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Nearshore Wave and Sediment Processes: An Evaluation of Storm Events at Duck, NC

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NEARSHORE WAVE AND SEDIMENT PROCESSES: AN EVALUATION OF STORM EVENTS AT DUCK, NC By JODI L. ESHLEMAN 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 2004

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Copyright 2004 by Jodi L. Eshleman

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This thesis is dedicated to my parents, who provided unconditional support throughout my entire education.

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ACKNOWLEDGMENTS I would like to thank the Army Corps of Engineers Field Research Facility (FRF) in Duck, NC for providing the data used in this investigation. I extend my greatest appreciation to the staff at the FRF, who gave me the opportunity to gain some valuable field experience and were always willing to offer advice and encouragement. I acknowledge specifically Kent Hathaway, Chuck Long, and Bill Birkemeier, whose input was vital to this research. I thank all of the FRF for spending countless hours helping me with everything from analyzing data through interpretation. I would also like to thank Rebecca Beavers for taking the time to provide additional sediment data. I thank my supervisory committee chair (Dr. Robert G. Dean) for his continual support and encouragement throughout this process, and for always finding time for my questions and concerns. I thank Dr. Robert Thieke for providing the teaching assistantship that allowed me to continue this research. I also thank Dr. Robert Thieke and Dr. Andrew Kennedy for serving on my supervisory committee. I also thank Jamie MacMahan: his patience and insight were invaluable assets to this investigation. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT.......................................................................................................................xi CHAPTER 1 INTRODUCTION........................................................................................................1 Study Location, Characteristics, and Instrumentation..................................................2 Geographic Location.............................................................................................2 Wave and Weather Conditions..............................................................................3 Bipod Instrumentation..................................................................................................4 Chapter Contents..........................................................................................................7 2 GENERAL NEARSHORE CHARACTERISTICS.....................................................8 Introduction...................................................................................................................8 Quality Control...........................................................................................................10 Data Screening.....................................................................................................10 Representative Data.............................................................................................11 Analysis......................................................................................................................11 Current Influence.................................................................................................12 Bipod Depth (m).........................................................................................................13 Bottom Change (cm)...................................................................................................13 Current (cm/s).............................................................................................................13 Wave Influence....................................................................................................17 Combined Waves and Currents...........................................................................19 Current Direction.................................................................................................19 Wind....................................................................................................................20 Variance of Total Current Acceleration..............................................................21 v

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3 SEDIMENTS..............................................................................................................24 Introduction.................................................................................................................24 Analysis......................................................................................................................26 Sediment Characteristics.....................................................................................26 Previous sediment data.................................................................................26 Sonar evaluation...........................................................................................26 Velocity Profile Calculations..............................................................................29 Critical shear velocity...................................................................................30 Error estimates..............................................................................................33 Combined wave-current influence...............................................................34 Apparent hydraulic roughness......................................................................37 4 WAVE TRANSFORMATION IN THE NEARSHORE...........................................42 Introduction.................................................................................................................42 Analysis......................................................................................................................44 Development of Analytical Spectrum.................................................................44 Dataset.................................................................................................................45 Development of Directional Spectrum from the Data.........................................48 Determination of m Values.................................................................................51 Comparison of Fourier coefficients..............................................................52 Two-sided nonlinear fit................................................................................53 Comparison of Data to Linear Wave Theory Calculations.................................57 Wave direction.............................................................................................60 Refracted m values.......................................................................................62 Wave height comparisons............................................................................65 Energy flux comparisons..............................................................................66 Friction factor...............................................................................................68 Reynolds Stresses................................................................................................72 Discussion...................................................................................................................74 5 CONCLUSIONS........................................................................................................77 LIST OF REFERENCES...................................................................................................81 BIOGRAPHICAL SKETCH.............................................................................................85 vi

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LIST OF TABLES Table page 2-1 Erosion events of 3 cm or greater.............................................................................13 2-2 Event-Based comparison of erosion events of 3 cm or greater................................14 4-1 Theoretical Fourier coefficients for different m values...........................................46 4-2 Measured mean wave directions at peak frequency.................................................51 4-3 Average % energy loss values between bipods........................................................69 4-4 Friction factor estimates from bottom current meter................................................72 4-5 Reynolds stresses for October 1997.........................................................................75 vii

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LIST OF FIGURES Figure page 1-1 Field Research Facility location.................................................................................3 1-2 Bipod instrumentation................................................................................................5 1-3 Bipod locations at initial deployment in 1994...........................................................6 2-1 November 1997 filtered mean current comparison with sonar................................15 2-2 May 1998 filtered mean current comparison with sonar..........................................16 2-3 October 1997 mean orbital velocity estimates vs. sonar measurements..................17 2-4 October 1997 cross-shore orbital velocity estimates vs. sonar measurements.........18 2-5 Wind vectors measured at the Field Research Facility............................................20 2-6 October 1997 current-wind comparison...................................................................22 2-7 November 1997 current-wind comparison...............................................................23 3-1 Median grain size variation with water depth..........................................................27 3-2 X-ray images of boxcores........................................................................................28 3-3 Sonar histogram at 13 m bipod, August 30, 1998....................................................29 3-4 Sonar histogram at 5.5 m bipod, August 12, 1998...................................................30 3-5 Sonar histogram at 8 m bipod, August 31, 1998......................................................31 3-6 Sonar histogram at 13 m bipod, August 29, 1998....................................................32 3-7 Shields curve...........................................................................................................33 3-8 Shear velocity vs. sonar at the 13 m bipod, October 18, 1997.................................34 3-9 Shear velocity vs. sonar at the 8 m bipod, August 19, 1998....................................35 3-10 Shear velocity vs. sonar at the 5.5 m bipod, October 18, 1997................................36 viii

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3-11. Surface roughness variation with mean currents at 5.5 m bipod for October 15-21, 1997..........................................................................................................................38 3-12 Surface roughness variation with mean currents at 8 m bipod for October 15-21, 1997..........................................................................................................................39 3-13 Surface roughness variation with mean currents at 13 m bipod for October 15-21, 1997..........................................................................................................................40 4-1 Coordinate system....................................................................................................45 4-2 Ratios of Fourier coefficients...................................................................................46 4-3 Significant wave heights measured in October 1997, November 1997, May 1998, and August 1998.......................................................................................................47 4-4 Bathymetry in vicinity of bipod instrumentation.....................................................48 4-5 Measured spectra for November 7, 1997 time=2200...............................................50 4-6 Error versus m value comparison for October 20, 1997 time=100..........................54 4-7 Comparison of measured and best-fit spectra from matching coefficients for October 20, 1997 time=100......................................................................................55 4-8 Error between spectra fitted from coefficient ratios for October 20, 1997 time=100...................................................................................................................56 4-9 Comparison of measured and best-fit spectra from curve fitting for October 20, 1997 time=100..........................................................................................................57 4-10 Error between spectra from curve fitting for October 20, 1997 time=100...............58 4-11 Variation of m values with frequency range at 8 m.................................................59 4-12 Directional spectrum variation with frequency at 8 m bipod for October 19, 1997 time=700...................................................................................................................59 4-13 Energy density spectral values for October 19, 1997 time=700..............................60 4-14 Mean wave direction comparison for October 19, 1997 time=700..........................61 4-15 Measured and calculated wave direction differences for October 19, 1997 time=700 at 5.5 m bipod..........................................................................................62 4-16 Average measured and calculated wave direction differences for October 1997....63 4-17 Measured and refracted directional spectra for November 13, 1997 time=1742.....64 ix

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4-18 Comparison of refracted and measured m values over frequency range for November 13, 1997 time=1742................................................................................65 4-19 Significant wave height ratios versus cross-shore position......................................67 4-20 Average measured and predicted energy flux values...............................................70 4-21 Surveyed bathymetry in vicinity of bipod instrumentation......................................71 4-22 Histogram of calculated friction factors at all current meters..................................73 4-23 Friction factor variation with wave height at the bottom current meter...................74 x

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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 NEARSHORE WAVE AND SEDIMENT PROCESSES: AN EVALUATION OF STORM EVENTS AT DUCK, NC By Jodi L. Eshleman May 2004 Chair: Robert G. Dean Major Department: Civil and Coastal Engineering Pressure, sonar, and current measurements were recorded at 5.5 m, 8 m, and 13 m water depths in the outer surf zone and inner continental shelf region off the coast of Duck, NC. This unique data set was analyzed to investigate erosion thresholds and wave evolution. A mean current threshold of 20 cm/s and combined wave and current threshold of 60 cm/s were identified for bed elevation decrease. Shear velocity was determined to be a good indicator of bottom elevation change at the 8 m and 13 m bipods, with erosion beginning 0 to 3 hours after it crossed a movement threshold of 1.17 cm/s. Surface roughness estimates at these same two water depths decreased with increasing mean currents. The combination of measured near bottom pressure and horizontal velocity components provides the basis for determining a directional spectrum. A simplified analytical directional spectrum based on a single cosine curve of varying power (m) was used to approximate these measured directional spectra. A nonlinear least squares curve xi

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fit to each side of the measured directional spectrum proved the most accurate method of determining the best representation of m values. Refracted mean wave directions were slightly overestimated by the theory and the decrease in width of the directional spectra with decreasing water depth was overestimated. Also, energy flux calculations combining shoaling and refraction theory showed smaller measured than predicted energy flux values with inshore distance (sometimes by more than one third) emphasizing the importance of considering energy loss in calculations for engineering design and planning. A representative friction factor for each record was determined by accounting for frictional energy loss in the energy flux calculation, using velocity time series measured at the bottom current meter. Calculated friction factors varied throughout storm events, but most fell within a range of 0 to 0.2. A representative value of 0.17 was identified for this location through the use of average energy flux and energy loss values over all storm events. Reynolds stresses were calculated and were found to be consistently different at the current meter at 0.55 m elevation, a result that remains unexplained. xii

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CHAPTER 1 INTRODUCTION The inner continental shelf off the open mid-Atlantic coast is a wave-driven environment, where sediment transport and nearshore circulation are primarily forced by wind-generated ocean surface waves (Wright 1995). This is a friction-dominated region, where boundary layers may occupy the entire length of the water column, transmitting effects of wind blowing on the water surface to the seabed (Wright 1995). Wave propagation is largely characterized by transformation through refraction, diffraction, energy dissipation, and shoaling. Mean currents are another important component in the nearshore zone, and can be driven by waves, wind, tides; and gradients in pressure, temperature, and density, among other things. Within this dynamic environment, sand movement is not uniform in all directions and at all locations. Harris and Wiberg (2002) suggest that gradients in bed shear stress may create gradients in suspended sediment flux. These cross-shelf gradients in sediment flux will in turn create cross-shelf gradients in sediment size as the higher orbital velocities on the inner shelf move finer sediment offshore (Harris and Wiberg 2002). Alongshore sediment flux is also an important component of the sediment transport discussion. Beach and Sternberg (1996) found that alongshore sediment flux is dependent on breaker type, and this information should be incorporated into sediment transport models. Their measurements showed that plunging waves were responsible for the greatest portion of suspended load and sediment flux, but other breaker types and 1

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2 nonbreaking waves combined still contributed almost half of the total suspended load and sediment flux (Beach and Sternberg 1996). There is variation in sand transport throughout the water column as well. Many investigators have found an inverse relationship between distance above the bed and suspended sediment concentration (Beach and Sternberg 1996; Conley and Beach 2003). A study conducted in the surf zone during the SandyDuck experiment showed that the increasing importance of wave-driven transport near the bed might lead to a reversal in the net cross-shore transport direction in the water column. The directions of transport at the bed may dominate even if much of the water column has an opposing transport direction since more than half of the depth-integrated net transport occurs within 5 cm of the bed (Conley and Beach 2003). Study Location, Characteristics, and Instrumentation Geographic Location Field data were obtained on the inner continental shelf off the coast of the Army Corps Field Research Facility (FRF) in Duck, North Carolina. The FRF facility is located on the Outer Banks of North Carolina, on the central portion of the Currituck Spit, which extends southeast continuously for over 100 km from Cape Henry, Virginia to Oregon Inlet, North Carolina (Figure 1-1). It is located in the southern portion of the Middle Atlantic Bight (36 10 57N; 75 45 50W) and bordered by Currituck Sound, a low-salinity estuarine environment, on the west; and the Atlantic Ocean on the east. Ocean tides are semi-diurnal, with a mean range of approximately 1 m (Birkemeier et al. 1981).

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3 Figure 1-1. Field Research Facility location (from http://www.frf.usace.army.mil) Wave and Weather Conditions Wave heights vary seasonally along the Outer Banks, with peak waves occurring in October and February, and mild conditions prevailing in late spring and early summer months (Birkemeier et al. 1981). A compilation of wave statistics for the time period of 1985 through 1995 resulted in an average annual wave height of 0.9 + 0.6 m, and a mean annual wave period of 8.8 + 2.7 s (Leffler et al. 1998). There have been many observations of water masses that interact with currents in the area, including low salinity slugs from the Chesapeake Bay and warm, clear Gulf Stream currents (Birkemeier et al. 1981).

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4 The majority of storm events that affect the Atlantic coast originate in the middle-latitude westerly wind belt and are often termed extra-tropical (Dolan et al. 1988). Tropical storms, including hurricanes, also affect the region, but less frequently. Dolan et al. (1992) discuss the importance of extra-tropical storms for erosion and note that they often generate wave heights that are comparable to or greater than those from hurricanes. A study that examined 1,349 northeast storms on the Atlantic coast found a distinct seasonality of frequency and duration, with maximum values in the winter and minimum in the summer (Dolan et al. 1988). When specifically examining extra-tropical storms, the most significant contribution to erosion is from northeasters. Xu and Wright (1998) determined that even though comparable winds from the southerly directions sometimes caused high wave heights, the alongshore current magnitudes recorded during these storms were only one-fifth of those achieved during northeasters. Cross-shore current magnitudes were also smaller, but differences were not as large as for alongshore currents (Xu and Wright 1998). Bipod Instrumentation The initial bipod instrumentation was deployed in October 1994 as part of a multi-year monitoring program to study shore-face dynamics on the inner continental shelf of the Field Research Facility in Duck, NC (Howd et al. 1994). The instrumentation consisted of three current meters at varying elevations, a pressure sensor, and a sonar altimeter, which were all attached to a bipod frame, secured by two 6.4 m pipes jetted vertically into the seabed (Beavers 1999). The original bipods collected data until October 1997 using three Marsh-McBirney electromagnetic current meters, which often experienced significant noise. The current meters were replaced with Sontek Acoustic Doppler Velocimeters for the SandyDuck experiment in October 1997, and the bipods

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5 were redeployed at depths of 5.5 m, 8 m, and 13 m relative to NGVD. They remained operational at these three simultaneous locations through December 1998. The data used in this analysis were collected during this second deployment. Figure 1-2 shows the bipod setup where A, B, and C are electronic housings; P is the pressure sensor; and S the sonar altimeter. General bipod locations at the time of initial deployment in 1994 are pictured with respect to local bathymetry in Figure 1-3. Figure 1-2. Bipod instrumentation A,B,C = electronic housings, P is pressure sensor, and S is sonar altimeter (from Beavers 1999) The bipod packages each contained three SonTek Acoustic Doppler Velocimeters (ADV), which sampled at 2 Hz and were located at elevations of 0.2 m 0.55 m and 1.5 m above the sea floor. The end of the frame containing the current meters was oriented toward the southeast to minimize interference of current meters and vertical supports with orbital velocity measurements, since storm events of interest would have primarily northeast waves (Beavers 1999). Digital Paroscientific gauges were used for pressure measurements, operating at 38 k Hz and a sampling rate of 2 Hz (Beavers 1999). A Datasonics PSA-900 sonar altimeter was used to record bottom elevation. The range was

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6 modified from 30 m to 3 m to increase the resolution, sampling at 1 Hz with a beam frequency of 210 kHz (Beavers 1999). Tests by Green and Boon (1988) of response characteristics found this model of altimeter to be accurate to one centimeter. Current meter and pressure data are output in 34-minute segments, with a 10-minute break in data every 3 h. Average values for each record represent a mean value for a 34-minute burst. Sonar measurements are determined through a histogram filtering technique, taking the highest bin value for the burst. Figure 1-3. Bipod locations at initial deployment in 1994 (from Beavers 1999) The lowest ADV records bottom measurements for a duration of 9 min every three hours to provide a second measurement of bottom elevation (Beavers 1999). This beam has a frequency of 4 MHz and a beam width of one degree, creating a 2 cm diameter footprint; whereas, the sonar altimeter operates at a frequency of 210 kHz and has a 10-degree beam width, creating a 20 cm diameter footprint (Beavers 1999). The differences in beam frequency and footprint size provide different optimum operating

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7 conditions. Beavers (1999) suggests that the ADV is more reliable under non-storm conditions and the sonar altimeter provides a better estimate of bottom elevation under storm conditions, when suspended sediment concentration within the water column is high. Chapter Contents The purpose of this investigation is to examine sediment movement and wave evolution within the inner continental shelf and outer surf zone region through the analysis of field measurements. Chapter 2 focuses on determining general relationships between waves, currents, and sonar measurements. Chapter 3 describes sediment characteristics, and discusses some aspects of bottom roughness by analyzing velocity profiles. Chapter 4 is the heart of the investigation and utilizes the data collected at all three bipod locations to provide a comparison with analytical predictions of evolution of wave characteristics.

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CHAPTER 2 GENERAL NEARSHORE CHARACTERISTICS Introduction Many researchers have attempted to establish a relationship between statistical properties of velocity measurements and sediment movement. Although there have been some velocity moments that have seemed more relevant than others, there does not seem to be any one parameter that shows a consistent significant correlation to sediment transport. A study by Guza and Thornton (1985) examined velocity moments from measurements at Torrey Pines Beach in San Diego, CA and found that oscillatory asymmetries and combined current-wave variance terms are significant to cross-shore transport. Several studies have shown that the oscillating velocity terms move sediment onshore and the mean velocities move sediment offshore (Guza and Thornton 1985; Osborne and Greenwood 1992; Conley and Beach 2003). Measurements of sandbar migration at Duck, NC showed maximum values of velocity asymmetry and acceleration skewness near the bar crest (Elgar et al. 2001). Hoefel and Elgar (2003) found that extending an energetics model to include fluid accelerations resulted in better predictions of onshore bar migration between storms. Velocity measurements taken in the surf zone during SandyDuck showed no significant correlation between velocity moments and wave driven transport, although acceleration skewness showed the strongest relationship (Conley and Beach 2003). These suggest that velocity asymmetry and acceleration skewness seem to have the strongest ties to sediment transport in past experimental results. 8

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9 There has been previous work with similar instrumentation done at this location. Several studies included instrumented tripods deployed during storm and fair-weather conditions, which also included suspended sediment measurements (Wright et al. 1986; Wright et al. 1991; Wright et al. 1994). The first tripod deployment was at a single depth and did not show a relationship between bed level changes and increased mean or orbital velocities. There was a gradual change in the bottom elevation throughout the middle and final stages of the storm, followed by significant accretion that was hypothesized to be the result of a migrating bedform. Suspended sediment measurements did not show a response to the onset of the storm or peak with mean currents, but peaked with oscillatory flow, suggesting that waves are the dominant source of sediment resuspension (Wright et al. 1986). The second study consisted of three separate deployments at the Field Research Facility and the results suggested that it is the near-bottom mean flows, not oscillatory components that play the dominant role in transporting suspended sediment (Wright et al., 1991). Mean flows may also play a role in the direction of sediment movement. A study conducted at Duck showed the tendency of a mean cross-shore velocity threshold around 30 or 40 cm/s directed offshore to be the divider between landward and seaward bar migration (Miller et al. 1999). Both mean and oscillatory flows are essential to the analysis and they are not independent. The wave boundary layer creates resistance for the current above and slows down that flow. Waves are often thought to be more efficient at initiating motion, whereas currents are more efficient at net transport, but the two interact nonlinearly (Grant and Madsen 1976). There are two critical differences between previous studies and this dataset. These include the length of time and number of instrumentation packages deployed.

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10 Many other studies have included one or two instrument packages deployed simultaneously for individual storm events or short periods of fair-weather conditions, but not three instrument packages with continuous measurements for this length of time. Some previous investigations have been carried out with this specific dataset that focused on the sonar data. Sonar Altimeter measurements were compared to surveyed profiles to discuss discrepancies in depth of closure concepts. The predicted depth of closure was around 8 m, yet for some storm events, the 13 m bipod showed the greatest change in bottom elevation. Net and range of seabed elevation changes were examined during storm events that were defined by wave thresholds. Finally, a comparison of sonar records to diver collected boxcores served to validate the sonar record and showed the sonar was capable of monitoring long-term bottom stratigraphy (Beavers 1999). The current and sonar measurements were also used as forcing and validation for a bottom boundary layer and sedimentation model (Keen et al. 2003). These analyses have shown some interesting relationships, but have neglected a major component of the dataset: the current measurements. The first level of this analysis focuses on the currents and the manner in which they affect the bottom during all weather conditions, not just storm events. Quality Control Data Screening Different levels of screening were applied in an attempt to eliminate noise and assure that the measurements presented here are representative of actual conditions in the nearshore environment. Spikes were removed using polynomial interpolation. Beam correlation and intensity values output by the ADV were used to identify low quality data. The second level of data screening was accomplished through determining several

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11 quality control parameters for each record. The quality control parameters included signal-to-noise ratios for current and pressure measurements, and a z test value based on a ratio of the wave heights calculated from pressure and current measurements. Data with signal-to-noise ratios less than 1.5 or z test values outside the range of 0.5 to1.5 were not used. Representative Data The following analysis is based on four months during which the described data standards were satisfied. These months: October 1997, November 1997, May 1998 and August 1998 were chosen for several reasons. They include a nearly complete data set that has been successfully edited. They have z-test values near 1, signal to noise ratios of 2 or higher, and wave directions that are consistent for all three current meters, suggesting that biofouling and problems with current meter rotation were minimal. They have bottom measurements from the lowest current meter recorded every three hours, so that trends in the sonar measurements can be validated. In addition to data quality, they encompass significantly different seasonal variations. Measured significant wave height values range from less than 1 m to almost 4 m, spanning storm and mild weather conditions. It is important to note that the data from these months includes some problems, but knowledge of data quality can be combined with analysis techniques to obtain results that account for the limitations of the data. Analysis Our knowledge of the dynamics of the nearshore system leads to the recognition that no single statistical property can explain sediment movement. Sand transport is governed by a complex combination of many factors. The following discussion of

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12 erosion refers to bed elevation decrease, rather than transport initiation, which cannot be measured by the available instrumentation. The continuity equation gives the following relationship between bed elevation, z, and gradients in cross-shore, alongshore and vertical sediment transport components at the bed, q x q y and q z respectively. zqyqxqdtdzpzyx1 where p represents the porosity. It is important to recognize that it is possible to have sediment transport without bed elevation change; however, if the bottom sediment is suspended or the gradient in cross-shore or alongshore sediment transport is positive, the bottom elevation will decrease. This initial analysis is an attempt to discern which properties appear to play a more significant role when considered individually. Current Influence There appears to be a mean current threshold of approximately 20 cm/s for erosion in most of the data. There is usually some erosion when the total mean current reaches 20 cm/s, yet there may be erosion for smaller currents. The currents were filtered with a cutoff of one day to remove tidal influences and to facilitate a comparison with sonar altimeter data. Table 2-1 shows events of bed elevation decrease of 3 cm or greater and the associated currents. There are many times when the mean current is very high and the bottom change is small and vice versa, indicating the possibility that other forces may be involved. One important thing to note is that often times erosion occurs when significant wave heights are fairly low. 54% of the erosion events identified in Table 2-1 occurred when the significant wave height was less than 2 m, which is often considered as the threshold between storm and calm conditions. This reinforces the need to examine

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13 Table 2-1. Erosion events of 3 cm or greater Bipod Depth (m) Bottom Change (cm) Current (cm/s) H mo (m) T (s) Time since last event (days) Oct-97 5.5 6 25 2.0 12.5 12.5 5.5 20 55 3.0 9.1 3.5 5.5 10 19 1.0 12.5 4.5 5.5 8 21 1.0 10.0 5.0 8 5 22 1.5 6.3 9.0 8 8 28 2.0 12.5 4.5 8 6 58 3.0 9.1 3.0 8 11 18 1.0 12.5 4.0 8 5 19 1.0 10.0 4.5 13 11 56 3.0 9.1 16.0 Nov-97 5.5 5 30 2.5 4.8 10.5 5.5 3 25 3.0 9.1 7.0 5.5 13 28 1.5 3.6 10.5 8 10 15 1.0 8.3 9.5 8 6 30 2.5 4.8 5.0 8 4 28 2.0 11.1 1.5 8 3.5 12 1.5 10.0 1.0 8 5 13 3.0 9.1 6.0 8 10 25 1.5 3.6 9.0 13 4 22 2.5 4.8 19.0 13 3 18 3.0 9.1 7.5 May-98 5.5 10 40 1.5 6.7 9.0 5.5 3 21 2.0 12.5 6.0 8 9 40 1.5 6.7 9.0 8 6 20 2.0 12.5 6.0 8 5 10 1.0 11.1 1.5 13 3.5 35 1.5 6.7 9.0 13 8 40 3.5 9.1 3.5 Aug-98 5.5 4 26 2.0 7.1 1.5 5.5 4 25 1.5 7.1 1.5 5.5 3 15 1.0 6.7 2.5 5.5 5 21 1.5 4.0 6.5 5.5 10 30 1.5 6.3 6.0 5.5 4 18 1.25 11.1 4.0 5.5 10 70 3.2 12.5 3.0 8 8 23 2.0 7.1 1.5 8 11 23 1.5 7.1 1.5 8 8 26 1.5 6.3 15.0 8 16 65 3.2 12.5 7.5 8 11 5 1.0 10.0 4.0 13 4 15 1.5 7.7 4.0 13 25 70 3.2 12.5 22.0

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14 the changes occurring during all types of conditions, since it is not necessarily during storm events that the sediment is moving. Table 2-2. Event-Based comparison of erosion events of 3 cm or greater Date Current (cm/s) Bottom Change (cm) 5.5 8 13 5.5 8 13 11-Oct 20 22 20 5 15-Oct 25 28 28 6 8 19-Oct 55 58 56 20 6 11 22-Oct 19 18 18 10 11 27-Oct 21 19 18 8 5 2-Nov 12 15 11 10 6-Nov 30 30 22 5 6 4 7-Nov 23 28 11 4 8-Nov 10 12 5 3.5 13-Nov 25 13 18 3 5 3 23-Nov 28 25 21 13 10 9-May 40 40 35 10 9 3.5 12-May 65 58 40 8 15-May 21 20 10 3 6 16-May 5 10 8 5 2-Aug 26 23 17 4 8 4-Aug 25 23 15 4 11 5-Aug 18 15 15 4 6-Aug 15 15 5 3 13-Aug 21 19 12 5 19-Aug 30 26 28 10 8 23-Aug 18 10 9 4 27-Aug 70 65 70 10 16 25 30-Aug 5 5 10 11 Major erosion events appear to be fairly consistent between bipods, although the magnitudes of bottom elevation changes are usually different. Table 2-2 presents the data from Table 2-1 by date, to facilitate a comparison between bipods (represents < 3 cm of bottom change). An interesting situation occurs in November 1997 and August of 1998, where the current reaches one of the maximum values for the month (above the 20 cm/s

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15 threshold), but the erosion is not consistent at all three bipods. Both instances show significant erosion at the 5.5 m and 8 m bipods (ranging from 8-13 cm), and less than 3 cm of erosion at the 13 m bipod. Figure 2-1 shows one case occurring around November 24, 1997. Currents are positive onshore and south. Figure 2-1. November 1997 filtered mean current comparison with sonar a) 5.5 m b) 8 m c) 13 m A situation occurred in May of 1998 that seems to be the reverse of this last observation and occurs around May 13 (see Figure 2-2). The currents were at their highest values for the month, in excess of 40 cm/s, causing minimal erosion at the 5.5 m and 8 m bipods and a more significant change at the 13 m bipod. For this situation, the ADV bottom measurement showed less erosion, indicating that there may have been fluffy material at the 13 m bipod that the sonar had trouble penetrating and the higher

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16 frequency ADV picked up. Here we see the 5.5 m and 8m bipods showing significant erosion at the onset of currents over 20 cm/s, but then the erosion leveled off as the currents continued to increase. The 13 m bipod did not show as much erosion initially, but as currents continued to increase there was a spike where the sonar based bottom elevation dropped 15 cm. If this sediment was of the finer type that is sometimes seen at 13 m, a higher current may have been required for movement due to cohesive properties, and once the current reached that threshold, the entire layer moved. The cause of this cannot be explained with certainty without more detailed sediment information. Figure 2-2. May 1998 filtered mean current comparison with sonar a) 5.5 m b) 8 m c) 13 m

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17 Wave Influence The root mean square current speeds were examined in different frequency ranges. These values were multiplied by the square root of two to obtain the amplitudes as substitutes for orbital speeds and represent the significant values for orbital speed. This should provide some insight into which frequency components contribute the most. A high frequency range from 0.04 to 0.35 Hz was identified to examine sea swell and a low frequency range of 0.004 to 0.04 Hz to investigate any infragravity contributions. Figure 2-3. October 1997 mean orbital velocity estimates vs. sonar measurements a) 5.5 m b) 8 m c) 13 m (solid black line represents sonar) The infragravity orbital speed was always smaller, but reached 20 cm/s at the 5.5 m bipod during storm events. Results for October 1997 are presented in Figure 2-3, which shows

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18 a peak at the maximum erosion event for the month, and slight increase for smaller erosion and accretion events. Figure 2-4. October 1997 cross-shore orbital velocity estimates vs. sonar measurements a) 5.5 m b) 8 m c) 13 m (solid black line represents sonar) This suggests that the infragravity component may be significant for this dataset. This is an interesting observation because other studies have had conflicting results for this location in the past. Wright et al. (1994) took similar measurements at this location at a depth of 13 m during the Halloween storm of 1991 and showed a significant infragravity component, reaching 20 cm/s near the peak of the storm, which is similar to these findings. They suggest that roughly half of the infragravity energy emanates from the surf zone (Wright et al. 1994). An earlier attempt to quantify wave reflection found no significant quantity of long wave energy, either incident or reflected from

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19 measurements taken at a depth of 6.5 m (Walton 1992). One possible explanation for this difference may be a difference in significant wave heights, since values recorded during this study were never greater than 3.5 m and those recorded during the Halloween storm reached 6.5 m. The plot of the cross-shore components (Figure 2-4) shows that the cross-shore is the major component of the R.M.S seaswell velocity, which enforces the need to consider cross-shore velocity for sediment transport even when mean values are small. The current amplitude increased at most erosion events for the month, but not all. Combined Waves and Currents Another approach to considering erosion causes examined the combined wave and current maximum velocities. The sum of the amplitude (used to estimate orbital velocity) and the component of the mean current in the wave direction was calculated. These are all positive values since they were taken in the wave direction and negative or positive wave orbital velocities could cause erosion. This was an attempt to consider not just the mean current or wave orbital velocity, but their combined effect; however, this did not take into account any nonlinear interactions between waves and currents, but provided a rough estimate of combined velocity. This analysis did not show any consistent threshold between maximum velocity and sediment movement, but there was a relationship between the two. Very high combined velocities in the range of 60 to100 cm/s always seemed to be associated with erosion, but below this range the effect varied. Current Direction The maximum erosion events for the month always occurred with a southerly longshore current and usually a downwelling (seaward) flow in the cross-shore component. One example is around the 28 of August 1998 in which a northerly

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20 longshore current reversed direction and caused the most significant erosion for the month. Wind Measurements of wind magnitude and direction are obtained from FRF wind gages 932 and 933. Figure 2-5 shows a vector plot of these values. Most peaks in mean longshore current velocity that are above the 20 cm/s threshold appear to coincide with peaks in longshore wind velocity. The notable exception to this is the month of November 1997, where scatter plots show a poor correlation between the longshore wind velocity and longshore mean current. Figure 2-5. Wind vectors measured at the Field Research Facility

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21 The cross-shore currents showed no significant correlation to cross-shore wind. Current-wind comparisons for the month of October 1997 are provided in Figure 2-6. Current and wind measurements are positive onshore and south. Another study by Xu and Wright (1998) of wind-current correlation at this same general location has shown that it is dependent on wind direction. The correlations were broken into quadrants, and it was found that the current and wind speeds are most correlated with winds from the Northeast or Northwest direction, showing much higher R squared values than winds blowing from the Southeast or Southwest (Xu and Wright 1998). Variance of Total Current Acceleration There seems to be some relationship between the variance of the acceleration of the total current and bottom change on a month-to-month basis. This follows some previous observations discussed in the introduction, although the acceleration skewness did not show any significant trends. There is an increase in this variance at times of maximum erosion for the month; however, this same trend was seen when considering current variance. Erosion due to the acceleration variance cannot be distinguished from erosion due to the current variance, since they differ only by the square of the radial frequency.

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22 Figure 2-6. October 1997 current-wind comparison

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23 Figure 2-7. November 1997 current-wind comparison

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CHAPTER 3 SEDIMENTS Introduction Past observations of bottom change from sonar altimeter measurements have often been supported by visual observation or other instrumentation since sonar measures only the elevation at a single point. One limitation of the analysis lies in the inability to distinguish whether sediment is moving as suspended load or bed load from a single sonar altimeter. It is possible to have sediment transport without elevation change, yet the sonar can only capture variation in the bed elevation. Topographic features moving, including bed forms or ripples, can also cause problems since they may be measured as the representative bed elevation, but their existence is localized. There have been observations of non-uniform topography in the vicinity of the bipod instrumentation. An array of seven sonar altimeters deployed in the surf zone during the SandyDuck experiment captured mega ripples which ranged from 15 cm to 30 cm high and moved through the sonar range in a period of about ten hours (Gallagher et al. 1998). The first tripod deployment by Wright et al. (1986) was supplemented by diver observations, pictures and side-scan sonar measurements. Side scan sonar images showed sediment lobes of fine material overlying coarser material which were up to one meter high and thought to be the cause of the rapid accretion at the 8 m tripod at the end of the storm event (Wright et al. 1986). Bottom features such as these are difficult, if not impossible to discern from sonar altimeter measurements alone. 24

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25 An important parameter when discussing sediment transport in relation to bottom topography is the bed shear stress, or equivalently, the shear velocity, /*b u. The von Karman-Prandtl equation 0*ln1zzuzucc can be used to estimate shear velocity and hydraulic roughness length values from measurements of the mean current at different elevations. Madsen et al. (1993) calculated shear velocity and apparent hydraulic roughness from the log-profile method for the data collected at the 13 m tripod during the Halloween storm of 1991. These estimates showed shear velocity values on the order of 2 to 3 cm/s and apparent hydraulic roughness values generally between 0.1 cm and 1 cm. These values were found using data obtained with similar instrumentation and at a very similar location, therefore the values found in the subsequent analysis are expected to be the same order of magnitude. They found a value of 1.5 mm for the Nikuradse sand grain roughness for a movable flat bed (Madsen et al. 1993). Past analysis of the dataset examined in this thesis used diver-collected boxcores to supplement sonar measurements. Beavers (1999) discussed the geologic features of these cores and the correlation between core layers and sonar records in detail. The positive correlation between these two records indicates that scour around the pipes was not appreciable, which will be assumed in the following analysis. Shear stress calculations showed that when the shear stress is a maximum, seabed elevation decreases and when shear stress decreases, the seabed elevation increases (Beavers 1999).

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26 Analysis Sediment Characteristics Previous sediment data Sediment data are available for the period 1984-1997 from locations adjacent to the bipod instrumentation. Figure 3-1 compares median grain size versus elevation for this time period and implies little variation in sediment size at the 5.5 m and 8 m bipods. Most measurements remain within a unit range. There is significantly more variation at the 13 m bipod with a 3/2 unit range. The left panel of Figure 3-2 shows an x-ray of a boxcore taken at a water depth of 13.2 m on August 18, 1997. The white region shows a section where the material is too fine for the x-ray to register and grain size analysis determined a median value of 4.02 for this section, as opposed to 3.10 for the rest of the sediment column (Beavers 1999). The right panel of Figure 3-2 shows a boxcore taken in 1992 at a water depth of 14 m, which also shows a layer of fine, silty material (Nearhoof 1992). It is important to be aware of the sediment range at the 13 m bipod when considering sonar measurements, since there are instances when the sonar may have trouble recognizing fine, silty material. Sonar evaluation Bed form migration can register on sonar measurements and changes in elevation may reflect localized change from large-scale bed forms moving through the sonar footprint. Tests of ripple fields under a similar sonar altimeter showed that the ripple could not be resolved if its height above the bed is more than eight times its wavelength (Green and Boone 1988). The possibility of non-uniform topography is difficult to resolve and one method of addressing this was to examine sonar histograms. One notable

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27 observation is that the raw sonar measurements were very noisy, although the outline of the bottom could generally be distinguished. A representative sonar value for each 34-minute record was taken as the max bin value of the histogram for that time series. The hypothesis was that at times when there was silty material at the 13 m bipod, the sonar might show two peaks, at the top and bottom of this layer. Another possibility was that during storms, the histograms may show more spread if the sonar was unable to consistently penetrate the suspended sediment in the water column. -14-13-12-11-10-9-8-7-6-5-422.533.544.5Median Grain Size (phi)Elevation (m,NGVD) Boxcore Samples (1994-1997) Profile Line 62 (1984-1985) Duck 94 Samples-Oct Duck 94 Samples-Aug SandyDuck 97 Samples Figure 3-1. Median grain size variation with water depth (data from FRF) Sonar histograms are included for each bipod location during the month of August 1998. In most instances, there is a very well defined peak at a specific value, and smaller peaks or spreading at depths less than this value (Figure 3-3). Secondary peaks are within a few centimeters of the major peak. There are times when this histogram

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28 deteriorates and the peak is less well defined with a greater spread (Figure 3-4). These times do not always correlate with storm events as anticipated. A. B. Figure 3-2. X-ray images of boxcores A) h=13.2 m on August 18, 1997 (Beavers 1999) B) h=14 m in 1992 (Nearhoof 1992) At the 5.5 m and 13 m bipods there is rarely spreading at depths greater than this peak, which lends confidence to sonar estimates of the bottom where spreading is most likely an indicator of noise within the water column. One very interesting observation is that the 8 m bipod shows almost all of the spreading and secondary peaks in the histograms to be at depths greater than the histogram peak, as evident in Figure 3-5. This is consistently different from the other bipods and remains unexplained. Another interesting situation occurred on August 29, 1998 and lasted for approximately a day, showing the variation in sonar histogram values with time at the 13 m bipod. Here two distinct peaks occurred that are over 20 cm apart and are of similar magnitude. One peak is at 13.37 m and another at 13.14 m (Figure 3-6). This occurs immediately after the major storm event for the month. One possible explanation is that there is a layer of very fine sediment here and the sonar sometimes pings off the top and

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29 sometimes penetrates the layer. An observation about this August storm event is that there are strong northerly alongshore currents reversing direction and reaching 100 cm/s in the southerly direction, and this is the only time that this alongshore-current reversal occurred within the four months analyzed. This dual sonar peak phenomenon was not repeated and with the limited sediment information available it cannot be explained with any degree of certainty. Figure 3-3. Sonar histogram at 13 m bipod, August 30, 1998 Velocity Profile Calculations The velocity profile method discussed earlier is used to estimate shear velocity and hydraulic roughness length values from the measured mean current values from the three different current meters. Bed elevation values from ADV measurements are

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30 incorporated to account for changing current meter elevations with time and bottom change. Figure 3-4. Sonar histogram at 5.5 m bipod, August 12, 1998 Critical shear velocity One attempt to examine further the shear velocity relationship with bottom change was to calculate a critical shear velocity value from the range of sediment sizes shown in Figure 3-1 for each bipod. This method utilized the form of Shields curve shown in Figure 3-7 to determine a value of shear stress for each mean sediment diameter based on an abscissa value of gDs23* The ordinate value of

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31 gDsc is used to determine a critical shear velocity through the relationship 2*ccu The next step was to identify the times during the four months analyzed when the bottom was just beginning to erode. A daily plot was generated for each of these times of erosion initiation to facilitate a visual comparison of shear velocity with measurements of sonar. Figure 3-5. Sonar histogram at 8 m bipod, August 31, 1998 The critical range of shear velocity values were overlain on the shear velocity plots to determine if the bottom elevation began to change around the same time that the shear velocity crossed the threshold for movement.

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32 Figure 3-6. Sonar histogram at 13 m bipod, August 29, 1998 Most situations at the 8 m and 13 m bipod locations show the bottom beginning to erode zero to three hours after the shear velocity crossed the critical threshold. Figure 3-8 shows a particular time when the two occur almost simultaneously. The blue line represents shear velocity with the red lines identifying the range of critical values for different sediment sizes, and the circles marking where the bottom begins to erode and the shear velocity crosses the threshold. Figure 3-9 shows a particular situation at the 8 m bipod where we see a phase lag between the two, and erosion does not occur until approximately 3 h later. At the 5.5 m bipod, the shear velocity value is always below the threshold for movement when sonar measurements show the bottom beginning to erode.

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33 One example is included as Figure 3-10. Peaks in shear velocity show some relationship to peaks in tidal currents. Figure 3-7. Shields curve Error estimates It is important to address the error in estimates of shear velocity, since values are calculated from a velocity profile method that fits a curve to three current measurements, leaving only two degrees of freedom. Error estimates for shear velocity are calculated for a 90% confidence interval using the student t distribution and they are very large, around an order of magnitude higher than most calculated values of shear velocity. This is a limitation of the method and data available, and most field measurements would demonstrate similar error estimates when using vertical arrays of individual current meters for measurements. Another factor is that the chosen critical value of shear velocity is dependent on sediment size, but the range of values does not vary widely when considering the range of sediment sizes measured at bipod locations. After taking

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34 into account the limitations of the shear velocity estimates the time lags between the shear velocity reaching a critical value and initiation of sonar change do not appear to be unreasonably long. The critical shear velocity seems to be a good indicator of when erosion will begin at the 8 m and 13 m bipods. Figure 3-8. Shear velocity vs. sonar at the 13 m bipod, October 18, 1997 (Note blue line is shear velocity, black line is sonar, red lines are critical shear velocity) Combined wave-current influence Another concern regarding shear stress and shear velocity estimates is that they are calculated based only on the current values and they do not take into account wave orbital velocities. The shear stress associated with combined waves and currents is different than with either alone, because of the turbulence generated by the wave-current interaction (Grant and Madsen 1979).

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35 Figure 3-9. Shear velocity vs. sonar at the 8 m bipod, August 19, 1998 (Note blue line is shear velocity, black line is sonar, red lines are critical shear velocity) This shear stress would be larger than that given by the mean current. Grant and Madsens model was applied to current measurements taken during the Halloween storm and the wave boundary layer was estimated to be a maximum of 11.6 cm thick, much lower than their bottom current meter at a 29 cm elevation (Madsen et al. 1993). This lends confidence to the assumption that our bottom current meter at an elevation of 20 cm above the bed is also outside that wave boundary layer. Analytical models have been tested which calculate a shear velocity based on both wave and current influence. These not only account for the individual wave and current influence, but also any nonlinear interactions between the two. Wiberg and Smith (1983)

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36 Figure 3-10. Shear velocity vs. sonar at the 5.5 m bipod, October 18, 1997 (Note blue line is shear velocity, black line is sonar, red lines are critical shear velocity) compared shear velocity estimates calculated from currents alone to those calculated from two different models, those of Grant and Madsen, and Smith. The field data used for the analysis was collected at a similar depth, 18 m, and in an area with a similar sediment size. They found that the shear velocities calculated using the wave-current models are similar to the values obtained from the measured average velocity profiles, although the estimates of surface roughness are very different (Wiberg and Smith 1983). This suggests that recalculating shear velocities with an added wave influence would not alter the estimates significantly. It raises the concern that estimates of the surface roughness may not be characteristic of actual values, and often may be higher by up to an order of magnitude. This paper also suggested that scour under the instrument frame

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37 caused original estimates of surface roughness from the data collected by Drake and Cacchione to be unrealistically high (Wiberg and Smith 1983). This may allow the surface roughness calculated through the velocity profile method to be used as a quality control parameter for the data, indicating situations where settling or scour might be a concern. Apparent hydraulic roughness An investigation into estimates of bottom surface roughness showed that some values are at the extreme limits for the sediment size present. A general idea of the magnitude of surface roughness values that are expected is determined from 300Dz Choosing a representative sediment size of 3 (0.125 mm) yields a value of surface roughness on the order of 10 -6 m. Calculated values may range from 10 -1 m to 10 -20 m with extreme outliers exhibiting a broader range, reaching 10 + 150 m at the 5.5 m bipod. Many of these values do not appear to significant physical meaning, but a relative comparison yields some interesting observations. One observation that occurs following a storm event is a decrease in surface roughness values estimated from velocity profiles. One possible explanation for this is that after the storm event, there is more suspended sediment, which may inhibit turbulence and subsequently cause greater velocities. Increased velocities would lower the surface roughness estimate by shifting the velocity profile. The 5.5 m bipod shows more scatter than the 8 m and 13 m bipods with a significant number of measurements reaching 10 -10 m or 10 -20 m. The surface roughness values calculated here do not always show a decrease with increasing currents. This may

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38 be realistic considering that this bipod may be inside the surf zone during peak waves and currents and may be influenced by breaking waves. Figure 3-11. Surface roughness variation with mean currents at 5.5 m bipod for October 15-21, 1997 Four different storm events were analyzed, one in each month, and all showed this decrease in surface roughness at the 8 m and 13 m bipods as mean currents increased. During periods of consistently large currents and waves there is a gradual decrease in surface roughness throughout the entire period. Plots of mean currents versus surface roughness trends for each bipod are included in Figures 3-11,12,13 for a single storm event in October of 1997. The different colors represent current measurements at three different elevations. At the 8 m bipod, we see a decrease in surface roughness values with the initial increase in currents to 40 cm/s, but then the currents increase rapidly to

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39 80 cm/s and the values of surface roughness are relatively stable. Perhaps the initial fine sediment has been removed with the first current increase. Figure 3-12. Surface roughness variation with mean currents at 8 m bipod for October 15-21, 1997 Comparison of surface roughness estimates at the 8 m and 13 m bipods for the week of October 15-21 show emerging trends. They both commence decreasing about the same time and have similar ending values, but there appears to be a phase lag between the two. The 13 m surface roughness values seem to increase first and decrease sooner than those at 8 m. Surface roughness values vs. mean currents at the 5.5 m bipod show much greater variation and do not follow the same relationships at the other two bipods. Surface roughnesses for the entire month of October were found to be largest during times of low currents and waves. These are on the order of one centimeter and

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40 would indicate unrealistically large bedforms, although this observation is consistent at all three bipods. These are on the same order of magnitude as the surface roughness estimates that were calculated by Smith and Wiberg (1983) when they used velocity profiles to estimate roughnesses and did not account for wave-current interaction. Figure 3-13. Surface roughness variation with mean currents at 13 m bipod for October 15-21, 1997 The possibility of error in shear velocity and surface estimates has already been addressed, but another potential problem is that the presence of bed forms would alter the shape of the velocity profile. Extensive research has examined bed forms in rivers and their effect on velocity profile estimates. Smith and McLean (1977) conducted a study in the Hood River in Oregon, which found that the velocity profile over a bedform has a

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41 convex shape in a semi-log plot, which is different than the traditional linear shape. This potential problem cannot be addressed with the limited dataset available here.

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CHAPTER 4 WAVE TRANSFORMATION IN THE NEARSHORE Introduction There is extensive research and theory in the field of Coastal Engineering that focuses on the evolution of wave properties with onshore propagation. Of particular interest due to implications for engineering design, are changes in wave direction and energy. Linear wave theory is generally accepted to provide reasonable estimates of these changes, with the understanding that there are many other nonlinear interactions involved in the process. The most basic application of linear wave theory considers a single direction and frequency, when in reality waves originate from many different directions with many different frequencies. Directional characteristics can be represented by a directional spectrum, describing, for each frequency, a range of directions with a mean wave direction. Based on wave refraction theory, the width of this directional spectrum should decrease with proximity to shore. Longuet-Higgins et al. (1991) developed a method for calculating directional spectral estimates from field data using measurements recorded by a floating buoy. Since then, many researchers have developed other formulations (Capon et al. 1967; Long and Hasselmann 1979; Herbers and Guza 1989). Borgman (1969) tested different models for design use, including what he termed a circular-normal, wrapped-around Gaussian, and a wrapped-around Hermite series expansion. There have been many other models of varying complexity developed, including some that adapt to specific properties of the data. Herbers et al. (1999) considered cross-shore evolution of the mean wave 42

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43 propagation direction and a directional spreading parameter. They tested measured values of these parameters at the spectral peak frequency against those calculated from linear wave theory and found that linear theory predicted mean wave direction and spreading well, except for the region inshore of the bar crest where waves were breaking. Calculations showed additional directional spreading of wave energy in this region, but consistency in mean propagation directions suggests that this spreading was nearly symmetric. Small amplitude wave theory assumes irrotational flow, and an impermeable and horizontal bottom, which are not realistic in a natural setting. Waves propagating over real seabeds will be affected by porosity and permeability of bottom sediment, bottom slope, and bottom surface roughness. They will also experience energy dissipation from bottom friction, due to nonlinear shear stresses created by a turbulent boundary layer at the bottom (Dean and Dalrymple 1991). White capping is an additional mechanism of energy loss, here considered to be secondary to bottom friction. There has been significant effort directed toward determining friction factors based on bottom velocity measurements. Jonsson (1966) related the friction factor to maximum bed shear stress and developed relationships with Reynolds number and bottom roughness parameters. Whitford and Thornton (1988) applied a momentum balance approach to determine bed shear stress coefficients from surf zone measurements taken at the FRF. Madsen (1994) gives explicit formulas for wave friction factors that are dependent on the relative magnitude of the current shear stress. Several recent studies have used turbulence measurements to determine near-bottom turbulent shear stress and friction factors (Trowbridge and Elgar 2001, Smyth and Hay 2002,2003). Although accomplished

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44 through many different computational techniques, these all apply linear wave theory to account for energy dissipation. One focus of the present study is to compare measured values of wave height, energy flux, and wave direction to linear wave theory estimates. Guza and Thornton (1980) investigated differences in energy density spectra predicted from horizontal velocity and calculated from pressure, and also compared measured and shoaled elevation spectra assuming onshore propagation. They found reasonably good agreement between measured and predicted spectra from measurements out to 10 m depths collected at Torrey Pines Beach in San Diego, California (Guza and Thornton 1980). Error estimates were around 20% in energy density and variance calculations, and even less for wave height comparisons, although differences determined from shoaling theory were more frequency dependent (Guza and Thornton 1980). Analysis Development of Analytical Spectrum The first step toward representing directional wave properties was to develop an analytical directional spectrum whose width could be varied to represent different wave directional spreads. The theoretical distribution that was used for the following analysis was 0220110022coscoscosmdmdmdAADmmmp where 0 is directed normal to shore and in both is limited to 22 to include only onshore wave directions (Figure 4-1). The above representation will be used to approximate the so-called measured spectra, determined from velocity and pressure

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45 measurements. D is normalized such that The subscript p represents the predicted spectrum for future nomenclature. Initially, integer values were chosen for m, but the realization that other values could be useful in fitting the data led to an extension of the analysis to non-integer values. The Fourier coefficients for several m values that are used to approximate the theoretical spectrum are included in Table 4-1. Figure 4-2 presents the ratios of the Fourier coefficients, 2/2/1dD 01dd and 02dd for different values of m. As m is increased, the theoretical spectrum becomes narrower and the ratios approach those for the delta function; which is applicable for a single direction. Figure 4-1. Coordinate system Dataset The analysis focuses on estimates of wave direction, transformation, and energy dissipation during storm conditions in the vicinity of the FRF pier at a longshore position of approximately 900 m. The dataset consists of current and pressure measurements recorded in three different water depths (nominally 5.5 m, 8 m, and 13 m), which are

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46 located at relatively similar alongshore locations, thus establishing a cross-shore array of instrumentation. Choosing records from the dataset that contain significant energy helps to assure that the measurements are meaningful. 00.511.522.500.511.52ndn/d0 m=0 m=0.5 m=1 m=2 m=3 m=4 m=5 m=6 delta fcn Figure 4-2. Ratios of Fourier coefficients (curves are fit to 3 points at n = 0,1,2) Table 4-1. Theoretical Fourier coefficients for different m values m A m d 0 d 1 d 2 d 1 /d 0 d 2 /d 0 0 0.318 0.500 0.637 0.000 1.274 0.000 0.5 0.500 0.318 0.500 0.212 1.572 0.667 1 0.637 0.250 0.424 0.250 1.696 1.000 1.5 0.751 0.212 0.375 0.255 1.769 1.203 2 0.848 0.188 0.340 0.250 1.809 1.330 2.5 0.936 0.170 0.312 0.243 1.835 1.429 3 1.019 0.156 0.291 0.234 1.865 1.500 3.5 1.090 0.146 0.273 0.226 1.870 1.548 4 1.164 0.137 0.259 0.219 1.891 1.599 4.5 1.234 0.129 0.246 0.212 1.907 1.643 5 1.293 0.123 0.235 0.205 1.911 1.667 6 1.408 0.113 0.217 0.193 1.920 1.708 fcn 1.000 0.159 0.318 0.318 2.000 2.000

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47 There are six significant storm events that occur within the four-month period discussed in previous chapters. Figure 4-3 shows a histogram of the significant wave height values measured in a water depth of eight meters for each thirty-four minute record of the four months. To obtain representative results, three samples were analyzed from each of the six storms. The range of significant wave heights included in this analysis is 1.75 m < Hs < 3.5 m. One assumption employed here is Snells Law considering bathymetry consisting of straight and parallel bottom contours. Figure 4-4 presents bathymetry in the area around the time that these data were collected and the red circles represent the approximate locations of the 5.5 and 8 m bipods. The bipods are located near profile line 66 in the plot, which is an area where this assumption is reasonable. Figure 4-3. Significant wave heights measured in October 1997, November 1997, May 1998, and August 1998

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48 Figure 4-4. Bathymetry in vicinity of bipod instrumentation (13 m bipod is located 690 m offshore of 8 m bipod; http://www.frf.usace.army.mil) Development of Directional Spectrum from the Data Directional spectral estimates were determined from the measured data during significant storm events using the p-u-v method, which follows the work of Longuet-Higgins et al (1961). The following equations used to calculate the directional spectrum are based on pressure represented in feet of water. The coordinate system is taken as positive onshore and south for the measured velocity components, u and v (Figure 4-1). For simplicity, this analysis considers the pressure sensor and current meter to be located at the same horizontal location and distance above the bottom. The auto and cross spectra are calculated with a segment length of N=128, which gives a resolution of

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49 0.015 Hz and 64 degrees of freedom. The actual number of degrees of freedom is somewhat greater due to the fact that half-lapped segments are used. The energy density spectrum is represented by ,,fDSfS where the directional spectrum is approximated by the Fourier series )2cos()cos(,0220110 fCfCfAfD The coefficients are calculated as follows (Longuet-Higgins et al., 1961) 210fA zkzkfSfSfApupu1 khzhkfzkusinhcosh2 khzhkzkpcoshcosh )(22zkfSfSfSfAuvvuu zkzkfSfSfBpupv1 zkfSfSfBuuv222 The values of C and n n0 are determined as 2,1,22nfBfAfCnnn 2,1,tan10nABfnnn

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50 The mean wave direction 0 for each frequency to be used in calculations is taken as the location of the maximum value of the computed directional spectrum. The directional spectrum as determined above will be referred to as the measured directional spectrum in future discussion, although this is an estimate from the data. Figure 4-5 presents an example of the measured directional spectra at the bottom current meter for the 5.5, 8, and 13 m bipods at the peak frequency of 0.094 Hz. Time is measured in hour-minutes, where 100 represent 1 h and 1 represents 1 min. Figure 4-5. Measured spectra for November 7, 1997 time=2200 Table 4-2 presents measured mean wave direction values in degrees for the peak frequency of each storm event. These values are averaged over the three current meters at each location. The last column includes corresponding peak direction values that were

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51 calculated by the FRF using the iterative maximum likelihood method from measurements recorded at the 8m array of 15 pressure gages. The 8 m array values are often different than the measured mean wave directions at the 8 m bipod, sometimes by up to 14 degrees. These are calculated for longer records of 2.5 h versus 34 min, but the differences bring up a concern for the accuracy of measured mean wave direction estimates. Measurements are expected to show mean wave directions approaching closer to onshore 00 at shallower water depths, and this is generally the case, with several exceptions. Table 4-2. Measured mean wave directions at peak frequency Date Time f (Hz) 130 80 50 mArrayp8 19-Oct-97 700 0.141 35.3 36.5 32.7 22.0 19-Oct-97 1216 0.125 39.7 33.7 32.0 20.0 20-Oct-97 100 0.094 18.4 19.2 16.5 12.0 7-Nov-97 2200 0.094 18.2 16.0 10.9 10.0 7-Nov-97 2342 0.094 17.7 11.3 14.5 10.0 8-Nov-97 208 0.094 18.7 20.8 12.8 10.0 13-Nov-97 1742 0.133 22.2 19.4 12.0 12.0 13-Nov-97 2008 0.125 12.2 16.0 14.5 10.0 13-Nov-97 2200 0.117 13.2 9.7 7.8 5.0 13-May-98 852 0.086 8.7 9.8 10.2 14.0 13-May-98 1442 0.078 12.4 7.5 12.7 6.0 13-May-98 1816 0.078 8.7 9.8 10.2 12.0 2-Aug-98 916 0.133 8.9 5.0 3.7 8.0 2-Aug-98 1300 0.133 4.2 3.5 1.7 -10.0 2-Aug-98 1516 0.133 6.8 1.9 3.2 -10.0 27-Aug-98 1408 0.094 -36.7 -31.8 -29.5 -32.0 27-Aug-98 1634 0.086 -35.2 -33.6 -31.4 -28.0 27-Aug-98 1816 0.086 -32.4 -23.2 -26.4 -28.0 Determination of m Values in 02cosmmpAD The m value that gives the best-fit analytical spectrum to the measured data is determined through implementation of two different approaches. The first approach

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52 deals directly with the coefficients of the measured and predicted spectra, while the second employs a curve fitting technique. The primary purpose of discussing the first approach is to emphasize that the second approach gives a greatly improved fit, although it has some limitations. Comparison of Fourier coefficients The spectrum 02cosmmpAD was determined by matching Fourier coefficient ratios 01 dd and 02dd This approach was based on determining m to minimize as follows fmz, 2022012020220101,fAfCfAfCddfAfCddfAfCfmzmm A cutoff of 6 was used for m in recognition that the measured spectra were generally wide and including higher m values would not provide an improved fit. Generally, the central frequencies give higher best-fit m coefficients on the order of 4 to 6, producing a narrower theoretical spectrum. The higher frequencies, and sometimes even the lower ones, give a smaller best-fit m coefficient on the order of 2. Figure 4-6 a, b show this trend. The 5.5 m bipod measurements often determine almost all best-fit values to be the maximum allowed in this analysis (m max =6). Plot c of Figure 4-6 is one example. These values follow the general trend expected; with larger m values at inshore bipods, yet the fit to measurements is not very good. Figure 4-7 compares the measured (solid line) and fit (dashed line) directional spectra for the same three runs at a frequency of 0.13 Hz. Predicted spectra are much too narrow. Error values determined from

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53 niipimDDn1221 are presented in Figure 4-8 over the entire frequency range and they are extremely high. Minimization of the error between coefficients does not imply that the error between the spectra is at a minimum. Two-sided nonlinear fit This second approach attempts to provide a better fit by focusing on direct least squares fit rather than matching directional spectral coefficient ratios. The measured spectrum is often very wide, extending past the offshore directional limit of 2 This makes it difficult for a spectrum 02cosmmpAD based on a single m value to give an accurate prediction, since it is forced between the limits of 2 and 2 This problem was overcome by fitting a different m value to each side of the measured spectrum. The modified formulation for the analytical spectrum is 02cos)(LmpLAD 02 02cosRmpRAD 20 The subscripts L and R denote values for the left and right side of the directional spectrum respectively, and A is the same for both sides. The best-fit values of m L m R and A are determined through a nonlinear least squares data fitting technique, utilizing the Gauss-Newton method. Plots are included (Figures 4-9,10) of measured and predicted spectra and error calculations for the same data included in Figures 4-7 and 4-8 to facilitate an appreciation

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54 Figure 4-6. Error versus m value comparison for October 20, 1997 time=100 a) 13 m b) 8 m c) 5.5 m

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55 Figure 4-7. Comparison of measured and best-fit spectra from matching coefficients for October 20, 1997 time=100 a) 13 m b) 8 m c) 5.5 m of the quality of the fit. It is evident that the fit is greatly improved, with significantly lower error values by more than an order of magnitude. Note that the predicted spectra are forced to zero at 90 degrees, because allowing waves to come from onshore would be unrealistic. The best-fit m values for each side of the spectrum vary with frequency. Representative plots are presented in Figure 4-11 for measurements from the 8 m bipod bottom current meter. There is a general trend of increasing separation between left and right m values with increasing frequency. The decrease of m R for 00 is a result of the increasing percentage of the measured spectrum that is outside of the 2 2 range

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56 with increasing frequency. This trend can be observed in Figure 4-12, which includes measured and predicted directional spectra at different frequencies, for the run included in plot c of Figure 4-11. The low frequency spectrum has the entire width contained within the range of onshore directions, since this energy probably represents storm swell that has traveled a significant distance and is dominantly oriented onshore. Higher frequency plots show an increasing portion of the width on the right side to be outside of this range as the mean direction increases, so best-fit m coefficients that provide the smallest error are not necessarily representative of the measured spectrum. Figure 4-8. Error between spectra fitted from coefficient ratios for October 20, 1997 time=100 The left side m values increase slightly with increasing frequency. The right side values show a decrease, but it is primarily due to a limitation of the method and probably not a meaningful trend. This problem arises because the width of the measured spectrum

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57 is very large. One way to overcome this would be to use a more accurate method of predicting the measured spectrum, which would most likely decrease the width and eliminate or minimize the percentage of the directional spectrum outside of the 2 range. Figure 4-9. Comparison of measured and best-fit spectra from curve fitting for October 20, 1997 time=100 a) 13 m b) 8 m c) 5.5 m Comparison of Data to Linear Wave Theory Calculations The bipod measurements provide a basis for testing linear wave theory by comparing theoretical values at inshore water depths to the associated measurements by the bipod instrumentation. In the following analysis, calculated directional spectrum values are determined by refracting data from the13 m bipod and will have a subscript

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58 c. Measured values are those determined directly from bipod instrumentation at the water depth of interest and will have a subscript m. Figure 4-10. Error between spectra from curve fitting for October 20, 1997 time=100 These comparisons are conducted within the frequency range of 0.05 to 0.2 Hz, which is the frequency range of significant energy evident from pressure measurements. The high frequency cutoff is chosen as 0.2 Hz because the water surface energy density spectral fS values that are calculated from the pressure response factor zkp begin to increase unrealistically at higher frequencies at the 13 m bipod, and are not representative of field conditions. This is evident in Figure 4-13. This cutoff is also consistent with linear wave theory since 0.2 Hz represents a wave period of 5 s, and at a

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59 water depth of 13 m waves with a period of less than 4 s would be deep-water waves and would not interact with the bottom. Figure 4-11. Variation of m values with frequency range at 8 m a) May 13, 1998 time=852 b) November 7, 1997 time=2200 c) October 19, 1997 time=700 Figure 4-12. Directional spectrum variation with frequency at 8 m bipod for October 19, 1997 time=700

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60 Figure 4-13. Energy density spectral values for October 19, 1997 time=700 a) 13 m b) 8 m c) 5.5 m Wave direction A first comparison is of measured and calculated central wave direction 0 values from directional spectral estimates. Snells Law is applied to find refracted wave direction values at the two inshore bipods. The calculated wave direction is defined as 1313818sinsinCCmc and the measured wave direction 8m as the direction of the maximum value of the computed directional spectrum. Figure 4-14 includes a plot of measured vs. calculated wave directions at the 5.5 m and 8 m bipods on October 19, 1997. The different symbols represent measurements from each of the three current meters. Measured mean wave

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61 directions at the 8 m bipod appear to be well predicted, while those at the 5.5 m bipod show a slight offset. Figure 4-15 compares these same values at the 5.5 m bipod in a different format. Plot a presents measured angles in degrees and plot b presents the difference in measured and calculated angles cm in degrees. There is a deterioration of measured and calculated directions in the low frequency range since there is not significant energy present and directional spectral estimates become less meaningful. This specific plot shows an overall slight offset of approximately seven degrees. Figure 4-14. Mean wave direction comparison for October 19, 1997 time=700 Average values between the three current meters for each of 3 records in October 1997 are presented in Figure 4-16. These values represent the difference in measured and calculated angles cm in degrees. It is important to note that the large variation between measured and calculated wave directions at low frequencies is a result of the wave direction deterioration shown in Figure 4-15. In the frequency range with significant energy, the differences fluctuate around zero, suggesting that angles are predicted fairly well by linear theory. When there does appear to be an offset, it is usually positive, which represents greater measured values. This suggests that linear

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62 theory refracts the angles too much toward normal incidence in these instances. m cm Figure 4-15. Measured and calculated wave direction differences for October 19, 1997 time=700 at 5.5 m bipod a) degrees b) degrees Refracted m values An extension of the refracted angle analysis is to determine how well the directional spectrum at inshore bipod locations can be predicted from refraction of directional spectral estimates from the offshore bipod. This is accomplished by comparing best-fit m values for a refracted directional spectrum versus those for a measured directional spectrum at 8 m and 5.5 m water depths. The refracted directional spectrum is (Lee et al. 1980)

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63 fkfkfDfDpc1313,, where has been normalized to have an area of one. The corresponding 13pD values for the refracted spectrum are 13131sinsinCCc The refracted spectrum is also normalized to one before fitting m values using Figure 4-16. Average measured and calculated wave direction differences for October 1997 a) cm degrees 8 m b) cm degrees 5.5 m

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64 2/2/,1,,dfDfDfDccc Best-fit m L and m R values for the refracted spectra are determined using the method discussed previously. The curve fitting procedure was used since this was determined to provide a much better fit than the alternate approach. Figure 4-17. Measured and refracted directional spectra for November 13, 1997 time=1742 Sample refracted and measured spectra for November 13, 1997 at a frequency of 0.13 Hz are presented in Figure 4-17. The refracted spectra are narrower than those measured at both inshore bipod locations. This suggests that linear theory predicts more refraction than associated with the measurements. This comparison is further reflected in the values of m coefficients. Figure 4-18 shows that refracted m values are greater than measured values, and show a slight decrease with increasing frequency as opposed to the slight increase of measured m values. The measured right side coefficients are much lower for reasons discussed previously. The difference between measured and refracted

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65 spectral widths may also be affected by the method chosen to estimate the measured directional spectra. Figure 4-18. Comparison of refracted and measured m values over frequency range for November 13, 1997 time=1742 a) 8 m b) 5.5 m Wave height comparisons The previous analysis focusing on direction leads to a comparison of significant wave height values by applying the concept of conservation of energy flux. Energy flux is defined as mgCgSf cos A calculated water surface spectrum was obtained at the 8 m inshore bipod location using the equation

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66 8)13(813)13(8coscoscmggmcCCfSfS and similarly for the 5.5 m inshore bipod. In the above equation the value of m was taken as the location of the maximum value of the computed directional spectrum. This leads to slightly larger energy flux values than if the entire range of directions was considered. The zero moment of the water surface spectrum gives a significant wave height value of 04mHmo dffSmHzHz2.005.00 and calculated and measured values are obtained by using the respective water surface spectra. Ratios of measured to predicted values of significant wave height for the 18 records considered are plotted in Figure 4-19. This shows most measured values being less than predicted since almost all of the ratios at the inshore bipods are less than 1, ranging from a 5% increase to a 25% decrease. This decrease is expected since friction losses have not yet been considered. Energy flux comparisons Measured energy flux values are found for each bipod location and compared by considering the percent loss between bipods. The percent energy loss between the 13 m and 8 m bipods is determined from

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67 %100*)()()(%2.005.0132.005.02.005.0813HzHzmHzHzHzHzmmdffdffdffloss and similarly for the distance between the 8 m and 5.5 m bipods. Table 4-3 shows the average energy loss values of the three current meters at the bipod for each record, with negative percent values representing cases that had greater measured energy flux values at inshore bipods. There are many instances of significant loss, with some reaching more than one third of the total energy flux. This enforces the need to consider energy loss in Figure 4-19. Significant wave height ratios versus cross-shore position (FRF coordinate system)

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68 engineering design and planning, since neglecting this component would lead to a significant overestimation of energy flux values in many cases, especially for propagation over long distances. Figure 4-20 shows the average energy flux variation over frequency range for all 18 storm events, and includes percent loss of average energy flux values. The dashed lines in plots b and c indicate the measured energy flux at the offshore bipod, which is the same as that which would be predicted with no energy loss. These are compared to the measured values shown by the solid lines. There are different cross-shore separation distances between the three bipods. The 13 m and 8 m bipods are separated by 690 m in the cross-shore direction, whereas the 8 m and 5.5 m bipods are separated by only 333 m. Of interest is that the average percent energy loss between the 8 m and 5.5 m bipods is greater than between the 13 m and 8 m bipods (Table 4-3), even though the separation distance for the smaller percentage energy loss is twice as long. The percent energy losses of the average values included in Figure 4-20 also indicate this trend. Of course, the reason is that bottom friction is more effective in causing energy loss in shallower water. Friction factor The wave height and energy flux analyses showed over-prediction from linear theory since energy loss was not considered. This analysis assumes friction is the only cause of energy change between bipods. In reality there are many other contributing factors, including the possibility of energy growth due to wind, energy loss due to white capping, or the redistribution of energy within the spectrum due to non-linear interactions. By accounting for frictional energy loss in the energy flux calculation, a representative friction factor can be determined for the site.

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69 Table 4-3. Average % energy loss values between bipods Year Month Day Time % Loss (13 8) % Loss (8 5.5) 1997 10 19 700 17.12 1.11 1997 10 19 1216 25.76 -1.18 1997 10 20 100 -7.11 10.13 1997 11 7 2200 2.45 3.28 1997 11 7 2342 35.57 -8.18 1997 11 8 208 -12.34 5.51 1997 11 13 1742 10.74 8.61 1997 11 13 2008 -17.13 27.13 1997 11 13 2200 17.58 22.75 1998 5 13 852 20.70 16.55 1998 5 13 1442 3.47 21.01 1998 5 13 1816 20.26 21.08 1998 8 2 916 10.87 0.84 1998 8 2 1300 -5.77 2.95 1998 8 2 1516 -2.99 14.12 1998 8 27 1408 14.65 28.41 1998 8 27 1634 25.24 27.74 1998 8 27 1816 15.61 25.81 Average 9.70 12.65 The friction factor is estimated using xdfdfDbDaHzHzbHzHza212.005.02.005.0 whereis the total cross-shore distance between the 13 and 5.5 m bipods, and x D is the energy loss term expressed as 38bbxyDuffu which accounts for energy damping by bottom friction. In this expression, uis the velocity time series measured at the bottom current meter, located approximately 20 cm above the bottom, and represents the friction factor. Figure 4-21 shows surveyed bathymetry that was collected near the bipod locations and around the same general b ff

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70 timeframe that the data were collected, giving some insight into the bottom characteristics between instruments. These survey lines were measured at the FRF using the Coastal Research Amphibious Buggy (CRAB) and Lighter Amphibious Resupply Cargo (LARC). Specific dates are included in the legend. Figure 4-20. Average measured and predicted energy flux values a) 13 m b) 8 m c) 5.5 m The calculated friction factors of interest are those resulting from total velocity measurements taken at the bottom current meter, since this velocity is the most representative of the bottom velocity. This total velocity is calculated as the magnitude of the instantaneous velocity vector. These friction factors are included in Table 4-4. Most values from the bottom current meter are in the range of 0 to 0.2, although there is a considerable spread from 0 to 0.32. The mean and standard deviation values for the

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71 bottom current meter are 0.116 and 0.105 respectively. The negative value on August 2, 1998 is probably not real, since the bottom current meter had a flag for low beam correlation. The other current meters gave estimates of 0.009 and 0.014 for that record, which are more reasonable. Friction factor estimates from velocities measured at the higher current meters were found to check for consistency. A histogram of all of the calculated values is shown in Figure 4-22. Combining values from all current meters gives a mean of 0.094 and a standard deviation of 0.08. Figure 4-21. Surveyed bathymetry in vicinity of bipod instrumentation It does not seem unreasonable to find a range of factors during storms and for different storm conditions since friction factors can change as currents increase and sediment is displaced. Figure 4-23 shows that friction factors generally increase with significant wave height values. It is important to note that if the highest waves were

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72 breaking before reaching the 5.5 m bipod, then friction factors would be unrealistically high, since the calculation assumes that all energy dissipation is from bottom friction. Table 4-4. Friction factor estimates from bottom current meter Date Time ff H mo 10/19/1997 700 0.101 2.28 10/19/1997 1216 0.111 2.86 10/20/1997 100 0.025 2.22 11/7/1997 2200 0.056 1.88 11/7/1997 2342 0.283 2.09 11/8/1997 208 -0.029 1.63 11/13/1997 1742 0.154 2.81 11/13/1997 2008 0.1 2.82 11/13/1997 2200 0.318 3.01 5/13/1998 852 0.165 3.31 5/13/1998 1442 0.094 2.99 5/13/1998 1816 0.246 3.43 8/2/1998 916 0.016 2.1 8/2/1998 1300 -0.083 2.19 8/2/1998 1516 0.042 2.11 8/27/1998 1408 0.129 3.35 8/27/1998 1634 0.177 3.45 8/27/1998 1816 0.186 3.13 Average 0.116 Standard Deviation 0.105 It seems useful to determine a single representative friction factor for this specific location. This was accomplished by using average energy flux and energy loss values over all 18 storm events in the above equation. This analysis resulted in a friction factor of 0.170 between the 13 m and 8 m water depths and 0.177 between 8 m and 5.5 m water depths. These two values are consistent and 0.17 is determined as a representative friction factor in the vicinity of the bipod instrumentation. Reynolds Stresses Another approach to examine shear stress was through calculation of the Reynolds stresses. These are related to shear stress by the following equations

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73 'wuzx ''wvzy where positive values are onshore and south. The time series were filtered to include only the frequencies within the range 0.05 to 0.2 Hz. It was expected that these values would be comparable to shear stress values calculated from the velocity profile method discussed in Chapter 3. Those values generally ranged from 0 to 0.5 N/m 2 as calculated based on mean velocities. The stresses based on Reynolds stresses are larger, but they represent shear stress values determined from the oscillatory velocity component. Examples of values for October 1997 are presented in Table 4-5. The notation X1, X2, and X3 represents the bottom, middle, and top current meters respectively. Figure 4-22. Histogram of calculated friction factors at all current meters

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74 -0.15-0.1-0.0500.050.10.150.20.250.30.3501234Hmo mff Figure 4-23. Friction factor variation with wave height at the bottom current meter One disturbingly consistent feature of these results is that the values at the middle current meter often have a different sign and magnitude than the other two current meters, at all three bipod locations. If there was flow reversal within the water column, these values would be expected to show a trend. If there was a problem with the current meter at a specific bipod, the anomalous value should be present only at one location. Neither of those situations occurs, and this consistency is present throughout all four months. At present, this feature cannot be explained. Discussion To reinforce the analysis presented in this chapter, this section provides a brief overview of primary discussion points. The analytical spectrum establishes a simplified representation of directional properties of the wave data that can be used to approximate the measured spectrum, obtained through a direct Fourier Transform method. Later comparisons are facilitated by considering the m value, or power of the cosine curve as a measure of the properties of the spectrum. The first approach matched Fourier

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75 coefficients to the data, but this resulted in a poor fit to the directional spectra. The second approach employed a curve fit to individual sides of the spectrum, which gave a vastly improved fit. One limitation of this approach is that measured spectra often extend beyond the 90 limits, giving unrealistically low right side m values for 00 Table 4-5. Reynolds stresses for October 1997 (X1, X2, X3 represent bottom, middle and top current meters respectively) Date Time Gage ''wuzx ''wvzy 10/19/1997 700 13X1 1.66 0.68 13X2 -2.34 -0.36 13X3 2.23 1.43 8X1 2.50 1.69 8X2 -6.79 -2.81 8X3 4.67 4.67 5X1 -0.96 -0.51 5X2 -15.27 -7.37 5X3 -1.34 -1.01 10/19/1997 1216 13X1 2.20 1.44 13X2 -8.20 -3.74 13X3 3.25 2.72 8X1 0.88 1.74 8X2 -10.23 -4.91 8X3 7.33 3.91 5X1 5.66 4.76 5X2 -15.23 -5.18 5X3 0.97 1.93 10/20/1997 100 13X1 3.77 0.74 13X2 -7.67 -2.87 13X3 3.77 1.79 8X1 6.68 2.44 8X2 -15.03 -5.58 8X3 3.88 3.15 5X1 -0.93 -0.59 5X2 -17.12 -4.23 5X3 -3.65 0.34 A second focus was to compare measurements with linear wave theory predictions. Refracted mean wave direction angles were similar to measurements. If

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76 offsets were present, they usually represented too much refraction by linear wave theory. Interestingly, when refracting the entire directional spectrum, the width was narrower than that which was measured, representing an overestimation by refraction theory on the whole. This trend is also reflected in the refracted and measured m value comparisons. The wave height and energy flux calculations combined shoaling and refraction theory and showed smaller measured values, as expected when energy losses are not accounted for. Friction factors were estimated by accounting for energy losses, and most values were in the range of 0 to 0.2, although these appear to vary with storm conditions. A representative value of 0.17 was identified for this location using average energy flux and energy loss values. Calculated Reynolds stresses were very strange with the middle current meter yielding significantly different values at all three water depths; this effect remains unexplained.

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CHAPTER 5 CONCLUSIONS A knowledge of wave characteristics, sediment characteristics, and bed elevation within the nearshore zone are imperative for engineering design and planning purposes. Predictions of these processes are utilized when making decisions regarding coastal development and beach preservation. Improving our knowledge of nearshore processes and the accuracy of current prediction results is required for coastal planners to make better decisions. This study presents analysis of sonar, pressure, and current measurements to evaluate erosion thresholds, wave evolution and bottom friction results. Comparisons between mean current and sonar measurements in Chapter 1 defined a mean current threshold of 20 cm/s for bed erosion. In addition, this comparison highlights the need to consider fair-weather conditions for sediment transport, since many significant bed elevation changes occurred when wave heights were less than 2 m. No orbital velocity threshold was determined, but combined waves and currents always caused a bed elevation change when velocities reached 60 cm/s. Alongshore currents appeared to coincide with wind velocities, though cross-shore currents did not. Sonar histograms at the 5.5 m and 13 m bipods generally showed a well-defined peak with minimal spreading, lending confidence to sonar estimates of bottom elevation. The 8 m bipod consistently showed spreading at depths greater than the peak, an observation that remains unexplained. One situation in late August 1998 at the 13 m bipod shows two peaks following a significant storm event. This may be an indication of 77

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78 the presence of fine, silty material, although this hypothesis cannot be validated with confidence. Velocity profile analyses provided estimates of shear velocity and surface roughness. The shear velocity proved a good indicator of bottom elevation change at the 8 m and 13 m bipods, with erosion beginning zero to three hours after it crossed the threshold for movement. Shear velocity estimates at the 5.5 m bipod always remained below this threshold. Surface roughness values at the 8 m and 13 m bipods decreased with increasing mean currents. The 5.5 m bipod experiences more scatter in surface roughness estimates and does not always follow this relationship. Comparisons of the variation in surface roughness values at the 8 m and 13 m bipods indicate a phase lag, with 13 m values increasing first and decreasing sooner than 8 m. Chapter 4 focused on evolution of wave characteristics. Measured directional spectra were obtained for each bipod location using the Direct Fourier Transform method. A simplified analytical spectrum based on a cosine curve of varying power (m) was used to approximate measured values. A nonlinear least-squares curve fit to each side of the measured spectrum proved the most accurate way of determining best-fit m values. Limiting wave directions to onshore introduced some problems with m R predictions being unrealistically low when measured spectra were outside of this range. Unfortunately, this could not be avoided since allowing waves to come from onshore would not be realistic. The comparison with theoretical calculations employed shoaling and refraction theory. Refracted mean wave directions were similar to those measured, with a slight overrefraction by the theory. On the whole, the theory predicted a narrower spectrum

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79 than that measured, representing overrefraction. This may be expected at the 5.5 m bipod if it were inside the surf zone, since there can be directional spreading associated with wave breaking. This same observation at the 8 m bipod seems more surprising. It is very possible that this result represents a limitation of the method used to estimate measured directional spectra. Energy flux calculations emphasized the need to consider energy loss, which reached as high as one third of measured energy flux values. Friction factors showed considerable variation with storm conditions, although most values fell within the range of 0 to 0.2. This is reasonable, as storm conditions encompass varying current intensities that interact with bottom sediment, affecting roughness and subsequently energy loss from bottom friction. Through utilization of average energy flux and energy loss values, a representative friction factor of 0.17 was determined for the area in the vicinity of bipod instrumentation. Reynolds stress calculations yielded unexpected results. The bottom and top current meter shear stress estimates were consistent in magnitude and direction. The middle current meter values were inconsistent at all three bipod locations. The systematic occurrence of this feature in measurements recorded by different instruments suggests validity, yet the cause remains unexplained. One specific area where these results could be improved for future discussion is in the representation of measured directional spectra. This analysis utilized a simple technique, and much work has been done to improve upon this method and develop techniques that are data adaptive. The measured spectra were very wide, which caused problems when fitting the analytical representation and may have influenced results from the refraction comparison. Another limitation of this analysis deals with the erosion

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80 discussion, since the sonar measurements only record bottom elevation change. Similar studies have incorporated suspended sediment measurements or side scan sonar images, which provide a more complete basis for sediment transport determination.

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LIST OF REFERENCES Beach, R. A. and R. W. Sternberg (1996). Suspended-sediment transport in the surf zone: response to breaking waves. Continental Shelf Research 16(15): 1989-2003. Beavers, R. L. (1999). "Storm Sedimentation on the Surf Zone and Inner Continental Shelf, Duck, North Carolina." Thesis. Geology, Duke University. Beavers, R. L., P. A. Howd, W. A. Birkemeier, and K. K. Hathaway (1999). "Evaluating profile data and depth of closure with sonar altimetry." Coastal Sediments 1: 479-490. Long Island, NY, ASCE. Birkemeier, W. A., A. W. Dewall, C. S. Gorbics, and H.C. Miller (1981). "A user's guide to CERC's Field Research Facility." CERC Miscellaneous Report 81-7, US Army Corps of Engineers (US ACE), Coastal Engineering Research Center, Fort Belvoir, Va. Borgman, L. E. (1969). "Directional spectra models for design use." Offshore Technology Conference 1: paper no. OTC-1069. Houston, Texas. Capon, J., Greenfield, R. J. and Kolker, R. J. (1967)."Multidimensional maximum-likelihood processing of a large aperture seismic array." Proc. IEEE 55 192-211. Conley, D. C. and R. A. Beach (2003). Cross-shore sediment transport partitioning in the nearshore during a storm event. Journal of Geophysical Research 108(C3): 3065. Dean, R. G. and R. A. Dalrymple (1991). Water Wave Mechanics for Engineers and Scientists World Scientific, Singapore. Dean, R. G. and R. A. Dalrymple (2002). Coastal Processes with Engineering Applications Cambridge, MA, Cambridge University Press. Dolan, R. and R. E. Davis (1992). Rating northeasters. Mariners Weather Log 36: 4-16. Dolan, R., H. Lins, and B. Hayden (1988). Mid-Atlantic coastal storms. Journal of Coastal Research 4: 417-433. Elgar, S., E. L. Gallagher, and R. T. Guza (2001). Nearshore sandbar migration. Journal of Geophysical Research 106(C6): 11,623-11,627. 81

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82 Gallagher, E. L., S. Elgar, and R. T. Guza (1998). Observations of sand bar evolution on a natural beach. Journal of Geophysical Research 103(C2): 3203-3215. Grant, W. D. and O. S. Madsen (1979). Combined wave and current interaction with a rough bottom. Journal of Geophysical Research 84(C4): 1797-1808. Green, M. O. and J. D. Boon (1988). Response characteristics of a short-range, high-resolution digital sonar altimeter. Marine Geology 81: 197-203. Guza, R. T. and E. B. Thornton (1980). Local and shoaled comparisons of sea surface elevations, pressures, and velocities. Journal of Geophysical Research 85(C3): 1524-1530. Guza, R. T. and E. B. Thornton (1985). Velocity moments in nearshore. ASCE Journal of Waterway, Port, Coastal and Ocean Engineering 111: 235-256. Harris, C. K. and P. Wiberg (2002). Across-shelf sediment transport: Interactions between suspended sediment and bed sediment. Journal of Geophysical ResearchOceans 107(C1): Art. No. 3008. Herbers, T. H. C., S. Elgar, and R. T. Guza (1999). Directional spreading of waves in the nearshore. Journal of Geophysical Research-Oceans 104(C4): 7683-7693. Herbers, T. H. C. and R. T. Guza (1989). "Estimation of wave radiation stresses from slope array data." Journal of Geophysical Research 94: 2099-2104. Hoefel, F and S. Elgar (2003). "Wave-induced sediment transport and sandbar migration." Science 299: 1885-1887. Howd, P. A., R. L. Beavers, and K. K. Hathaway (1994). Shoreface morphodynamics I: Cross-shore scales of fluid flows. EOS, Transactions, American Geophysical Union : 339. Jonsson, I. G. (1966). "Wave boundary layers and friction factors." Proceedings of the 10th International Conference on Coastal Engineering 1: 127-148. Tokyo, Japan, ASCE. Keen, T. R., R. L. Beavers, P. A. Howd, and K. K. Hathaway (2003). Shoreface sedimentation during a northeaster at Duck, North Carolina, U.S.A. Journal of Coastal Research 19(1): 24-40. Lee, Y. K., F. H. Wu, W. Wier, P. Parnicky, and D. DeMers (1980). "Methodology for computing coastal flood statistics in southern California." Pasadena, CA, Tetra Tech Inc. Leffler, M. W., C. F. Baron, B. L. Scarborough, P. R. Hodges, C. R. Townsend (1998). "Annual data summary for 1995 CHL Field Research Facility." Technical Report CHL 97-14, USACE, Waterways Experiment Station, Vicksburg, MS.

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83 Long, R. B. and K. Hasselmann (1979). "A variational technique for extracting directional spectra from multi-component wave data." Journal of Physical Oceanography 9: 373-381. Longuet-Higgins, M. S., D. E. Cartwright, and N. D. Smith (1963). "Observations of the directional spectrum of sea waves Using the motions of a floating buoy." Ocean Wave Spectra Easton, MD, Prentice-Hall. Madsen, O. S., Y. Poon, and H. C. Graber (1988). "Spectral wave attenuation by bottom friction: Theory." Proceedings of the 21st International Conference on Coastal Engineering 1: 492-504. Delft, Netherlands, ASCE. Madsen, O. S., L. D. Wright, J. D. Boon, and T. A. Chisholm (1993). Wind stress, bed roughness and sediment suspension on the inner shelf during an extreme storm event. Continental Shelf Research 13(11): 1303-1324. Miller, H. C., S. J. Smith, D. G. Hamilton, and D. T. Resio (1999). "Cross-shore transport processes during onshore bar migration." Coastal Sediments 2: 1065-1080. Long Island, NY, ASCE. Nearhoof, S. L. (1992). Box core data set survey line 62. Duck, NC, CERC Field Research Facility. Osborne, P. D. and B. Greenwood (1992). Frequency dependent cross-shore suspended sediment transport. 1. A non-barred shoreface. Marine Geology 106: 1-24. Smith, J. D. and S. R. McLean (1977). Spatially averaged flow over a wavy surface. Journal of Geophysical Research 82(12): 1735-1746. Smyth, C. and A. E. Hay (2002). Wave friction factors in nearshore sands. Journal of Physical Oceanography 32: 3490-3498. Smyth, C. and A. E. Hay (2003). Near-bed turbulence and bottom friction during SandyDuck97. Journal of Geophysical Research 108(C6): 3197. Stauble, D. K. (1992). "Long term profile and sediment morphodynamics: Field Research Facility case history." Technical Report CERC-92-7, US ACE, Waterways Experiment Station, Vicksburg, MS. Stauble, D. K. and M. A. Cialone (1996). "Sediment dynamics and profile interactions: Duck94." Proceedings of the 25th International Conference on Coastal Engineering 4: 3921-3934. Orlando, FL, ASCE. Trowbridge, J. and S. Elgar (2001). Turbulence measurements in the surf zone. Journal of Physical Oceanography 31: 2403-2417. US ACE. SandyDuck '97 sediment samples, CHL Field Research Facility, http://frf.usace.army.mil/geology/sediments.stm. Accessed November, 2003.

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84 Whitford, D. J. and E. B. Thornton (1988). "Longshore current forcing at a barred beach." Proceedings of the 21st International Conference on Coastal Engineering 1: 77-90. Costa del Sol-Malaga, Spain, ASCE. Wiberg, P. and J. D. Smith (1983). A comparison of field data and theoretical models for wave-current interactions at the bed on the continental shelf. Continental Shelf Research 2: 147-162. Wright, L. D. (1995). Morphodynamics of Inner Continental Shelves Boca Raton, FL, CRC Press. Wright, L. D., J. D. Boon, S. C. Kim, and J. H. List (1991). Modes of cross-shore sediment transport on the shoreface of the Middle Atlantic Bight. Marine Geology 96: 19-51. Wright, L. D., J. D. Boon, III, M. O. Green, and J. H. List (1986). Response of the mid shoreface of the southern mid-Atlantic bight to a "Northeaster". Geo-Marine Letters 6: 153-160. Wright, L. D., J. P. Xu, and O. S. Madsen (1994). Across-shelf benthic transports on the inner shelf of the middle Atlantic bight during the "Halloween Storm" of 1991. Marine Geology 118: 61-77. Xu, J. P. and L. D. Wright (1998). Observations of wind-generated shoreface currents off Duck, North Carolina. Journal of Coastal Research 14(2): 610-619.

PAGE 97

BIOGRAPHICAL SKETCH Jodi Eshleman was born in Pittsburgh, Pennsylvania on May 22, 1980. After graduating high school in 1998, she attended Lehigh University, located in Bethlehem, Pa. There she developed a passion for addressing water-related issues worldwide. She completed a bachelors degree in Civil Engineering in the spring of May, 2002. Many summer vacations spent along the Atlantic coast gave her a love of the beach; and recent trips to the Outer Banks of North Carolina brought an awareness of the sensitive balance between coastal development and beach sustainability. This led her to the Coastal Engineering program at the University of Florida, to pursue a Master of Science degree. 85


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NEARSHORE WAVE AND SEDIMENT PROCESSES: AN EVALUATION OF
STORM EVENTS AT DUCK, NC















By

JODI L. ESHLEMAN


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


2004


































Copyright 2004

by

Jodi L. Eshleman

































This thesis is dedicated to my parents, who provided unconditional support throughout
my entire education.















ACKNOWLEDGMENTS

I would like to thank the Army Corps of Engineers Field Research Facility (FRF)

in Duck, NC for providing the data used in this investigation. I extend my greatest

appreciation to the staff at the FRF, who gave me the opportunity to gain some valuable

field experience and were always willing to offer advice and encouragement. I

acknowledge specifically Kent Hathaway, Chuck Long, and Bill Birkemeier, whose input

was vital to this research. I thank all of the FRF for spending countless hours helping me

with everything from analyzing data through interpretation. I would also like to thank

Rebecca Beavers for taking the time to provide additional sediment data.

I thank my supervisory committee chair (Dr. Robert G. Dean) for his continual

support and encouragement throughout this process, and for always finding time for my

questions and concerns. I thank Dr. Robert Thieke for providing the teaching

assistantship that allowed me to continue this research. I also thank Dr. Robert Thieke

and Dr. Andrew Kennedy for serving on my supervisory committee. I also thank Jamie

MacMahan: his patience and insight were invaluable assets to this investigation.

















TABLE OF CONTENTS

page

ACKNOW LEDGM ENTS ........................................ iv

LIST OF TA BLE S ............... ................... ................... ........ .... ............. vii

LIST OF FIGURES .............. ................. ............................... ..............viii

ABSTRACT.................. .................. xi

CHAPTER

1 INTRODUCTION ...................................... .............. .... ......... .......

Study Location, Characteristics, and Instrumentation................................................2
G geographic Location ............................ ....... .........................2
W ave and W weather Conditions.........................................................................3
Bipod Instrumentation ................................................ ........... .4
Chapter Contents .......................................................7

2 GENERAL NEARSHORE CHARACTERISTICS ........................................ 8

Introduction .......... ......... ......... ......................... 8
Quality Control ............. ............. ....................10
Data Screening............................... ..10
Representative Data............... ... ......... ........ ...............1
Analysis ....................................... ........1.......1
Current Influence................... ............. ..........12
Bipod Depth (m)..................... .................... ............................13
Bottom Change (cm).................................... .........13
Current (cm/s) ............................................. ................. ........ 13
Wave Influence.......................................... ........17
Combined W aves and Currents......................................................... .........19
Current Direction ................... ............ .. ........ ......... .. ... ............ 19
Wind ........................... .... .........................20
Variance of Total Current Acceleration ........................................21







v


................................. ..................................... 19
C current D direction ................................................ ..... ... .. ............ 19
W in d ................... .... ....... .. ..................................................................... 2 0
Variance of Total Current Acceleration ................................... .................21







v









3 SE D IM E N T S .....................................................................................2 4

In tro d u ctio n .......................................................................................2 4
A n aly sis ............................................................................2 6
Sediment Characteristics .......................................................26
P rev iou s sedim ent data .................................................................. ...............2 6
Sonar evalu ation .......... .................................................... .. ........ .... 26
V elocity Profile Calculations ........................................ ......................... 29
Critical shear velocity................................... .............. 30
E rror estim ates................................................. ................3 3
Combined wave-current influence .................................... ............... 34
Apparent hydraulic roughness .......................................... ..............37

4 WAVE TRANSFORMATION IN THE NEARSHORE ..........................................42

In tro d u ctio n ........................................................................................................... 4 2
A n a ly sis ................................................................................................................ 4 4
Development of Analytical Spectrum ..................... ............... ...............44
D ataset ................... ........... ....... ..... ................................................................ 4 5
Development of Directional Spectrum from the Data............... ... ........... 48
D eterm nation of m V alues ........................... ....... .................. ............... 51
Comparison of Fourier coefficients.............. ...... ............. 52
Tw o-sided nonlinear fit .......................................... ...................... .......... 53
Comparison of Data to Linear Wave Theory Calculations .............................57
W av e direction .............................. ........................ .. ........ .... ............6 0
R efracted m values ............................................... .. .. .. .. ........ .... 62
W ave height com prisons ........................................ ........................ 65
Energy flux com parisons......................................... ........... ............66
Friction factor .................. ............................ .. ...... ................. 68
R eynolds Stresses ...................... ...... ............ ................. .... ....... 72
D isc u ssio n ............................................................................................................. 7 4

5 CON CLU SION S .................................. .. .......... .. .............77

L IST O F R E F E R E N C E S ........................................................................ .......... ...........8 1

B IO G R A PH IC A L SK E TCH ..................................................................... ..................85
















LIST OF TABLES

Table pge

2-1 Erosion events of 3 cm or greater ............... ................................... ............. .. 13

2-2 Event-Based comparison of erosion events of 3 cm or greater.............................14

4-1 Theoretical Fourier coefficients for different m values .......................................46

4-2 Measured mean wave directions at peak frequency...................... ............... 51

4-3 Average % energy loss values between bipods............................................ 69

4-4 Friction factor estimates from bottom current meter..................... ..............72

4-5 Reynolds stresses for October 1997 ................................... .................... 75
















LIST OF FIGURES


Figure p

1-1 Field Research Facility location......................................... .............. ... 3

1-2 B ipod instrum entation ...... ............................. ................... ........ .. ..

1-3 Bipod locations at initial deploym ent in 1994 ................................... .....................6

2-1 November 1997 filtered mean current comparison with sonar.............................15

2-2 May 1998 filtered mean current comparison with sonar.......................................16

2-3 October 1997 mean orbital velocity estimates vs. sonar measurements.................. 17

2-4 October 1997 cross-shore orbital velocity estimates vs. sonar measurements .........18

2-5 Wind vectors measured at the Field Research Facility ........................................20

2-6 October 1997 current-wind comparison....................................... 22

2-7 November 1997 current-wind comparison.................................... ..................23

3-1 M edian grain size variation with water depth ................................ ............... 27

3-2 X -ray im ages of boxcores ............................................................. .....................28

3-3 Sonar histogram at 13 m bipod, August 30, 1998........ ....................... ............... 29

3-4 Sonar histogram at 5.5 m bipod, August 12, 1998................................................30

3-5 Sonar histogram at 8 m bipod, August 31, 1998 ................................................31

3-6 Sonar histogram at 13 m bipod, August 29, 1998..............................................32

3-7 Shield's curve ............................................................. ..... ..........33

3-8 Shear velocity vs. sonar at the 13 m bipod, October 18, 1997..............................34

3-9 Shear velocity vs. sonar at the 8 m bipod, August 19, 1998 ..................................35

3-10 Shear velocity vs. sonar at the 5.5 m bipod, October 18, 1997.............................36









3-11. Surface roughness variation with mean currents at 5.5 m bipod for October 15-21,
19 9 7 .............................................................................................. 3 8

3-12 Surface roughness variation with mean currents at 8 m bipod for October 15-21,
19 9 7 ...............................................................................................3 9

3-13 Surface roughness variation with mean currents at 13 m bipod for October 15-21,
1 9 9 7 ....................................................................... ...... 4 0

4-1 C coordinate system .......................... .............. ................. .... ....... 45

4-2 R atios of Fourier coefficients................................................................................46

4-3 Significant wave heights measured in October 1997, November 1997, May 1998,
and A ugu st 1998 .....................................................................47

4-4 Bathymetry in vicinity of bipod instrumentation.............. .... ...............48

4-5 Measured spectra for November 7, 1997 time=2200......................... ............50

4-6 Error versus m value comparison for October 20, 1997 time=100........................54

4-7 Comparison of measured and best-fit spectra from matching coefficients for
O ctober 20, 1997 tim e= 100........................................................... ............... 55

4-8 Error between spectra fitted from coefficient ratios for October 20, 1997
tim e= 100 ............... ..................................... ........................... 56

4-9 Comparison of measured and best-fit spectra from curve fitting for October 20,
19 9 7 tim e= 10 0 ............................. .................................................... ............... 5 7

4-10 Error between spectra from curve fitting for October 20, 1997 time=100 .............58

4-11 Variation of m values with frequency range at 8 m ...........................................59

4-12 Directional spectrum variation with frequency at 8 m bipod for October 19, 1997
tim e = 7 0 0. ...................................................... ................ 5 9

4-13 Energy density spectral values for October 19, 1997 time=700 ...........................60

4-14 Mean wave direction comparison for October 19, 1997 time=700........................61

4-15 Measured and calculated wave direction differences for October 19, 1997
tim e=700 at 5.5 m bipod ................................................ .............................. 62

4-16 Average measured and calculated wave direction differences for October 1997 ....63

4-17 Measured and refracted directional spectra for November 13, 1997 time=1742.....64









4-18 Comparison of refracted and measured m values over frequency range for
November 13, 1997 time=1742...................... .... ............................. 65

4-19 Significant wave height ratios versus cross-shore position...................................67

4-20 Average measured and predicted energy flux values.............................................70

4-21 Surveyed bathymetry in vicinity of bipod instrumentation............... ..................71

4-22 Histogram of calculated friction factors at all current meters.............................73

4-23 Friction factor variation with wave height at the bottom current meter...................74
















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

NEARSHORE WAVE AND SEDIMENT PROCESSES: AN EVALUATION OF
STORM EVENTS AT DUCK, NC

By

Jodi L. Eshleman

May 2004

Chair: Robert G. Dean
Major Department: Civil and Coastal Engineering

Pressure, sonar, and current measurements were recorded at 5.5 m, 8 m, and 13 m

water depths in the outer surf zone and inner continental shelf region off the coast of

Duck, NC. This unique data set was analyzed to investigate erosion thresholds and wave

evolution. A mean current threshold of 20 cm/s and combined wave and current

threshold of 60 cm/s were identified for bed elevation decrease. Shear velocity was

determined to be a good indicator of bottom elevation change at the 8 m and 13 m bipods,

with erosion beginning 0 to 3 hours after it crossed a movement threshold of 1.17 cm/s.

Surface roughness estimates at these same two water depths decreased with increasing

mean currents.

The combination of measured near bottom pressure and horizontal velocity

components provides the basis for determining a directional spectrum. A simplified

analytical directional spectrum based on a single cosine curve of varying power (m) was

used to approximate these measured directional spectra. A nonlinear least squares curve









fit to each side of the measured directional spectrum proved the most accurate method of

determining the best representation of m values. Refracted mean wave directions were

slightly overestimated by the theory and the decrease in width of the directional spectra

with decreasing water depth was overestimated. Also, energy flux calculations

combining shoaling and refraction theory showed smaller measured than predicted

energy flux values with inshore distance (sometimes by more than one third) emphasizing

the importance of considering energy loss in calculations for engineering design and

planning.

A representative friction factor for each record was determined by accounting for

frictional energy loss in the energy flux calculation, using velocity time series measured

at the bottom current meter. Calculated friction factors varied throughout storm events,

but most fell within a range of 0 to 0.2. A representative value of 0.17 was identified for

this location through the use of average energy flux and energy loss values over all storm

events. Reynolds stresses were calculated and were found to be consistently different at

the current meter at 0.55 m elevation, a result that remains unexplained.














CHAPTER 1
INTRODUCTION

The inner continental shelf off the open mid-Atlantic coast is a wave-driven

environment, where sediment transport and nearshore circulation are primarily forced by

wind-generated ocean surface waves (Wright 1995). This is a friction-dominated region,

where boundary layers may occupy the entire length of the water column, transmitting

effects of wind blowing on the water surface to the seabed (Wright 1995). Wave

propagation is largely characterized by transformation through refraction, diffraction,

energy dissipation, and shoaling. Mean currents are another important component in the

nearshore zone, and can be driven by waves, wind, tides; and gradients in pressure,

temperature, and density, among other things.

Within this dynamic environment, sand movement is not uniform in all directions

and at all locations. Harris and Wiberg (2002) suggest that gradients in bed shear stress

may create gradients in suspended sediment flux. These cross-shelf gradients in sediment

flux will in turn create cross-shelf gradients in sediment size as the higher orbital

velocities on the inner shelf move finer sediment offshore (Harris and Wiberg 2002).

Alongshore sediment flux is also an important component of the sediment transport

discussion. Beach and Sternberg (1996) found that alongshore sediment flux is

dependent on breaker type, and this information should be incorporated into sediment

transport models. Their measurements showed that plunging waves were responsible for

the greatest portion of suspended load and sediment flux, but other breaker types and









nonbreaking waves combined still contributed almost half of the total suspended load and

sediment flux (Beach and Sternberg 1996).

There is variation in sand transport throughout the water column as well. Many

investigators have found an inverse relationship between distance above the bed and

suspended sediment concentration (Beach and Sternberg 1996; Conley and Beach 2003).

A study conducted in the surf zone during the SandyDuck experiment showed that the

increasing importance of wave-driven transport near the bed might lead to a reversal in

the net cross-shore transport direction in the water column. The directions of transport at

the bed may dominate even if much of the water column has an opposing transport

direction since more than half of the depth-integrated net transport occurs within 5 cm of

the bed (Conley and Beach 2003).

Study Location, Characteristics, and Instrumentation

Geographic Location

Field data were obtained on the inner continental shelf off the coast of the Army

Corps Field Research Facility (FRF) in Duck, North Carolina. The FRF facility is

located on the Outer Banks of North Carolina, on the central portion of the Currituck

Spit, which extends southeast continuously for over 100 km from Cape Henry, Virginia

to Oregon Inlet, North Carolina (Figure 1-1). It is located in the southern portion of the

Middle Atlantic Bight (36 10' 57"N; 75 45' 50"W) and bordered by Currituck Sound, a

low-salinity estuarine environment, on the west; and the Atlantic Ocean on the east.

Ocean tides are semi-diurnal, with a mean range of approximately 1 m (Birkemeier et al.

1981).





































Figure 1-1. Field Research Facility location (from http://www.frfusace.army.mil)

Wave and Weather Conditions

Wave heights vary seasonally along the Outer Banks, with peak waves occurring

in October and February, and mild conditions prevailing in late spring and early summer

months (Birkemeier et al. 1981). A compilation of wave statistics for the time period of

1985 through 1995 resulted in an average annual wave height of 0.9 + 0.6 m, and a mean

annual wave period of 8.8 + 2.7 s (Leffler et al. 1998). There have been many

observations of water masses that interact with currents in the area, including low salinity

slugs from the Chesapeake Bay and warm, clear Gulf Stream currents (Birkemeier et al.

1981).









The majority of storm events that affect the Atlantic coast originate in the middle-

latitude westerly wind belt and are often termed extra-tropical (Dolan et al. 1988).

Tropical storms, including hurricanes, also affect the region, but less frequently. Dolan et

al. (1992) discuss the importance of extra-tropical storms for erosion and note that they

often generate wave heights that are comparable to or greater than those from hurricanes.

A study that examined 1,349 northeast storms on the Atlantic coast found a distinct

seasonality of frequency and duration, with maximum values in the winter and minimum

in the summer (Dolan et al. 1988). When specifically examining extra-tropical storms,

the most significant contribution to erosion is from northeasters. Xu and Wright (1998)

determined that even though comparable winds from the southerly directions sometimes

caused high wave heights, the alongshore current magnitudes recorded during these

storms were only one-fifth of those achieved during northeasters. Cross-shore current

magnitudes were also smaller, but differences were not as large as for alongshore currents

(Xu and Wright 1998).

Bipod Instrumentation

The initial bipod instrumentation was deployed in October 1994 as part of a

multi-year monitoring program to study shore-face dynamics on the inner continental

shelf of the Field Research Facility in Duck, NC (Howd et al. 1994). The instrumentation

consisted of three current meters at varying elevations, a pressure sensor, and a sonar

altimeter, which were all attached to a bipod frame, secured by two 6.4 m pipes jetted

vertically into the seabed (Beavers 1999). The original bipods collected data until

October 1997 using three Marsh-McBirney electromagnetic current meters, which often

experienced significant noise. The current meters were replaced with Sontek Acoustic

Doppler Velocimeters for the SandyDuck experiment in October 1997, and the bipods









were redeployed at depths of 5.5 m, 8 m, and 13 m relative to NGVD. They remained

operational at these three simultaneous locations through December 1998. The data used

in this analysis were collected during this second deployment. Figure 1-2 shows the

bipod setup where A, B, and C are electronic housings; P is the pressure sensor; and S the

sonar altimeter. General bipod locations at the time of initial deployment in 1994 are

pictured with respect to local bathymetry in Figure 1-3.




(Ii




I i








Figure 1-2. Bipod instrumentation A,B,C = electronic housings, P is pressure sensor,
and S is sonar altimeter (from Beavers 1999)

The bipod packages each contained three SonTek Acoustic Doppler Velocimeters

(ADV), which sampled at 2 Hz and were located at elevations of 0.2 m 0.55 m and 1.5 m

above the sea floor. The end of the frame containing the current meters was oriented

toward the southeast to minimize interference of current meters and vertical supports with

orbital velocity measurements, since storm events of interest would have primarily

northeast waves (Beavers 1999). Digital Paroscientific gauges were used for pressure

measurements, operating at 38 k Hz and a sampling rate of 2 Hz (Beavers 1999). A

Datasonics PSA-900 sonar altimeter was used to record bottom elevation. The range was









modified from 30 m to 3 m to increase the resolution, sampling at 1 Hz with a beam

frequency of 210 kHz (Beavers 1999). Tests by Green and Boon (1988) of response

characteristics found this model of altimeter to be accurate to one centimeter. Current

meter and pressure data are output in 34-minute segments, with a 10-minute break in data

every 3 h. Average values for each record represent a mean value for a 34-minute burst.

Sonar measurements are determined through a histogram filtering technique, taking the

highest bin value for the burst.









o I I
q r 1 i
i ^ 'I J i I





rIn*sums t
Bipds I -




Figure 1-3. Bipod locations at initial deployment in 1994 (from Beavers 1999)

The lowest ADV records bottom measurements for a duration of 9 min every

three hours to provide a second measurement of bottom elevation (Beavers 1999). This

beam has a frequency of 4 MI[Hz and a beam width of one degree, creating a 2 cm

diameter footprint; whereas, the sonar altimeter operates at a frequency of 210 kHz and

has a 10-degree beam width, creating a 20 cm diameter footprint (Beavers 1999). The

differences in beam frequency and footprint size provide different optimum operating












conditions. Beavers (1999) suggests that the ADV is more reliable under non-storm

conditions and the sonar altimeter provides a better estimate of bottom elevation under

storm conditions, when suspended sediment concentration within the water column is

high.

Chapter Contents

The purpose of this investigation is to examine sediment movement and wave

evolution within the inner continental shelf and outer surf zone region through the

analysis of field measurements. Chapter 2 focuses on determining general relationships

between waves, currents, and sonar measurements. Chapter 3 describes sediment

characteristics, and discusses some aspects of bottom roughness by analyzing velocity

profiles. Chapter 4 is the heart of the investigation and utilizes the data collected at all

three bipod locations to provide a comparison with analytical predictions of evolution of

wave characteristics.














CHAPTER 2
GENERAL NEARSHORE CHARACTERISTICS

Introduction

Many researchers have attempted to establish a relationship between statistical

properties of velocity measurements and sediment movement. Although there have been

some velocity moments that have seemed more relevant than others, there does not seem

to be any one parameter that shows a consistent significant correlation to sediment

transport. A study by Guza and Thornton (1985) examined velocity moments from

measurements at Torrey Pines Beach in San Diego, CA and found that oscillatory

asymmetries and combined current-wave variance terms are significant to cross-shore

transport. Several studies have shown that the oscillating velocity terms move sediment

onshore and the mean velocities move sediment offshore (Guza and Thornton 1985;

Osborne and Greenwood 1992; Conley and Beach 2003). Measurements of sandbar

migration at Duck, NC showed maximum values of velocity asymmetry and acceleration

skewness near the bar crest (Elgar et al. 2001). Hoefel and Elgar (2003) found that

extending an energetic model to include fluid accelerations resulted in better predictions

of onshore bar migration between storms. Velocity measurements taken in the surf zone

during SandyDuck showed no significant correlation between velocity moments and

wave driven transport, although acceleration skewness showed the strongest relationship

(Conley and Beach 2003). These suggest that velocity asymmetry and acceleration

skewness seem to have the strongest ties to sediment transport in past experimental

results.










There has been previous work with similar instrumentation done at this location.

Several studies included instrumented tripods deployed during storm and fair-weather

conditions, which also included suspended sediment measurements (Wright et al. 1986;

Wright et al. 1991; Wright et al. 1994). The first tripod deployment was at a single depth

and did not show a relationship between bed level changes and increased mean or orbital

velocities. There was a gradual change in the bottom elevation throughout the middle

and final stages of the storm, followed by significant accretion that was hypothesized to

be the result of a migrating bedform. Suspended sediment measurements did not show a

response to the onset of the storm or peak with mean currents, but peaked with oscillatory

flow, suggesting that waves are the dominant source of sediment resuspension (Wright et

al. 1986). The second study consisted of three separate deployments at the Field

Research Facility and the results suggested that it is the near-bottom mean flows, not

oscillatory components that play the dominant role in transporting suspended sediment

(Wright et al., 1991). Mean flows may also play a role in the direction of sediment

movement. A study conducted at Duck showed the tendency of a mean cross-shore

velocity threshold around 30 or 40 cm/s directed offshore to be the divider between

landward and seaward bar migration (Miller et al. 1999). Both mean and oscillatory

flows are essential to the analysis and they are not independent. The wave boundary

layer creates resistance for the current above and slows down that flow. Waves are often

thought to be more efficient at initiating motion, whereas currents are more efficient at

net transport, but the two interact nonlinearly (Grant and Madsen 1976).

There are two critical differences between previous studies and this dataset.

These include the length of time and number of instrumentation packages deployed.









Many other studies have included one or two instrument packages deployed

simultaneously for individual storm events or short periods of fair-weather conditions,

but not three instrument packages with continuous measurements for this length of time.

Some previous investigations have been carried out with this specific dataset that

focused on the sonar data. Sonar Altimeter measurements were compared to surveyed

profiles to discuss discrepancies in depth of closure concepts. The predicted depth of

closure was around 8 m, yet for some storm events, the 13 m bipod showed the greatest

change in bottom elevation. Net and range of seabed elevation changes were examined

during storm events that were defined by wave thresholds. Finally, a comparison of

sonar records to diver collected boxcores served to validate the sonar record and showed

the sonar was capable of monitoring long-term bottom stratigraphy (Beavers 1999). The

current and sonar measurements were also used as forcing and validation for a bottom

boundary layer and sedimentation model (Keen et al. 2003). These analyses have shown

some interesting relationships, but have neglected a major component of the dataset: the

current measurements. The first level of this analysis focuses on the currents and the

manner in which they affect the bottom during all weather conditions, not just storm

events.

Quality Control

Data Screening

Different levels of screening were applied in an attempt to eliminate noise and

assure that the measurements presented here are representative of actual conditions in the

nearshore environment. Spikes were removed using polynomial interpolation. Beam

correlation and intensity values output by the ADV were used to identify low quality

data. The second level of data screening was accomplished through determining several









quality control parameters for each record. The quality control parameters included

signal-to-noise ratios for current and pressure measurements, and a z test value based on

a ratio of the wave heights calculated from pressure and current measurements. Data

with signal-to-noise ratios less than 1.5 or z test values outside the range of 0.5 tol.5

were not used.

Representative Data

The following analysis is based on four months during which the described data

standards were satisfied. These months: October 1997, November 1997, May 1998 and

August 1998 were chosen for several reasons. They include a nearly complete data set

that has been successfully edited. They have z-test values near 1, signal to noise ratios of

2 or higher, and wave directions that are consistent for all three current meters,

suggesting that biofouling and problems with current meter rotation were minimal. They

have bottom measurements from the lowest current meter recorded every three hours, so

that trends in the sonar measurements can be validated. In addition to data quality, they

encompass significantly different seasonal variations. Measured significant wave height

values range from less than 1 m to almost 4 m, spanning storm and mild weather

conditions.

It is important to note that the data from these months includes some problems,

but knowledge of data quality can be combined with analysis techniques to obtain results

that account for the limitations of the data.

Analysis

Our knowledge of the dynamics of the nearshore system leads to the recognition

that no single statistical property can explain sediment movement. Sand transport is

governed by a complex combination of many factors. The following discussion of









erosion refers to bed elevation decrease, rather than transport initiation, which cannot be

measured by the available instrumentation. The continuity equation gives the following

relationship between bed elevation, z, and gradients in cross-shore, alongshore and

vertical sediment transport components at the bed, qx, qy, and qz respectively.

dz (aq, c
(1-p) +
dt ax ay z)

where p represents the porosity. It is important to recognize that it is possible to have

sediment transport without bed elevation change; however, if the bottom sediment is

suspended or the gradient in cross-shore or alongshore sediment transport is positive, the

bottom elevation will decrease. This initial analysis is an attempt to discern which

properties appear to play a more significant role when considered individually.

Current Influence

There appears to be a mean current threshold of approximately 20 cm/s for

erosion in most of the data. There is usually some erosion when the total mean current

reaches 20 cm/s, yet there may be erosion for smaller currents. The currents were filtered

with a cutoff of one day to remove tidal influences and to facilitate a comparison with

sonar altimeter data. Table 2-1 shows events of bed elevation decrease of 3 cm or greater

and the associated currents. There are many times when the mean current is very high

and the bottom change is small and vice versa, indicating the possibility that other forces

may be involved. One important thing to note is that often times erosion occurs when

significant wave heights are fairly low. 54% of the erosion events identified in Table 2-1

occurred when the significant wave height was less than 2 m, which is often considered

as the threshold between storm and calm conditions. This reinforces the need to examine









Table 2-1. Erosion events of 3 cm or greater


Oct-97











Nov-97












May-98







Aug-98


Bipod Depth
(m)


Bottom Change
(cm)


Current
(cm/s)


Hmo
(m)


T (s)


5.5 6 25 2.0 12.5 12.5
5.5 20 55 3.0 9.1 3.5
5.5 10 19 1.0 12.5 4.5
5.5 8 21 1.0 10.0 5.0
8 5 22 1.5 6.3 9.0
8 8 28 2.0 12.5 4.5
8 6 58 3.0 9.1 3.0
8 11 18 1.0 12.5 4.0
8 5 19 1.0 10.0 4.5
13 11 56 3.0 9.1 16.0
5.5 5 30 2.5 4.8 10.5
5.5 3 25 3.0 9.1 7.0
5.5 13 28 1.5 3.6 10.5
8 10 15 1.0 8.3 9.5
8 6 30 2.5 4.8 5.0
8 4 28 2.0 11.1 1.5
8 3.5 12 1.5 10.0 1.0
8 5 13 3.0 9.1 6.0
8 10 25 1.5 3.6 9.0
13 4 22 2.5 4.8 19.0
13 3 18 3.0 9.1 7.5
5.5 10 40 1.5 6.7 9.0
5.5 3 21 2.0 12.5 6.0
8 9 40 1.5 6.7 9.0
8 6 20 2.0 12.5 6.0
8 5 10 1.0 11.1 1.5
13 3.5 35 1.5 6.7 9.0
13 8 40 3.5 9.1 3.5
5.5 4 26 2.0 7.1 1.5
5.5 4 25 1.5 7.1 1.5
5.5 3 15 1.0 6.7 2.5
5.5 5 21 1.5 4.0 6.5
5.5 10 30 1.5 6.3 6.0
5.5 4 18 1.25 11.1 4.0
5.5 10 70 3.2 12.5 3.0
8 8 23 2.0 7.1 1.5
8 11 23 1.5 7.1 1.5
8 8 26 1.5 6.3 15.0
8 16 65 3.2 12.5 7.5
8 11 5 1.0 10.0 4.0
13 4 15 1.5 7.7 4.0


Time since last event
(days)


12.5


22.0









the changes occurring during all types of conditions, since it is not necessarily during

storm events that the sediment is moving.

Table 2-2. Event-Based comparison of erosion events of 3 cm or greater
Date Current (cm/s) Bottom Change (cm)
5.5 8 13 5.5 8 13
11-Oct 20 22 20 5 -
15-Oct 25 28 28 6 8 -
19-Oct 55 58 56 20 6 11
22-Oct 19 18 18 10 11
27-Oct 21 19 18 8 5
2-Nov 12 15 11 10
6-Nov 30 30 22 5 6 4
7-Nov 23 28 11 4
8-Nov 10 12 5 3.5
13-Nov 25 13 18 3 5 3
23-Nov 28 25 21 13 10
9-May 40 40 35 10 9 3.5
12-May 65 58 40 8
15-May 21 20 10 3 6 -
16-May 5 10 8 5 -
2-Aug 26 23 17 4 8
4-Aug 25 23 15 4 11
5-Aug 18 15 15 4
6-Aug 15 15 5 3
13-Aug 21 19 12 5 -
19-Aug 30 26 28 10 8
23-Aug 18 10 9 4 -
27-Aug 70 65 70 10 16 25
30-Aug 5 5 10 11


Major erosion events appear to be fairly consistent between bipods, although the

magnitudes of bottom elevation changes are usually different. Table 2-2 presents the data

from Table 2-1 by date, to facilitate a comparison between bipods (- represents < 3 cm of

bottom change). An interesting situation occurs in November 1997 and August of 1998,

where the current reaches one of the maximum values for the month (above the 20 cm/s












threshold), but the erosion is not consistent at all three bipods. Both instances show


significant erosion at the 5.5 m and 8 m bipods (ranging from 8-13 cm), and less than


3 cm of erosion at the 13 m bipod. Figure 2-1 shows one case occurring around


November 24, 1997. Currents are positive onshore and south.


E J


a8.8
Jf.28 C


06 11 16 21


___ 01
l1


-0.
.'l


11 16 21
24 Hour Fiered Currnts vs Sonar Novmber 1997


Figure 2-1. November 1997 filtered mean current comparison with sonar a) 5.5 m b) 8 m
c) 13 m


A situation occurred in May of 1998 that seems to be the reverse of this last


observation and occurs around May 13 (see Figure 2-2). The currents were at their


highest values for the month, in excess of 40 cm/s, causing minimal erosion at the 5.5 m


and 8 m bipods and a more significant change at the 13 m bipod. For this situation, the


ADV bottom measurement showed less erosion, indicating that there may have been


fluffy material at the 13 m bipod that the sonar had trouble penetrating and the higher








16



frequency ADV picked up. Here we see the 5.5 m and 8m bipods showing significant


erosion at the onset of currents over 20 cm/s, but then the erosion leveled off as the


currents continued to increase. The 13 m bipod did not show as much erosion initially,


but as currents continued to increase there was a spike where the sonar based bottom


elevation dropped 15 cm. If this sediment was of the finer type that is sometimes seen at


13 m, a higher current may have been required for movement due to cohesive properties,


and once the current reached that threshold, the entire layer moved. The cause of this


cannot be explained with certainty without more detailed sediment information.



05 10 15 20 25 30
5.95 G1" -







05 10 15 20 25 30


E"

p
825

0 1




1Z.95


s 1-.05


1315
0$ iS


Z4 Hour Filtred OCjres us Sonar May 1993


lobo

v I I \
-D2 ]I:;

.Z
!
2; :*;


Figure 2-2. May 1998 filtered mean current comparison with sonar a) 5.5 m b) 8 m
c) 13 m


'"'








17



Wave Influence


The root mean square current speeds were examined in different frequency


ranges. These values were multiplied by the square root of two to obtain the amplitudes


as substitutes for orbital speeds and represent the significant values for orbital speed.


This should provide some insight into which frequency components contribute the most.


A high frequency range from 0.04 to 0.35 Hz was identified to examine sea swell and a


low frequency range of 0.004 to 0.04 Hz to investigate any infragravity contributions.



I T r i2i "l
I I I-

f i ,F tI
E -' 6.5 ,:


ill fj'

O? 07


*~~~* rr*'


IOcbr 1997
Wdober 1997


n ~ 7 l1
'U

i "A



ci
1 I 1 6
'' 1* .. : -
i f fl *: 1 ..
^ L_-: .^..,,^_
r^ i: u


Figure 2-3. October 1997 mean orbital velocity estimates vs. sonar measurements
a) 5.5 m b) 8 m c) 13 m (solid black line represents sonar)


The infragravity orbital speed was always smaller, but reached 20 cm/s at the 5.5 m bipod


during storm events. Results for October 1997 are presented in Figure 2-3, which shows


E "
8.25
8.3
8.35





13-15

13 i2
ia 2 -







18


a peak at the maximum erosion event for the month, and slight increase for smaller

erosion and accretion events.


02 07 12 17 22 27 01




02 0 12 17 22 27 .



0V 07 12 17 22 27
I cross shr u cfty
815 RM1S easwel melocdv2
Lb ,.. .- '..r-'
i .j i 1 I r n I ii









8.35 0
,35- .- -,,, ,,-^* -4



h_0 II )J IS
|,i \ i '----- a'






02 07 12 17 22 27 61

I I . '_ _


I3 1
E.15|- R.M.$ seawmll elo tt *_,














Sitob2r 19977



Figure 2-4. October 1997 cross-shore orbital velocity estimates vs. sonar measurements
a) 5.5 m b) 8 m c) 13 m (solid black line represents sonar)

This suggests that the infragravity component may be significant for this dataset.

This is an interesting observation because other studies have had conflicting results for

this location in the past. Wright et al. (1994) took similar measurements at this location

at a depth of 13 m during the Halloween storm of 1991 and showed a significant

infragravity component, reaching 20 cm/s near the peak of the storm, which is similar to

these findings. They suggest that roughly half of the infragravity energy emanates from

the surf zone (Wright et al. 1994). An earlier attempt to quantify wave reflection found

no significant quantity of long wave energy, either incident or reflected from









measurements taken at a depth of 6.5 m (Walton 1992). One possible explanation for this

difference may be a difference in significant wave heights, since values recorded during

this study were never greater than 3.5 m and those recorded during the "Halloween"

storm reached 6.5 m. The plot of the cross-shore components (Figure 2-4) shows that the

cross-shore is the major component of the R.M.S seaswell velocity, which enforces the

need to consider cross-shore velocity for sediment transport even when mean values are

small. The current amplitude increased at most erosion events for the month, but not all.

Combined Waves and Currents

Another approach to considering erosion causes examined the combined wave

and current maximum velocities. The sum of the amplitude (used to estimate orbital

velocity) and the component of the mean current in the wave direction was calculated.

These are all positive values since they were taken in the wave direction and negative or

positive wave orbital velocities could cause erosion. This was an attempt to consider not

just the mean current or wave orbital velocity, but their combined effect; however, this

did not take into account any nonlinear interactions between waves and currents, but

provided a rough estimate of combined velocity. This analysis did not show any

consistent threshold between maximum velocity and sediment movement, but there was a

relationship between the two. Very high combined velocities in the range of 60 tol00

cm/s always seemed to be associated with erosion, but below this range the effect varied.

Current Direction

The maximum erosion events for the month always occurred with a southerly

longshore current and usually a downwelling (seaward) flow in the cross-shore

component. One example is around the 28 of August 1998 in which a northerly












longshore current reversed direction and caused the most significant erosion for the


month.


Wind


Measurements of wind magnitude and direction are obtained from FRF wind


gages 932 and 933. Figure 2-5 shows a vector plot of these values. Most peaks in mean


longshore current velocity that are above the 20 cm/s threshold appear to coincide with


peaks in longshore wind velocity. The notable exception to this is the month of


November 1997, where scatter plots show a poor correlation between the longshore wind


velocity and longshore mean current.




16-

E V I..f'.q-.- -. ."^ -^ ; ;
C -* -
10
1-16----
02 07 12 17 22 27
October 1997
16-




16-
06 11 16 21 26
November 1997
m 16-



0 -
'-16------------------------------------
05 10 15 20 25 30
May 1998
16-




'-16----
03 08 13 18 23 28
August 1998


Figure 2-5. Wind vectors measured at the Field Research Facility









The cross-shore currents showed no significant correlation to cross-shore wind. Current-

wind comparisons for the month of October 1997 are provided in Figure 2-6. Current

and wind measurements are positive onshore and south. Another study by Xu and

Wright (1998) of wind-current correlation at this same general location has shown that it

is dependent on wind direction. The correlations were broken into quadrants, and it was

found that the current and wind speeds are most correlated with winds from the Northeast

or Northwest direction, showing much higher R squared values than winds blowing from

the Southeast or Southwest (Xu and Wright 1998).

Variance of Total Current Acceleration

There seems to be some relationship between the variance of the acceleration of

the total current and bottom change on a month-to-month basis. This follows some

previous observations discussed in the introduction, although the acceleration skewness

did not show any significant trends. There is an increase in this variance at times of

maximum erosion for the month; however, this same trend was seen when considering

current variance. Erosion due to the acceleration variance cannot be distinguished from

erosion due to the current variance, since they differ only by the square of the radial

frequency.

















5m Bipod 5m Bipod
0.1 1

0.8
0.05
05 0.6

0 -- -0.4 2
a







0.15 0.4
-10 -5 0 5 10 -20 -10 0 10 20
Cross-shore wind m/s Longshore wind m/s

8m Bipod 8m Bipod
0.1 1

00.8

0.05 0.8
++ + *

S0.1 0.6



-0.05 0.4







-10 5 0 5 10 -20 -10 0 10 20
Cross shore wind mis Longshore wind mis

13m Bipod 13m Bipod
0.1 ,. 0.2
0.15 '0
02 + 02 + ,













-0.25 -0.4
10 5 0 5 10 20 10 0 10 20
Cross shore wind mis Longshore wind mis
13m Bipod 13m Bipod
0.15 1

0.1 0.8

E 0.05 E.0.6 +: 'o.

0 0.4

0 -0.05 0. ..

0 0.1 0. : D .d

0.15 0.2

-0.2 -0.4
10 5 0 5 10 20 10 0 10 20
Cross-shore wind m/s Longshore wind m/s


Figure 2-6. October 1997 current-wind comparison


















5m Bipod
0.15

0.1















-0.2 '
-15 -10 -5 0 5 10 15
Cross-shore wind m/s

8m Bipod
0.15

0.1 .
0.05 .





0.05




0.15

0n 2


-10 -5 0 5
Cross-shore wind mis

13m Bipod


10 15


-5 0 5 10 15
Cross-shore wind mis


5m Bipod
0.5

0.4

0.3






-0.2
0.1










Longshore wind mis

8m Bipod
0.5

0.4
















-15 -10 -5 0 5 10 15
Longshore wind m/s
13m Bipod










0.5

0.4




-0.3 *
0.1

03

















-0.2 ---------------
-15 -10 -5 0 5 10 15
Longshore wind mis
13m Bipod

0.5

0.4













-0.3


15 10 5 0 5 10 15
Longshore wind mis


Figure 2-7. November 1997 current-wind comparison














CHAPTER 3
SEDIMENTS

Introduction

Past observations of bottom change from sonar altimeter measurements have

often been supported by visual observation or other instrumentation since sonar measures

only the elevation at a single point. One limitation of the analysis lies in the inability to

distinguish whether sediment is moving as suspended load or bed load from a single

sonar altimeter. It is possible to have sediment transport without elevation change, yet

the sonar can only capture variation in the bed elevation. Topographic features moving,

including bed forms or ripples, can also cause problems since they may be measured as

the representative bed elevation, but their existence is localized. There have been

observations of non-uniform topography in the vicinity of the bipod instrumentation. An

array of seven sonar altimeters deployed in the surf zone during the SandyDuck

experiment captured mega ripples which ranged from 15 cm to 30 cm high and moved

through the sonar range in a period of about ten hours (Gallagher et al. 1998). The first

tripod deployment by Wright et al. (1986) was supplemented by diver observations,

pictures and side-scan sonar measurements. Side scan sonar images showed sediment

lobes of fine material overlying coarser material which were up to one meter high and

thought to be the cause of the rapid accretion at the 8 m tripod at the end of the storm

event (Wright et al. 1986). Bottom features such as these are difficult, if not impossible

to discern from sonar altimeter measurements alone.









An important parameter when discussing sediment transport in relation to bottom

topography is the bed shear stress, or equivalently, the shear velocity, u, = T Ip The

von Karman-Prandtl equation

uc (Z) 1 Inz
Uc K ^Z0

can be used to estimate shear velocity and hydraulic roughness length values from

measurements of the mean current at different elevations. Madsen et al. (1993)

calculated shear velocity and apparent hydraulic roughness from the log-profile method

for the data collected at the 13 m tripod during the "Halloween" storm of 1991. These

estimates showed shear velocity values on the order of 2 to 3 cm/s and apparent hydraulic

roughness values generally between 0.1 cm and 1 cm. These values were found using

data obtained with similar instrumentation and at a very similar location, therefore the

values found in the subsequent analysis are expected to be the same order of magnitude.

They found a value of 1.5 mm for the Nikuradse sand grain roughness for a movable flat

bed (Madsen et al. 1993).

Past analysis of the dataset examined in this thesis used diver-collected boxcores

to supplement sonar measurements. Beavers (1999) discussed the geologic features of

these cores and the correlation between core layers and sonar records in detail. The

positive correlation between these two records indicates that scour around the pipes was

not appreciable, which will be assumed in the following analysis. Shear stress

calculations showed that when the shear stress is a maximum, seabed elevation decreases

and when shear stress decreases, the seabed elevation increases (Beavers 1999).









Analysis

Sediment Characteristics

Previous sediment data

Sediment data are available for the period 1984-1997 from locations adjacent to

the bipod instrumentation. Figure 3-1 compares median grain size versus elevation for

this time period and implies little variation in sediment size at the 5.5 m and 8 m bipods.

Most measurements remain within a 1/2 q unit range. There is significantly more

variation at the 13 m bipod with a 3/2 0 unit range. The left panel of Figure 3-2 shows an

x-ray of a boxcore taken at a water depth of 13.2 m on August 18, 1997. The white

region shows a section where the material is too fine for the x-ray to register and grain

size analysis determined a median q value of 4.02 for this section, as opposed to 3.10 for

the rest of the sediment column (Beavers 1999). The right panel of Figure 3-2 shows a

boxcore taken in 1992 at a water depth of 14 m, which also shows a layer of fine, silty

material (Nearhoof 1992). It is important to be aware of the sediment range at the 13 m

bipod when considering sonar measurements, since there are instances when the sonar

may have trouble recognizing fine, silty material.

Sonar evaluation

Bed form migration can register on sonar measurements and changes in elevation

may reflect localized change from large-scale bed forms moving through the sonar

footprint. Tests of ripple fields under a similar sonar altimeter showed that the ripple

could not be resolved if its height above the bed is more than eight times its wavelength

(Green and Boone 1988). The possibility of non-uniform topography is difficult to

resolve and one method of addressing this was to examine sonar histograms. One notable










observation is that the raw sonar measurements were very noisy, although the outline of

the bottom could generally be distinguished. A representative sonar value for each

34-minute record was taken as the max bin value of the histogram for that time series.

The hypothesis was that at times when there was silty material at the 13 m bipod, the

sonar might show two peaks, at the top and bottom of this layer. Another possibility was

that during storms, the histograms may show more spread if the sonar was unable to

consistently penetrate the suspended sediment in the water column.


10 -




12

13

1A
-712 U __ _


* Boxcore Samples (1994-1997)

* Profile Line 62 (1984-1985)

A Duck 94 Samples-Oct

A Duck 94 Samples-Aug

* SandyDuck 97 Samples


2 2.5 3 3.5 4 4.5
Median Grain Size (phi)


Figure 3-1. Median grain size variation with water depth (data from FRF)

Sonar histograms are included for each bipod location during the month of August

1998. In most instances, there is a very well defined peak at a specific value, and smaller

peaks or spreading at depths less than this value (Figure 3-3). Secondary peaks are

within a few centimeters of the major peak. There are times when this histogram


s than this value (Figure 3-3). Secondary peaks are


within a few centimeters of the major peak. There are times when this histogram









deteriorates and the peak is less well defined with a greater spread (Figure 3-4). These

times do not always correlate with storm events as anticipated.


92A 330 I













A. B. B.

Figure 3-2. X-ray images ofboxcores A) h=13.2 m on August 18, 1997 (Beavers 1999)
B) h=14 m in 1992 (Nearhoof 1992)

At the 5.5 m and 13 m bipods there is rarely spreading at depths greater than this

peak, which lends confidence to sonar estimates of the bottom where spreading is most

likely an indicator of noise within the water column. One very interesting observation is

that the 8 m bipod shows almost all of the spreading and secondary peaks in the

histograms to be at depths greater than the histogram peak, as evident in Figure 3-5. This

is consistently different from the other bipods and remains unexplained.

Another interesting situation occurred on August 29, 1998 and lasted for

approximately a day, showing the variation in sonar histogram values with time at the 13

m bipod. Here two distinct peaks occurred that are over 20 cm apart and are of similar

magnitude. One peak is at 13.37 m and another at 13.14 m (Figure 3-6). This occurs

immediately after the major storm event for the month. One possible explanation is that

there is a layer of very fine sediment here and the sonar sometimes pings off the top and










sometimes penetrates the layer. An observation about this August storm event is that

there are strong northerly alongshore currents reversing direction and reaching 100 cm/s

in the southerly direction, and this is the only time that this alongshore-current reversal

occurred within the four months analyzed. This dual sonar peak phenomenon was not

repeated and with the limited sediment information available it cannot be explained with

any degree of certainty.





500


400


300




100


0
12:00 i IJ1
09:36 ,- I -
-i ,-I' 'i' .
07:12 -'o



0.6 0.7 0.8 0.9 1 1.1 1.2
Time
Depth, m


Figure 3-3. Sonar histogram at 13 m bipod, August 30, 1998

Velocity Profile Calculations

The velocity profile method discussed earlier is used to estimate shear velocity

and hydraulic roughness length values from the measured mean current values from the

three different current meters. Bed elevation values from ADV measurements are











incorporated to account for changing current meter elevations with time and bottom

change.






900,
800
700
600
o 500
400
300




0
21:36 r ,
19:12 .







Depth, m


Figure 3-4. Sonar histogram at 5.5 m bipod, August 12, 1998

Critical shear velocity

One attempt to examine further the shear velocity relationship with bottom change

was to calculate a critical shear velocity value from the range of sediment sizes shown in

Figure 3-1 for each bipod. This method utilized the form of Shield's curve shown in


Figure 3-7 to determine a value of shear stress (r,) for each mean sediment diameter


based on an abscissa value of


S3 (P, p)g
uD p


The ordinate value of


alue of












(p, p)gD

is used to determine a critical shear velocity through the relationship

2
Tc = u,cp

The next step was to identify the times during the four months analyzed when the bottom

was just beginning to erode. A daily plot was generated for each of these times of erosion

initiation to facilitate a visual comparison of shear velocity with measurements of sonar.


0.6 0.7 0.8 0.9 1 1.1 1.2
Depth, m


I 00:00
F 21:36

1 T

1-2i- Time


Figure 3-5. Sonar histogram at 8 m bipod, August 31, 1998

The critical range of shear velocity values were overlain on the shear velocity plots to

determine if the bottom elevation began to change around the same time that the shear

velocity crossed the threshold for movement.




















400- I

350-

300 ,I I|i
,) I "I
I ,' I ,I l ii
250 I
c'ciI

S150 t .... 'I0 .:
2 ,00- '.i





0.6 0.7 0.8 0.9 1 11 1. Time

Depth, m
--






Figure 3-6. Sonar histogram at 13 m bipod, August 29, 1998

Most situations at the 8 m and 13 m bipod locations show the bottom beginning to

erode zero to three hours after the shear velocity crossed the critical threshold. Figure 3-8

shows a particular time when the two occur almost simultaneously. The blue line

represents shear velocity with the red lines identifying the range of critical values for

different sediment sizes, and the circles marking where the bottom begins to erode and

the shear velocity crosses the threshold. Figure 3-9 shows a particular situation at the

8 m bipod where we see a phase lag between the two, and erosion does not occur until

approximately 3 h later. At the 5.5 m bipod, the shear velocity value is always below the

threshold for movement when sonar measurements show the bottom beginning to erode.


e


threshold for movement when sonar measurements show the bottom beginning to erode.










One example is included as Figure 3-10. Peaks in shear velocity show some relationship

to peaks in tidal currents.






o009o -

\-- SHIELDS' EXTRAPOLATION
0,08 -

o 007
o \
B \BASED ON WHITE'S DATA FOR a 0.06
S0.06 NONCOHESIVE SILT GRAINS



0 04


10 10 I 10 104 10& 106 107




Figure 3-7. Shield's curve

Error estimates

It is important to address the error in estimates of shear velocity, since values are

calculated from a velocity profile method that fits a curve to three current measurements,

leaving only two degrees of freedom. Error estimates for shear velocity are calculated for

a 90% confidence interval using the student t distribution and they are very large, around

an order of magnitude higher than most calculated values of shear velocity. This is a

limitation of the method and data available, and most field measurements would

demonstrate similar error estimates when using vertical arrays of individual current

meters for measurements. Another factor is that the chosen critical value of shear

velocity is dependent on sediment size, but the range of values does not vary widely

when considering the range of sediment sizes measured at bipod locations. After taking











into account the limitations of the shear velocity estimates the time lags between the


shear velocity reaching a critical value and initiation of sonar change do not appear to be


unreasonably long. The critical shear velocity seems to be a good indicator of when


erosion will begin at the 8 m and 13 m bipods.


M41 0712 0 ,:35 12-00 14 4 16:4 1912 21 36


12 [


Octobr IB, 1997


I I I I
1, 1r~3 I~I rlJ


Figure 3-8. Shear velocity vs. sonar at the 13 m bipod, October 18, 1997 (Note blue line
is shear velocity, black line is sonar, red lines are critical shear velocity)

Combined wave-current influence

Another concern regarding shear stress and shear velocity estimates is that they


are calculated based only on the current values and they do not take into account wave

orbital velocities. The shear stress associated with combined waves and currents is


different than with either alone, because of the turbulence generated by the wave-current


interaction (Grant and Madsen 1979).


'.1 ;'











02:24 MS48 0712 03:3B 12:0 14,24 16:48 1912 2136










029 -
85 ~--\--------I---------------------------- I ----------------------------------------------[l






















shear velocity, black line is sonar, red lines are critical shear velocity)

This shear stress would be larger than that given by the mean current. Grant and

Madsen's model was applied to current measurements taken during the "Halloween"
storm and the wave boundary layer was estimated to be a maximum of 11.6 cm thick,















much lower than their bottom current meter at a 29 cm elevation (Madsen et al. 1993).

This lends confidence to the assumption that our bottom current meter at an elevation of

20 cm above the bed is also outside that wave boundary layer.

Analytical models have been tested which calculate a shear velocity based on both

wave and current influence. These not only account for the individual wave and current

influence, but also any nonlinear interactions between the two. Wiberg and Smith (1983)
I I I ',, 1


i ,





l: ; M C- Ii I.K l.Ji IJ L r1Ji
Augur IS, 199B



Figure 3-9. Shear velocity vs. sonar at the 8 m bipod, August 19, 1998 (Note blue line is
shear velocity, black line is sonar, red lines are critical shear velocity)

This shear stress would be larger than that given by the mean current. Grant and

Madsen's model was applied to current measurements taken during the "Halloween"

storm and the wave boundary layer was estimated to be a maximum of 11.6 cm thick,

much lower than their bottom current meter at a 29 cm elevation (Madsen et al. 1993).

This lends confidence to the assumption that our bottom current meter at an elevation of

20 cm above the bed is also outside that wave boundary layer.

Analytical models have been tested which calculate a shear velocity based on both

wave and current influence. These not only account for the individual wave and current

influence, but also any nonlinear interactions between the two. Wiberg and Smith (1983)











02'24 048 0712 09:35 1200 1424 16:4B 19:12 21 30





6.16 l


















0..24 04 4S 07.12 05!35 1M00 141Z4 1W-48 19.12 2I,36
October 1 1997



Figure 3-10. Shear velocity vs. sonar at the 5.5 m bipod, October 18, 1997 (Note blue
line is shear velocity, black line is sonar, red lines are critical shear velocity)

compared shear velocity estimates calculated from currents alone to those calculated

from two different models, those of Grant and Madsen, and Smith. The field data used

for the analysis was collected at a similar depth, 18 m, and in an area with a similar

sediment size. They found that the shear velocities calculated using the wave-current

models are similar to the values obtained from the measured average velocity profiles,

although the estimates of surface roughness are very different (Wiberg and Smith 1983).

This suggests that recalculating shear velocities with an added wave influence would not

alter the estimates significantly. It raises the concern that estimates of the surface

roughness may not be characteristic of actual values, and often may be higher by up to an

order of magnitude. This paper also suggested that scour under the instrument frame









caused original estimates of surface roughness from the data collected by Drake and

Cacchione to be unrealistically high (Wiberg and Smith 1983). This may allow the

surface roughness calculated through the velocity profile method to be used as a quality

control parameter for the data, indicating situations where settling or scour might be a

concern.

Apparent hydraulic roughness

An investigation into estimates of bottom surface roughness showed that some

values are at the extreme limits for the sediment size present. A general idea of the

magnitude of surface roughness values that are expected is determined from

D
30

Choosing a representative sediment size of 3 q (0.125 mm) yields a value of surface

roughness on the order of 10-6 m. Calculated values may range from 10-1 m to 10-20 m

with extreme outliers exhibiting a broader range, reaching 10150 m at the 5.5 m bipod.

Many of these values do not appear to significant physical meaning, but a relative

comparison yields some interesting observations. One observation that occurs following

a storm event is a decrease in surface roughness values estimated from velocity profiles.

One possible explanation for this is that after the storm event, there is more suspended

sediment, which may inhibit turbulence and subsequently cause greater velocities.

Increased velocities would lower the surface roughness estimate by shifting the velocity

profile. The 5.5 m bipod shows more scatter than the 8 m and 13 m bipods with a

significant number of measurements reaching 10-10 m or 10-20 m. The surface roughness

values calculated here do not always show a decrease with increasing currents. This may













be realistic considering that this bipod may be inside the surf zone during peak waves and


currents and may be influenced by breaking waves.


20

r


-5
10


N' x -\-
Xx 1;
x*


X A


I,.
' I 1


x "x



i! x x \


t 6! '




SI I
I II
A 1 11



lx


October 1997


Figure 3-11. Surface roughness variation with mean currents at 5.5 m bipod for October
15-21, 1997


Four different storm events were analyzed, one in each month, and all showed this


decrease in surface roughness at the 8 m and 13 m bipods as mean currents increased.


During periods of consistently large currents and waves there is a gradual decrease in


surface roughness throughout the entire period. Plots of mean currents versus surface


roughness trends for each bipod are included in Figures 3-11,12,13 for a single storm


event in October of 1997. The different colors represent current measurements at three


different elevations. At the 8 m bipod, we see a decrease in surface roughness values


with the initial increase in currents to 40 cm/s, but then the currents increase rapidly to


21
x
c3 X
S-ffI x x I




x





I- o;l, .rrr. t.j cm
tIfrfl ::~.ir(r~l *i 5.:T.
- >ti:.?r. ^...rc.T y Ij^ :T.


I -0.;





0

22


I'- .-d







39


80 cm/s and the values of surface roughness are relatively stable. Perhaps the initial fine

sediment has been removed with the first current increase.



1Q15 Is 17 7 I 20 21
-- Man culret 2@ Z cm
Mean current @ 56 cm
-07
102


1I I






A 0.5

ii X U
C U'' I -U


r-I




15 1 17 021 2




Oober 197



Figure 3-12. Surface roughness variation with mean currents at 8 m bipod for October
15-21, 1997

Comparison of surface roughness estimates at the 8 m and 13 m bipods for the week of

October 15-21 show emerging trends. They both commence decreasing about the same

time and have similar ending values, but there appears to be a phase lag between the two.

The 13 m surface roughness values seem to increase first and decrease sooner than those

at 8 m. Surface roughness values vs. mean currents at the 5.5 m bipod show much

greater variation and do not follow the same relationships at the other two bipods.

Surface roughnesses for the entire month of October were found to be largest

during times of low currents and waves. These are on the order of one centimeter and


ghnesses for the entire month of October were found to be largest


during times of low currents and waves. These are on the order of one centimeter and








40



would indicate unrealistically large bedforms, although this observation is consistent at


all three bipods. These are on the same order of magnitude as the surface roughness


estimates that were calculated by Smith and Wiberg (1983) when they used velocity


profiles to estimate roughnesses and did not account for wave-current interaction.


M
M
kv
* t


Us

4ean cunenrt 0 2 cm
ocan cunrCnt@ 56 cm
lean cuBent@ 150 can


II:
I,,,,
S' '

K k. *,/










----------
is


i''1 I
I. r, Ii


October 1997


r'{


IC











IC

10


10






1'


Figure 3-13. Surface roughness variation with mean currents at 13 m bipod for October
15-21, 1997


The possibility of error in shear velocity and surface estimates has already been


addressed, but another potential problem is that the presence of bed forms would alter the


shape of the velocity profile. Extensive research has examined bed forms in rivers and


their effect on velocity profile estimates. Smith and McLean (1977) conducted a study in


the Hood River in Oregon, which found that the velocity profile over a bedform has a


10"'


20


X
,. -


x x






41


convex shape in a semi-log plot, which is different than the traditional linear shape. This

potential problem cannot be addressed with the limited dataset available here.














CHAPTER 4
WAVE TRANSFORMATION IN THE NEARSHORE

Introduction

There is extensive research and theory in the field of Coastal Engineering that

focuses on the evolution of wave properties with onshore propagation. Of particular

interest due to implications for engineering design, are changes in wave direction and

energy. Linear wave theory is generally accepted to provide reasonable estimates of

these changes, with the understanding that there are many other nonlinear interactions

involved in the process. The most basic application of linear wave theory considers a

single direction and frequency, when in reality waves originate from many different

directions with many different frequencies. Directional characteristics can be represented

by a directional spectrum, describing, for each frequency, a range of directions with a

mean wave direction. Based on wave refraction theory, the width of this directional

spectrum should decrease with proximity to shore.

Longuet-Higgins et al. (1991) developed a method for calculating directional

spectral estimates from field data using measurements recorded by a floating buoy. Since

then, many researchers have developed other formulations (Capon et al. 1967; Long and

Hasselmann 1979; Herbers and Guza 1989). Borgman (1969) tested different models for

design use, including what he termed a circular-normal, wrapped-around Gaussian, and a

wrapped-around Hermite series expansion. There have been many other models of

varying complexity developed, including some that adapt to specific properties of the

data. Herbers et al. (1999) considered cross-shore evolution of the mean wave









propagation direction and a directional spreading parameter. They tested measured

values of these parameters at the spectral peak frequency against those calculated from

linear wave theory and found that linear theory predicted mean wave direction and

spreading well, except for the region inshore of the bar crest where waves were breaking.

Calculations showed additional directional spreading of wave energy in this region, but

consistency in mean propagation directions suggests that this spreading was nearly

symmetric.

Small amplitude wave theory assumes irrotational flow, and an impermeable and

horizontal bottom, which are not realistic in a natural setting. Waves propagating over

real seabeds will be affected by porosity and permeability of bottom sediment, bottom

slope, and bottom surface roughness. They will also experience energy dissipation from

bottom friction, due to nonlinear shear stresses created by a turbulent boundary layer at

the bottom (Dean and Dalrymple 1991). White capping is an additional mechanism of

energy loss, here considered to be secondary to bottom friction. There has been

significant effort directed toward determining friction factors based on bottom velocity

measurements. Jonsson (1966) related the friction factor to maximum bed shear stress

and developed relationships with Reynolds number and bottom roughness parameters.

Whitford and Thornton (1988) applied a momentum balance approach to determine bed

shear stress coefficients from surf zone measurements taken at the FRF. Madsen (1994)

gives explicit formulas for wave friction factors that are dependent on the relative

magnitude of the current shear stress. Several recent studies have used turbulence

measurements to determine near-bottom turbulent shear stress and friction factors

(Trowbridge and Elgar 2001, Smyth and Hay 2002,2003). Although accomplished









through many different computational techniques, these all apply linear wave theory to

account for energy dissipation.

One focus of the present study is to compare measured values of wave height,

energy flux, and wave direction to linear wave theory estimates. Guza and Thornton

(1980) investigated differences in energy density spectra predicted from horizontal

velocity and calculated from pressure, and also compared measured and shoaled elevation

spectra assuming onshore propagation. They found reasonably good agreement between

measured and predicted spectra from measurements out to 10 m depths collected at

Torrey Pines Beach in San Diego, California (Guza and Thornton 1980). Error estimates

were around 20% in energy density and variance calculations, and even less for wave

height comparisons, although differences determined from shoaling theory were more

frequency dependent (Guza and Thornton 1980).

Analysis

Development of Analytical Spectrum

The first step toward representing directional wave properties was to develop an

analytical directional spectrum whose width could be varied to represent different wave

directional spreads. The theoretical distribution that was used for the following analysis

was

D, (0) = Am cos2m(O- ,0) Am[do (m)+ d, (m)cos(O -00 )+ d2 (m)cos(2( -002))]


where 0 = 0 is directed normal to shore and 0 in both is limited to < 0 < to
2 2

include only onshore wave directions (Figure 4-1). The above representation will be used

to approximate the so-called "measured" spectra, determined from velocity and pressure









iZ/2
measurements. D(O) is normalized such that ID(O)dO = 1. The subscript "p"
-;/2

represents the predicted spectrum for future nomenclature. Initially, integer values were

chosen for m, but the realization that other values could be useful in fitting the data led to

an extension of the analysis to non-integer values. The Fourier coefficients for several m

values that are used to approximate the theoretical spectrum are included in Table 4-1.

d d
Figure 4-2 presents the ratios of the Fourier coefficients, and 2 for different values
do do

of m. As m is increased, the theoretical spectrum becomes narrower and the ratios

approach those for the delta function; which is applicable for a single direction.



/ X

/

/









Figure 4-1. Coordinate system

Dataset

The analysis focuses on estimates of wave direction, transformation, and energy

dissipation during storm conditions in the vicinity of the FRF pier at a longshore position

of approximately 900 m. The dataset consists of current and pressure measurements

recorded in three different water depths (nominally 5.5 m, 8 m, and 13 m), which are







46


located at relatively similar alongshore locations, thus establishing a cross-shore array of

instrumentation. Choosing records from the dataset that contain significant energy helps

to assure that the measurements are meaningful.


_-m=0
--m=0.5
--m=1
--m=2
--m=3
--m=4
--m=5
--m=6
--delta fcn


n



Figure 4-2. Ratios of Fourier coefficients (curves are fit to 3 points at n = 0,1,2)

Table 4-1. Theoretical Fourier coefficients for different m values
m Am do di d2 di/do d2/do
0 0.318 0.500 0.637 0.000 1.274 0.000
0.5 0.500 0.318 0.500 0.212 1.572 0.667
1 0.637 0.250 0.424 0.250 1.696 1.000
1.5 0.751 0.212 0.375 0.255 1.769 1.203
2 0.848 0.188 0.340 0.250 1.809 1.330
2.5 0.936 0.170 0.312 0.243 1.835 1.429
3 1.019 0.156 0.291 0.234 1.865 1.500
3.5 1.090 0.146 0.273 0.226 1.870 1.548
4 1.164 0.137 0.259 0.219 1.891 1.599
4.5 1.234 0.129 0.246 0.212 1.907 1.643
5 1.293 0.123 0.235 0.205 1.911 1.667
6 1.408 0.113 0.217 0.193 1.920 1.708
oo(Sfcn) 1.000 0.159 0.318 0.318 2.000 2.000







47


There are six significant storm events that occur within the four-month period discussed

in previous chapters. Figure 4-3 shows a histogram of the significant wave height values

measured in a water depth of eight meters for each thirty-four minute record of the four

months. To obtain representative results, three samples were analyzed from each of the

six storms. The range of significant wave heights included in this analysis is 1.75 m < Hs

< 3.5 m.

One assumption employed here is Snell's Law considering bathymetry consisting

of straight and parallel bottom contours. Figure 4-4 presents bathymetry in the area

around the time that these data were collected and the red circles represent the

approximate locations of the 5.5 and 8 m bipods. The bipods are located near profile line

66 in the plot, which is an area where this assumption is reasonable.


Significant Wave Height Histogram


0.25-0.5 0.75-1 1.25-1.5 1.75-2 2.25-2.5 2.75-3 3.25-3.5 3.75-4
Wave Height Range (m)


Figure 4-3. Significant wave heights measured in October 1997, November 1997, May
1998, and August 1998











FRF Bathynetry, 25 Ocd 97, depth Tn meters
1100 11 58
I I I59
1DOO- 62

I 67
WAVE GAUGE 111 73
-00 76


171
76-
160
WAVE WU'A G 61-2 1


/ / I '
I1' F 1r87






is icrce. r








Figure 4-4. Bathymetry in vicinity of bipod instrumentation (13 m bipod is located
690 m offshore of 8 m bipod; http://www.frfusace.army.mil)









Development of Directional Spectrum from the Data

Directional spectral estimates were determined from the measured data during

significant storm events using the p-u-v method, which follows the work of Longuet-

Higgins et al (1961). The following equations used to calculate the directional spectrum

are based on pressure represented in "feet of water." The coordinate system is taken as

positive onshore and south for the measured velocity components, u and v (Figure 4-1).

For simplicity, this analysis considers the pressure sensor and current meter to be located

at the same horizontal location and distance above the bottom. The auto and cross

spectra are calculated with a segment length of N=128, which gives a resolution of
20fl 1i






D stance. m

Figure 4-4. Bathymetry in vicinity ofbipod instrumentation (13 m bipod is located
690 m offshore of 8 m bipod; http://www.frf~usace.army.mil)

Development of Directional Spectrum from the Data

Directional spectral estimates were determined from the measured data during

significant storm events using the p-u-v method, which follows the work of Longuet-

Higgins et al (1961). The following equations used to calculate the directional spectrum

are based on pressure represented in "feet of water." The coordinate system is taken as

positive onshore and south for the measured velocity components, u and v (Figure 4-1).

For simplicity, this analysis considers the pressure sensor and current meter to be located

at the same horizontal location and distance above the bottom. The auto and cross

spectra are calculated with a segment length of N=128, which gives a resolution of








0.015 Hz and 64 degrees of freedom. The actual number of degrees of freedom is
somewhat greater due to the fact that half-lapped segments are used.
The energy density spectrum is represented by

S7 (f, ) = S, ()D(f, 0)
where the directional spectrum is approximated by the Fourier series

D(f, 0) = A (f) + C, ()cos( 00) + C2 (f)cos(2( -002))
The coefficients are calculated as follows (Longuet-Higgins et al., 1961)


A (f/)


s (f)
A, (f)= S.(
S,, (f )k, (z)k, (z)

k (z) 2f cosh(k(h + z))
sinh(kh)

kp = cosh(k(h + z))
cosh(kh)


2' (f )k ((z)

B, W()
S, ( f )ku (z)kp (z)

Bf= 2S. (f)
M (Jf )k (z)

The values of C, and 0o are determined as

C,(f)= A (f)+B(f),n= 1,2

00(f)= tan- B,n= 1,2
"il \ / l'IAJ)







50


The mean wave direction (00) for each frequency to be used in calculations is taken as


the location of the maximum value of the computed directional spectrum.

The directional spectrum as determined above will be referred to as the

"measured" directional spectrum in future discussion, although this is an estimate from

the data. Figure 4-5 presents an example of the measured directional spectra at the

bottom current meter for the 5.5, 8, and 13 m bipods at the peak frequency of 0.094 Hz.

Time is measured in hour-minutes, where 100 represent 1 h and 1 represents 1 min.


Measured Directional Spectra


-80 -60 -40 -20 0 20 40 60 80
theta, degrees


Figure 4-5. Measured spectra for November 7, 1997 time=2200

Table 4-2 presents measured mean wave direction values in degrees for the peak

frequency of each storm event. These values are averaged over the three current meters at

each location. The last column includes corresponding peak direction values that were


13m
8m
- 5.5 m









calculated by the FRF using the iterative maximum likelihood method from

measurements recorded at the 8m array of 15 pressure gages. The 8 m array values are

often different than the measured mean wave directions at the 8 m bipod, sometimes by

up to 14 degrees. These are calculated for longer records of 2.5 h versus 34 min, but the

differences bring up a concern for the accuracy of measured mean wave direction

estimates. Measurements are expected to show mean wave directions approaching closer

to onshore (00 = 0) at shallower water depths, and this is generally the case, with several

exceptions.

Table 4-2. Measured mean wave directions at peak frequency
Date Time f (Hz) 00(13) 00(8) 00(5) p (8mArray)
19-Oct-97 700 0.141 35.3 36.5 32.7 22.0
19-Oct-97 1216 0.125 39.7 33.7 32.0 20.0
20-Oct-97 100 0.094 18.4 19.2 16.5 12.0
7-Nov-97 2200 0.094 18.2 16.0 10.9 10.0
7-Nov-97 2342 0.094 17.7 11.3 14.5 10.0
8-Nov-97 208 0.094 18.7 20.8 12.8 10.0
13-Nov-97 1742 0.133 22.2 19.4 12.0 12.0
13-Nov-97 2008 0.125 12.2 16.0 14.5 10.0
13-Nov-97 2200 0.117 13.2 9.7 7.8 5.0
13-May-98 852 0.086 8.7 9.8 10.2 14.0
13-May-98 1442 0.078 12.4 7.5 12.7 6.0
13-May-98 1816 0.078 8.7 9.8 10.2 12.0
2-Aug-98 916 0.133 8.9 5.0 3.7 8.0
2-Aug-98 1300 0.133 4.2 3.5 1.7 -10.0
2-Aug-98 1516 0.133 6.8 1.9 3.2 -10.0
27-Aug-98 1408 0.094 -36.7 -31.8 -29.5 -32.0
27-Aug-98 1634 0.086 -35.2 -33.6 -31.4 -28.0
27-Aug-98 1816 0.086 -32.4 -23.2 -26.4 -28.0


Determination of m Values in Dp (0)


A cos2m(O )


The m value that gives the best-fit analytical spectrum to the measured data is

determined through implementation of two different approaches. The first approach








deals directly with the coefficients of the measured and predicted spectra, while the

second employs a curve fitting technique. The primary purpose of discussing the first

approach is to emphasize that the second approach gives a greatly improved fit, although

it has some limitations.

Comparison of Fourier coefficients

The spectrum Dp (0) = Am cos2m (0 00) was determined by matching Fourier


coefficient ratios and d. This approach was based on determining m to minimize
d, d,

z(m, f) as follows

C W ) d ~] CW ) d,2
SA,(f) d, Ao () o(f)
z(m, f ) =-- C(f
Ao (f)) A(f )


A cutoff of 6 was used for m in recognition that the measured spectra were generally

wide and including higher m values would not provide an improved fit. Generally, the

central frequencies give higher best-fit m coefficients on the order of 4 to 6, producing a

narrower theoretical spectrum. The higher frequencies, and sometimes even the lower

ones, give a smaller best-fit m coefficient on the order of 2. Figure 4-6 a, b show this

trend. The 5.5 m bipod measurements often determine almost all best-fit values to be the

maximum allowed in this analysis (mmax=6). Plot c of Figure 4-6 is one example. These

values follow the general trend expected; with larger m values at inshore bipods, yet the

fit to measurements is not very good. Figure 4-7 compares the measured (solid line) and

fit (dashed line) directional spectra for the same three runs at a frequency of 0.13 Hz.

Predicted spectra are much too narrow. Error values determined from









-- 1 "
2 = ^-D ()]2
n ,=\

are presented in Figure 4-8 over the entire frequency range and they are extremely high.

Minimization of the error between coefficients does not imply that the error between the

spectra is at a minimum.

Two-sided nonlinear fit

This second approach attempts to provide a better fit by focusing on direct least

squares fit rather than matching directional spectral coefficient ratios. The measured

spectrum is often very wide, extending past the offshore directional limit of 0 = +-
2

This makes it difficult for a spectrum D ,()= Am cos2m( 00) based on a single m


value to give an accurate prediction, since it is forced between the limits of and .
2 2

This problem was overcome by fitting a different m value to each side of the measured

spectrum. The modified formulation for the analytical spectrum is

DpL(0)=Acos2m( 0-0) <0<00


DpR(0)= Acos2mR-(O0) 0<0 <

The subscripts "L" and "R" denote values for the left and right side of the directional

spectrum respectively, and A is the same for both sides. The best-fit values of mL, mR,

and A are determined through a nonlinear least squares data fitting technique, utilizing

the Gauss-Newton method.

Plots are included (Figures 4-9,10) of measured and predicted spectra and error

calculations for the same data included in Figures 4-7 and 4-8 to facilitate an appreciation


ation



















6r Xx xXx X


0 3 4 5 6
0 1 2 3 4 5 6


0.1 0.15 0.2 0.25


6

5.5

5

4.5

4

S3.5

3

2.5

2

1-s


1 2 3 4 5 6


0.05 0.1 0.15 0.2 0.25


5.5 F


E 5


cm 4.5


4


0 1 2 3 4 5 6
m


0.05 0.1 0.15
f(Hz)


Figure 4-6. Error versus m value comparison for October 20, 1997 time=100 a) 13 m

b) 8 m c) 5.5 m


0.2 0.25


:xxx


6r xxxxxxx












13m bipod 8m bipod
1.5 1.5
measured /
S predicted
B 1 cc 1
.3 m=3 / m=6 /
S/ /
cc 0.5 c 0.5 i

a 0 --


0.5 0.5
-50 0 50 -50 0 50
theta, degrees theta, degrees

5m bipod
1.5


m=6
c 1 -















October 20, 1997 time=100 a) 13 m b) 8 m c) 5.5 m
c 0.5 /








of the quality of the t. It is evident that the fit is greatly improved, with signiantly









lower error values by more than an order of magnitude. Note that the predicted spectra
6 0


-0.5
50 0 50
theta, degrees



Figure 4-7. Comparison of measured and best-fit spectra from matching coefficients for
October 20, 1997 time=100 a) 13 m b) 8 m c) 5.5 m

of the quality of the fit. It is evident that the fit is greatly improved, with significantly


lower error values by more than an order of magnitude. Note that the predicted spectra


are forced to zero at 90 degrees, because allowing waves to come from onshore would be


unrealistic.


The best-fit m values for each side of the spectrum vary with frequency.


Representative plots are presented in Figure 4-11 for measurements from the 8 m bipod


bottom current meter. There is a general trend of increasing separation between left and


right m values with increasing frequency. The decrease of mR for 00 > 0 is a result of the



increasing percentage of the measured spectrum that is outside of the < 0 < range
2 2










with increasing frequency. This trend can be observed in Figure 4-12, which includes

measured and predicted directional spectra at different frequencies, for the run included

in plot c of Figure 4-11. The low frequency spectrum has the entire width contained

within the range of onshore directions, since this energy probably represents storm swell

that has traveled a significant distance and is dominantly oriented onshore. Higher

frequency plots show an increasing portion of the width on the right side to be outside of

this range as the mean direction increases, so best-fit m coefficients that provide the

smallest error are not necessarily representative of the measured spectrum.


0.1 1
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
frequency, Hz


Figure 4-8. Error between spectra fitted from coefficient ratios for October 20, 1997
time=100

The left side m values increase slightly with increasing frequency. The right side

values show a decrease, but it is primarily due to a limitation of the method and probably

not a meaningful trend. This problem arises because the width of the measured spectrum











is very large. One way to overcome this would be to use a more accurate method of

predicting the measured spectrum, which would most likely decrease the width and


eliminate or minimize the percentage of the directional spectrum outside of the +-
2

range.


13m bipod


8m bipod


50 0 50
theta, degrees

5m bipod


-50 0 50
theta, degrees


50 0 50
theta, degrees


Figure 4-9. Comparison of measured and best-fit spectra from curve fitting for October
20, 1997 time=100 a) 13 m b) 8 m c) 5.5 m

Comparison of Data to Linear Wave Theory Calculations

The bipod measurements provide a basis for testing linear wave theory by

comparing theoretical values at inshore water depths to the associated measurements by

the bipod instrumentation. In the following analysis, calculated directional spectrum

values are determined by refracting data from thel3 m bipod and will have a subscript











"c". Measured values are those determined directly from bipod instrumentation at the


water depth of interest and will have a subscript "m".



0.004i
13m
8m
5.5 m
0.0035 -


0.003 -


0.0025/


0.002 -


0.0015 -


0.001 -


0.0005 -


.00 I
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
frequency, Hz



Figure 4-10. Error between spectra from curve fitting for October 20, 1997 time=100

These comparisons are conducted within the frequency range of 0.05 to 0.2 Hz,


which is the frequency range of significant energy evident from pressure measurements.


The high frequency cutoff is chosen as 0.2 Hz because the water surface energy density


spectral (S,, (f)) values that are calculated from the pressure response factor (k (z))


begin to increase unrealistically at higher frequencies at the 13 m bipod, and are not


representative of field conditions. This is evident in Figure 4-13. This cutoff is also


consistent with linear wave theory since 0.2 Hz represents a wave period of 5 s, and at a











59



water depth of 13 m waves with a period of less than 4 s would be deep-water waves and


would not interact with the bottom.


a _- m1
2 mR



0x


0.05 0.1 0.15 0.2
b



2-
1.5 -



0
0.05 0.1 0.15 0.2
2.5
2. |--------------------------------------






2 -
1.5 -
1-






05
Or-


frequency, Hz


Figure 4-11. Variation of m values with frequency range at 8 m a) May 13, 1998
time=852 b) November 7, 1997 time=2200 c) October 19, 1997 time=700


f. 0.08 Hz


r\







I \ :


-50 0 50
thetn, degees


-50 0 50 -50 0 50
thea, degrees teta, degrees


Figure 4-12. Directional spectrum variation with frequency at 8 m bipod for October 19,
1997 time=700







60




6 6
S-- pressure s -- pressure
5 .eta 5 eta
E E
24 4





0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

f (Hz) f (Hz)

6
pressure
S5 e eta
E
a a
1 '
2o2







0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2
f(Hz) f(Hz)











Figure 4-13. Energy density spectral values for October 19, 1997 time=700 a) 13 m
b) 8 m c) 5.5 m
Wave directionpressure












A first comparison is of measured and calculated central wave direction (00)values


from directional spectral estimates. Snell's Law is applied to find refracted wave


direction values at the two inshore bipods. The calculated wave direction is defined as
E 5 eta






























\ C(13)
0 0.i 0.2 0.3 0.4 0.5
f(Hz)



Figure 4-13. Energy density spectral values for October 19, 1997 time=700 a) 13 m
b) 8 m c) 5.5 m

Wave direction

A first comparison is of measured and calculated central wave direction (6^ )values


from directional spectral estimates. Snell's Law is applied to find refracted wave


direction values at the two inshore bipods. The calculated wave direction is defined as



OC(8) sin -KC( 2,; -


and the measured wave direction (O(8)) as the direction of the maximum value of the


computed directional spectrum. Figure 4-14 includes a plot of measured vs. calculated


wave directions at the 5.5 m and 8 m bipods on October 19, 1997. The different symbols


represent measurements from each of the three current meters. Measured mean wave







61


directions at the 8 m bipod appear to be well predicted, while those at the 5.5 m bipod

show a slight offset. Figure 4-15 compares these same values at the 5.5 m bipod in a

different format. Plot a presents measured angles in degrees and plot b presents the

difference in measured and calculated angles (0, -0,) in degrees. There is a


deterioration of measured and calculated directions in the low frequency range since there

is not significant energy present and directional spectral estimates become less

meaningful. This specific plot shows an overall slight offset of approximately seven

degrees.


8 m Bipod 5.5 m Bipod
60
60 meas @ 20cm -
meas @ 55cm /,


S20 5'ur
_n .

19 -5
-O XX0 /
o 0* u


-20 20 "
20 0 20 40 60 20 0 20 40 60
Measured Measured


Figure 4-14. Mean wave direction comparison for October 19, 1997 time=700

Average values between the three current meters for each of 3 records in October

1997 are presented in Figure 4-16. These values represent the difference in measured and

calculated angles (,,, ,) in degrees. It is important to note that the large variation


between measured and calculated wave directions at low frequencies is a result of the

wave direction deterioration shown in Figure 4-15. In the frequency range with

significant energy, the differences fluctuate around zero, suggesting that angles are

predicted fairly well by linear theory. When there does appear to be an offset, it is

usually positive, which represents greater measured values. This suggests that linear







62


theory refracts the angles too much toward normal incidence in these


instances.






50- \


:, ---l.. 2- :-

0 menc @ 55cm
cac @ 150cm






-10
it5 ,j I 1}15 I















0.05 0.1 015 0.2
Frequency Hz




Figure 4-15. Measured and calculated wave direction differences for October 19, 1997
time=700 at 5.5 m bipod a) 0,,,, degrees b) (0,,, 0), degrees


Refracted m values

An extension of the refracted angle analysis is to determine how well the


directional spectrum at inshore bipod locations can be predicted from refraction of


directional spectral estimates from the offshore bipod. This is accomplished by


comparing best-fit m values for a refracted directional spectrum versus those for a

measured directional spectrum at 8 m and 5.5 m water depths. The refracted directional

spectrum is (Lee et al. 1980)
spectrum is (Lee et al. 1980)






63



D,(f,O)= Dp(13)(f0 k)(f)I


where Dp(13) has been normalized to have an area of one. The corresponding 0 values

for the refracted spectrum are

C sin 0(13)
= sin
C(13)

The refracted spectrum is also normalized to one before fitting m values using


,,-~ 7 -


/y


/~


Figure 4-16. Average measured and calculated wave direction differences for October
1997 a) (O C), degrees 8 m b) (Om ), degrees 5.5 m


,;~ Z


't-""
~














11/2
D,(f,0)= D(f, 0) -12

fD,(f,O)dO



Best-fit mL and mR values for the refracted spectra are determined using the method


discussed previously. The curve fitting procedure was used since this was determined to


provide a much better fit than the alternate approach.


8 m Bipod 5.5 m Bipod
Measured
1 Refracted 1
c/ \
u 0.8 0.8
Q/ I
Y/ )-
S0.6 0.6

e 0.4 0.4 \

0.2 \0.2

0 0
50 0 50 -50 0 50
theta theta


Figure 4-17. Measured and refracted directional spectra for November 13, 1997
time=1742

Sample refracted and measured spectra for November 13, 1997 at a frequency of


0.13 Hz are presented in Figure 4-17. The refracted spectra are narrower than those


measured at both inshore bipod locations. This suggests that linear theory predicts more


refraction than associated with the measurements. This comparison is further reflected in


the values of m coefficients. Figure 4-18 shows that refracted m values are greater than


measured values, and show a slight decrease with increasing frequency as opposed to the


slight increase of measured m values. The measured right side coefficients are much


lower for reasons discussed previously. The difference between measured and refracted











spectral widths may also be affected by the method chosen to estimate the measured


directional spectra.




--------- -- --r -- -- ml '- -
r- eIr..-t *A



E UIS





0.04 P -6 (B %1 0 0014 01 10 02 0.2
frequency













b
0.04 0.06 0.8 0.1 0.12 0.14 0.16 0.1 0.2 0. Z2
frequency




Figure 4-18. Comparison of refracted and measured m values over frequency range for
November 13, 1997 time=1742 a) 8 m b) 5.5 m


Wave height comparisons


The previous analysis focusing on direction leads to a comparison of significant


wave height values by applying the concept of conservation of energy flux. Energy flux


is defined as


i3(f )= pgS,,C, cos ,


A calculated water surface spectrum was obtained at the 8 m inshore bipod location using


the equation



is defined as


i3(f) = pgS,,C, cos 0


A calculated water surface spectrum was obtained at the 8 m inshore bipod location using


the equation











rv g(13) c (183)
iW C -g(8) A Co s O(s )

and similarly for the 5.5 m inshore bipod. In the above equation the value of m was

taken as the location of the maximum value of the computed directional spectrum. This

leads to slightly larger energy flux values than if the entire range of directions was

considered. The zero moment of the water surface spectrum gives a significant wave

height value of

Hmo = 4m

0 2Hz
m,= 0 S,, (f 7 f
0 05Hz

and calculated and measured values are obtained by using the respective water surface

spectra.

Ratios of measured to predicted values of significant wave height for the 18

records considered are plotted in Figure 4-19. This shows most measured values being

less than predicted since almost all of the ratios at the inshore bipods are less than 1,

ranging from a 5% increase to a 25% decrease. This decrease is expected since friction

losses have not yet been considered.

Energy flux comparisons

Measured energy flux values are found for each bipod location and compared by

considering the percent loss between bipods. The percent energy loss between the 13 m

and 8 m bipods is determined from







67


02Hz 02Hz


0%los Hz 2Hz

f3, (3)(f)df
005Hz


and similarly for the distance between the 8 m and 5.5 m bipods. Table 4-3 shows the


average energy loss values of the three current meters at the bipod for each record, with


negative percent values representing cases that had greater measured energy flux values


at inshore bipods. There are many instances of significant loss, with some reaching more


than one third of the total energy flux. This enforces the need to consider energy loss in



1.1 ,


1,f5


400 600 100 1000
Csssh ar Posiaon, m


12)0 1400


Figure 4-19. Significant wave height ratios versus cross-shore position (FRF coordinate
system)


0e a-









engineering design and planning, since neglecting this component would lead to a

significant overestimation of energy flux values in many cases, especially for propagation

over long distances.

Figure 4-20 shows the average energy flux variation over frequency range for all

18 storm events, and includes percent loss of average energy flux values. The dashed

lines in plots b and c indicate the measured energy flux at the offshore bipod, which is the

same as that which would be predicted with no energy loss. These are compared to the

measured values shown by the solid lines. There are different cross-shore separation

distances between the three bipods. The 13 m and 8 m bipods are separated by 690 m in

the cross-shore direction, whereas the 8 m and 5.5 m bipods are separated by only 333 m.

Of interest is that the average percent energy loss between the 8 m and 5.5 m bipods is

greater than between the 13 m and 8 m bipods (Table 4-3), even though the separation

distance for the smaller percentage energy loss is twice as long. The percent energy

losses of the average values included in Figure 4-20 also indicate this trend. Of course,

the reason is that bottom friction is more effective in causing energy loss in shallower

water.

Friction factor

The wave height and energy flux analyses showed over-prediction from linear

theory since energy loss was not considered. This analysis assumes friction is the only

cause of energy change between bipods. In reality there are many other contributing

factors, including the possibility of energy growth due to wind, energy loss due to white

capping, or the redistribution of energy within the spectrum due to non-linear

interactions. By accounting for frictional energy loss in the energy flux calculation, a

representative friction factor can be determined for the site.










Table 4-3. Average % energy loss values between bipods
% Loss % Loss
Year Month Day Time (13-8) (8 5.5)
1997 10 19 700 17.12 1.11
1997 10 19 1216 25.76 -1.18
1997 10 20 100 -7.11 10.13
1997 11 7 2200 2.45 3.28
1997 11 7 2342 35.57 -8.18
1997 11 8 208 -12.34 5.51
1997 11 13 1742 10.74 8.61
1997 11 13 2008 -17.13 27.13
1997 11 13 2200 17.58 22.75
1998 5 13 852 20.70 16.55
1998 5 13 1442 3.47 21.01
1998 5 13 1816 20.26 21.08
1998 8 2 916 10.87 0.84
1998 8 2 1300 -5.77 2.95
1998 8 2 1516 -2.99 14.12
1998 8 27 1408 14.65 28.41
1998 8 27 1634 25.24 27.74
1998 8 27 1816 15.61 25.81
Average 9.70 12.65


The friction factor is estimated using


J3,df- J..bdf. 1[D +,Db]AX
005Hz 0 05Hz

where Ax is the total cross-shore distance between the 13 and 5.5 m bipods, and D is the

energy loss term expressed as

"' pif 3
D = TyUb =- II,


which accounts for energy damping by bottom friction. In this expression, u, is the

velocity time series measured at the bottom current meter, located approximately 20 cm

above the bottom, and ff represents the friction factor. Figure 4-21 shows surveyed

bathymetry that was collected near the bipod locations and around the same general


nI I


nI I








70



timeframe that the data were collected, giving some insight into the bottom


characteristics between instruments. These survey lines were measured at the FRF using


the Coastal Research Amphibious Buggy (CRAB) and Lighter Amphibious Resupply


Cargo (LARC). Specific dates are included in the legend.


Z3 -





0.05 0.1 0.15 0.2
x 10
4
-- Measured @ 8 m
Z 3 -- Measured @ 13m

S- % Total Loss =12.50
2 /
b -----
b ---1
0.05 0.1 0.15 0.2
x 10
4
Measured @ 5.5 m
z 3- -- Measured @ 8 m
Iu- /% Total Loss =14.28



0.05 0. 0.15 0.2
0.05 0.1 0.15 0.2


Figure 4-20. Average measured and predicted energy flux values a) 13 m b) 8 m
c) 5.5 m


The calculated friction factors of interest are those resulting from total velocity


measurements taken at the bottom current meter, since this velocity is the most


representative of the bottom velocity. This total velocity is calculated as the magnitude


of the instantaneous velocity vector. These friction factors are included in Table 4-4.


Most values from the bottom current meter are in the range of 0 to 0.2, although there is a


considerable spread from 0 to 0.32. The mean and standard deviation values for the








71



bottom current meter are 0.116 and 0.105 respectively. The negative value on August 2,


1998 is probably not real, since the bottom current meter had a flag for low beam


correlation. The other current meters gave estimates of 0.009 and 0.014 for that record,


which are more reasonable. Friction factor estimates from velocities measured at the


higher current meters were found to check for consistency. A histogram of all of the


calculated values is shown in Figure 4-22. Combining values from all current meters


gives a mean of 0.094 and a standard deviation of 0.08.






"1 Orlgn11i P:iVOP ,o M,"3!
4 LARC Lie 52
LARC LMbc 7
\ CRAB- 102s 7
CRAB- 1Z17l97
CRAB /el&rd,
CRAEIG V
S-- CRAB aW18

e A ",









10 -

11

12-




Csos shore, m
0 2M 400 S00 800 1000 1U00 14WO 16G00 18n0




Figure 4-21. Surveyed bathymetry in vicinity of bipod instrumentation


It does not seem unreasonable to find a range of factors during storms and for


different storm conditions since friction factors can change as currents increase and


sediment is displaced. Figure 4-23 shows that friction factors generally increase with


significant wave height values. It is important to note that if the highest waves were









breaking before reaching the 5.5 m bipod, then friction factors would be unrealistically

high, since the calculation assumes that all energy dissipation is from bottom friction.

Table 4-4. Friction factor estimates from bottom current meter
Date Time ff Hmo
10/19/1997 700 0.101 2.28
10/19/1997 1216 0.111 2.86
10/20/1997 100 0.025 2.22
11/7/1997 2200 0.056 1.88
11/7/1997 2342 0.283 2.09
11/8/1997 208 -0.029 1.63
11/13/1997 1742 0.154 2.81
11/13/1997 2008 0.1 2.82
11/13/1997 2200 0.318 3.01
5/13/1998 852 0.165 3.31
5/13/1998 1442 0.094 2.99
5/13/1998 1816 0.246 3.43
8/2/1998 916 0.016 2.1
8/2/1998 1300 -0.083 2.19
8/2/1998 1516 0.042 2.11
8/27/1998 1408 0.129 3.35
8/27/1998 1634 0.177 3.45
8/27/1998 1816 0.186 3.13
Average 0.116
Standard Deviation 0.105

It seems useful to determine a single representative friction factor for this specific

location. This was accomplished by using average energy flux and energy loss values

over all 18 storm events in the above equation. This analysis resulted in a friction factor

of 0.170 between the 13 m and 8 m water depths and 0.177 between 8 m and 5.5 m water

depths. These two values are consistent and 0.17 is determined as a representative

friction factor in the vicinity of the bipod instrumentation.

Reynolds Stresses

Another approach to examine shear stress was through calculation of the

Reynolds stresses. These are related to shear stress by the following equations










Tr = -PitW


Tz =-pu'w'


where positive values are onshore and south. The time series were filtered to include only

the frequencies within the range 0.05 to 0.2 Hz. It was expected that these values would

be comparable to shear stress values calculated from the velocity profile method

discussed in Chapter 3. Those values generally ranged from 0 to 0.5 N/m2, as calculated

based on mean velocities. The stresses based on Reynolds stresses are larger, but they

represent shear stress values determined from the oscillatory velocity component.

Examples of values for October 1997 are presented in Table 4-5. The notation Xl, X2,

and X3 represents the bottom, middle, and top current meters respectively.



6



5 -
5



4


0



Enli


I M W L M E UM f
0.15 0.1 0.05 0 0.05 0.1
Friction Factor Range


0.15 0.20 0.25 030


Figure 4-22. Histogram of calculated friction factors at all current meters











0.35
0.3
0.25
0.2
0.15 -
t 0.1 #
0.05
0
-0.05 0 1 2 3
-0.1
-0.15
Hmo m


Figure 4-23. Friction factor variation with wave height at the bottom current meter

One disturbingly consistent feature of these results is that the values at the middle

current meter often have a different sign and magnitude than the other two current

meters, at all three bipod locations. If there was flow reversal within the water column,

these values would be expected to show a trend. If there was a problem with the current

meter at a specific bipod, the anomalous value should be present only at one location.

Neither of those situations occurs, and this consistency is present throughout all four

months. At present, this feature cannot be explained.

Discussion

To reinforce the analysis presented in this chapter, this section provides a brief

overview of primary discussion points. The analytical spectrum establishes a simplified

representation of directional properties of the wave data that can be used to approximate

the measured spectrum, obtained through a direct Fourier Transform method. Later

comparisons are facilitated by considering the m value, or power of the cosine curve as a

measure of the properties of the spectrum. The first approach matched Fourier









coefficients to the data, but this resulted in a poor fit to the directional spectra. The

second approach employed a curve fit to individual sides of the spectrum, which gave a

vastly improved fit. One limitation of this approach is that measured spectra often extend

beyond the 900 limits, giving unrealistically low right side m values for 00 > 0.

Table 4-5. Reynolds stresses for October 1997 (XI, X2, X3 represent bottom, middle
and top current meters respectively)

Date Time Gage Z.x = -puHw1 Zy = -PVWI
10/19/1997 700 13X1 1.66 0.68
13X2 -2.34 -0.36
13X3 2.23 1.43
8X1 2.50 1.69
8X2 -6.79 -2.81
8X3 4.67 4.67
5X1 -0.96 -0.51
5X2 -15.27 -7.37
5X3 -1.34 -1.01
10/19/1997 1216 13X1 2.20 1.44
13X2 -8.20 -3.74
13X3 3.25 2.72
8X1 0.88 1.74
8X2 -10.23 -4.91
8X3 7.33 3.91
5X1 5.66 4.76
5X2 -15.23 -5.18
5X3 0.97 1.93
10/20/1997 100 13X1 3.77 0.74
13X2 -7.67 -2.87
13X3 3.77 1.79
8X1 6.68 2.44
8X2 -15.03 -5.58
8X3 3.88 3.15
5X1 -0.93 -0.59
5X2 -17.12 -4.23
5X3 -3.65 0.34


A second focus was to compare measurements with linear wave theory

predictions. Refracted mean wave direction angles were similar to measurements. If









offsets were present, they usually represented too much refraction by linear wave theory.

Interestingly, when refracting the entire directional spectrum, the width was narrower

than that which was measured, representing an overestimation by refraction theory on the

whole. This trend is also reflected in the refracted and measured m value comparisons.

The wave height and energy flux calculations combined shoaling and refraction theory

and showed smaller measured values, as expected when energy losses are not accounted

for. Friction factors were estimated by accounting for energy losses, and most values

were in the range of 0 to 0.2, although these appear to vary with storm conditions. A

representative value of 0.17 was identified for this location using average energy flux and

energy loss values. Calculated Reynolds stresses were very strange with the middle

current meter yielding significantly different values at all three water depths; this effect

remains unexplained.














CHAPTER 5
CONCLUSIONS

A knowledge of wave characteristics, sediment characteristics, and bed elevation

within the nearshore zone are imperative for engineering design and planning purposes.

Predictions of these processes are utilized when making decisions regarding coastal

development and beach preservation. Improving our knowledge of nearshore processes

and the accuracy of current prediction results is required for coastal planners to make

better decisions. This study presents analysis of sonar, pressure, and current

measurements to evaluate erosion thresholds, wave evolution and bottom friction results.

Comparisons between mean current and sonar measurements in Chapter 1 defined

a mean current threshold of 20 cm/s for bed erosion. In addition, this comparison

highlights the need to consider fair-weather conditions for sediment transport, since many

significant bed elevation changes occurred when wave heights were less than 2 m. No

orbital velocity threshold was determined, but combined waves and currents always

caused a bed elevation change when velocities reached 60 cm/s. Alongshore currents

appeared to coincide with wind velocities, though cross-shore currents did not.

Sonar histograms at the 5.5 m and 13 m bipods generally showed a well-defined

peak with minimal spreading, lending confidence to sonar estimates of bottom elevation.

The 8 m bipod consistently showed spreading at depths greater than the peak, an

observation that remains unexplained. One situation in late August 1998 at the 13 m

bipod shows two peaks following a significant storm event. This may be an indication of









the presence of fine, silty material, although this hypothesis cannot be validated with

confidence.

Velocity profile analyses provided estimates of shear velocity and surface

roughness. The shear velocity proved a good indicator of bottom elevation change at the

8 m and 13 m bipods, with erosion beginning zero to three hours after it crossed the

threshold for movement. Shear velocity estimates at the 5.5 m bipod always remained

below this threshold. Surface roughness values at the 8 m and 13 m bipods decreased

with increasing mean currents. The 5.5 m bipod experiences more scatter in surface

roughness estimates and does not always follow this relationship. Comparisons of the

variation in surface roughness values at the 8 m and 13 m bipods indicate a phase lag,

with 13 m values increasing first and decreasing sooner than 8 m.

Chapter 4 focused on evolution of wave characteristics. Measured directional

spectra were obtained for each bipod location using the Direct Fourier Transform

method. A simplified analytical spectrum based on a cosine curve of varying power (m)

was used to approximate measured values. A nonlinear least-squares curve fit to each

side of the measured spectrum proved the most accurate way of determining best-fit m

values. Limiting wave directions to onshore introduced some problems with mR

predictions being unrealistically low when measured spectra were outside of this range.

Unfortunately, this could not be avoided since allowing waves to come from onshore

would not be realistic.

The comparison with theoretical calculations employed shoaling and refraction

theory. Refracted mean wave directions were similar to those measured, with a slight

overrefraction by the theory. On the whole, the theory predicted a narrower spectrum









than that measured, representing overrefraction. This may be expected at the 5.5 m bipod

if it were inside the surf zone, since there can be directional spreading associated with

wave breaking. This same observation at the 8 m bipod seems more surprising. It is very

possible that this result represents a limitation of the method used to estimate measured

directional spectra. Energy flux calculations emphasized the need to consider energy

loss, which reached as high as one third of measured energy flux values. Friction factors

showed considerable variation with storm conditions, although most values fell within the

range of 0 to 0.2. This is reasonable, as storm conditions encompass varying current

intensities that interact with bottom sediment, affecting roughness and subsequently

energy loss from bottom friction. Through utilization of average energy flux and energy

loss values, a representative friction factor of 0.17 was determined for the area in the

vicinity of bipod instrumentation.

Reynolds stress calculations yielded unexpected results. The bottom and top

current meter shear stress estimates were consistent in magnitude and direction. The

middle current meter values were inconsistent at all three bipod locations. The

systematic occurrence of this feature in measurements recorded by different instruments

suggests validity, yet the cause remains unexplained.

One specific area where these results could be improved for future discussion is in

the representation of measured directional spectra. This analysis utilized a simple

technique, and much work has been done to improve upon this method and develop

techniques that are data adaptive. The measured spectra were very wide, which caused

problems when fitting the analytical representation and may have influenced results from

the refraction comparison. Another limitation of this analysis deals with the erosion






80


discussion, since the sonar measurements only record bottom elevation change. Similar

studies have incorporated suspended sediment measurements or side scan sonar images,

which provide a more complete basis for sediment transport determination.
















LIST OF REFERENCES


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BIOGRAPHICAL SKETCH

Jodi Eshleman was born in Pittsburgh, Pennsylvania on May 22, 1980. After

graduating high school in 1998, she attended Lehigh University, located in Bethlehem,

Pa. There she developed a passion for addressing water-related issues worldwide. She

completed a bachelor's degree in Civil Engineering in the spring of May, 2002. Many

summer vacations spent along the Atlantic coast gave her a love of the beach; and recent

trips to the Outer Banks of North Carolina brought an awareness of the sensitive balance

between coastal development and beach sustainability. This led her to the Coastal

Engineering program at the University of Florida, to pursue a Master of Science degree.