add_text_to_page	Finished reading and writing the file