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Quantification of surf zone velocities and turbulence using digital particle image velocimetry

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Title:
Quantification of surf zone velocities and turbulence using digital particle image velocimetry
Series Title:
UFLCOEL-98008
Creator:
Roebuck, Gregory J., 1973-
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville Fla
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Coastal & Oceanographic Engineering Dept.
Publication Date:
Language:
English
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x, 122 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Ocean waves -- Measurement ( lcsh )
Fluid dynamic measurements ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.S.)--University of Florida, 1998.
Bibliography:
Includes bibliographical references (leaves 120-121).
General Note:
Typescript.
Statement of Responsibility:
by Gregory J. Roebuck.

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University of Florida
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University of Florida
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41567277 ( OCLC )

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UFL/COEL-98/008

QUANTIFICATION OF SURF ZONE VELOCITIES AND TURBULENCE USING DIGITAL PARTICLE IMAGE VELOCIMETRY by
Gregory J. Roebuck Thesis

1998




QUANTIFICATION OF SURF ZONE VELOCITIES
AND TURBULENCE USING
DIGITAL PARTICLE IMAGE VELOCIMETRY
By
GREGORY J. ROEBUCK

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

1998




ACKNOWLEDGMENTS

I would like to express my sincere appreciation and gratitude to my advisor and supervisory committee chairman, Dr. Robert Thieke, for his suggestions, support, and guidance over the past two years. His never-ending interest and concern for students, qualities sometimes lost by professors, will not soon be forgotten.
Dr. Robert Dean deserves special thanks for being both my professor for several classes and a member of my supervisory committee. It has been an honor to work with Dr. Dean on a level which has shown his concern for students and his incredible enthusiasm for coastal engineering. My thanks also extend to Dr. Daniel Hanes for serving on my supervisory committee.
My thanks also go all of the staff at the Coastal and Oceanographic Laboratory at the University of Florida. Jim Joiner and Vernon Sparkman especially were extremely helpful in assisting me in my endeavors at the lab. Their generosity will be remembered for years to come.
Individual staff throughout the department, including Becky Hudson, Helen, Lucy, and Sandra have made my time here enjoyable. I am forever indebted for your assistance over the past two years.
I would like to thank many of the students I have grown to know, especially, Eric, Al, Matt, Jamie, Pete, Nicholas, Roberto, Carrie, Kerry-Anne, Wendy, Gus, and Mike T. The best of luck to all of you in your future endeavors.




I would like to thank my parents and family for their continued support, and to Beavis for many, many games of Cribbage (of which I retire with a commanding lead). Finally, I would especially like to thank Laura for staying with me for the past two years, overcoming the "long distance relationship" and believing in us.




TABLE OF CONTENTS
page
A CKN OW LED GM EN TS .................................................................................................. ii
LIST OF TABLES ............................................................................................................. vi
LIST OF FIGU RES .......................................................................................................... vii
AB STRA CT ....................................................................................................................... ix
1 INTRODU CTION ......................................................................................................... 1
2 LITERATURE REVIEW AND THEORETICAL BACKGROUND ........................... 4
Development of a Digital Particle Image Velocimetry Technique .......................... 4
M easurem ent of V elocity Com ponents ................................................................... 8
M easurem ent of Surf Zone Quantities ................................................................... 10
Calculation of Tw o-D im ensional V olum etric Flow .............................................. 14
Calculation of Radiation Stress (due to waves and turbulence) ............................. 15
3 EXPERIMENTAL SETUP AND PROCEDURES ..................................................... 17
Experim ental Sum m ary ......................................................................................... 17
W ave Conditions .................................................................................................... 17
D ata Collection/Analysis Equipm ent ..................................................................... 18
Physical Setup ........................................................................................................ 20
Experim ental Procedures ....................................................................................... 23
D ata Processing ...................................................................................................... 26
4 EXPERIM EN TAL RESULTS ..................................................................................... 33
Im age Processing ................................................................................................... 33
Free Surface Elevations/Bed D ata ......................................................................... 34
Instantaneous V elocity Fields (IVFs) .................................................................... 34
Filtered/U filtered Ensem ble Averaged Velocity Fields ....................................... 37
Eulerian M ean V elocities ....................................................................................... 39
V olum etric Transport ............................................................................................. 40
Turbulence ............................................................................................................. 43
Radiation Stress ..................................................................................................... 50
5 CONCLUSIONS AND RECOMMENDATIONS ...................................................... 53




APPENDICES
A POST PROCESSING INFORMATION ............................................................... 56
B PLOTS OF MEASURED QUANTITIES FOR TEST DI ...................................... 57
C PLOTS OF MEASURED QUANTITIES FOR TEST D2 ...................................... 62
D PLOTS OF MEASURED QUANTITIES FOR TEST GI ..................................... 67
E PLOTS OF MEASURED QUANTITIES FOR TEST G2 ...................................... 72
F PLOTS OF MEASURED QUANTITIES FOR TEST J2 ....................................... 77
G PLOTS OF MEASURED QUANTITIES FOR TEST J3 ....................................... 82
H PLOTS OF MEASURED QUANTITIES FOR TEST J4 ....................................... 87
1 PLOTS OF MEASURED QUANTITIES FOR TEST J5 ........................................ 92
J COM PU TER PRO GR AM S ..................................................................................... 97
LIST O F R EFER EN CE S ................................................................................................. 120
BIO GR A PH ICA L SK ETCH ........................................................................................... 122




LIST OF TABLES

Table page
3.1 Wave conditions for experiments run. H( 1-3) represents Test H, film
positions 1, 2, and 3 ........................................................................ 18
4.1 Comparing ratio of horizontal to vertical turbulence (u' / w'). % difference
is based on the value of the ratio, 1.3 1, for plane wake theory from
Svendsen (1987) ............................................................................ 45




LIST OF FIGURES

Figure page
2.1 Comparison between Video PIV measurements with (a) time interval = 2Oms
and (b) time interval = 5 ins. Note that most velocities are correctly detected
with shorter time interval of 5 ms in (b), Huang and Fiedler (1994)................... 7
2.2 Eulerian Averaging Definitions from Roebuck et al. (1997) ........................... 8
2.3 Experimental Data and Model Predictions by (a) Stive and Wind (1982)
and (b) Deigaard et al. (1986) for dimensionless turbulent kinetic energy (TKE) in
a surf zone, Svendsen (19 87)............................................................... 12
3.1 Wave Tank Schematic. (a) End View; (b) Front View .................................. 22
3.2 Actual and measured displacements generated as a result of low particle seeding
density........................................................................................ 30
3.3 Test G2, Image 38. Digitized free surface and bed information. Note that the
lines depicting free surface and bed data have been enlarged for visual purposes. ..32
3.4 Unfiltered and filtered ensemble averaged velocity data determined through the
use of digitized free surface and bed data................................................. 32
4.1 Evolution of the free surface, digitized bed, q (-), and still water level (-)
Test G2. Note that only every 5' instantaneous free surface is plotted
corresponding to every 5/6Offi or 1/12~h of a second ...................................... 35
4.2 Examples of low resolution IVFs due to (a) low particle seeding density
and (b) high aeration of the water column ................................................ 37
4.3 (a-d) Examples of IVFs with high resolution for Test G2, H.=3.03 cm.,
T = 1.37 sec................................................................................ 38
4.4 (a-b) Unfiltered and filtered ensemble averaged velocities. Test G2 Phase
32 of 76. H. =3.03 cm, T =1.37 sec ..................................................... 39
4.5 Eulerian Mean Velocity field, Test G2. The mean ratio of crest (shoreward)
to trough (seaward) horizontal velocities is 0.3 ......................................... 41




4.6 Eulerian Mean Velocity field, Test J5. Note the poor measurements obtained
in the bore of the wave due to significant aeration, yet trough measurements
still yield reliable data ...................................................................... 41
4.7 Two Dimensional volumetric transport showing conservation of mass,
Test G2, H,, = 3.03 cm, T = 1.37 sec. Note the domination of seaward velocities
due to better resolution in the trough ...................................................... 42
4.8 Two Dimensional volumetric transport, Test J5, H0 = 2.67 cm, T =1.35 sec.
Note the expected decrease in transport below the trough level, and constant
transport in the crest due to unreliable data caused by significant aeration........... 43
4.9 Vertical Profiles of wave fluctuating velocities Test G2,
HO = 3.03 cm, T=1.37 sec. (a) U",; (b) W,,, ............................................ 46
4. 10 Evolution of Non-Dimension Turbulent Kinetic Energy ( T~
HO = 2.67, T = 1.35, h~b= 7.87 cm. Note that h,, = still water depth
and hob = the still water depth at the location of breaking. (a) Test J2; (b) Test
B3; (c) Test J4; (d) Test J5 ................................................................. 49
4.11 Evolution of Non-Dimension Turbulent Kinetic Energy ( -r-7
HO = 3.03 cm, T = 1.37 sec, hob = 8.69 cm. (a) Test Gi; (b) Test G2................50
4.12 Turbulence Induced Radiation Stress, Sxx' (N/in), from three separate tests
under the same wave conditions. Tests J2, J3, J4 ...................................... 52
4.13 Wave Induced Radiation Stress, Sxx" (N/in), from three separate tests
under the same wave conditions. Tests J2, B3 and J4................................... 52




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
QUANTIFICATION OF SURF ZONE VELOCITIES AND TURBULENCE USING
DIGITAL PARTICLE IMAGE VELOCIMETRY By
Gregory J. Roebuck
August 1998
Chairman: Dr. Robert J. Thieke
Major Department: Coastal and Oceanographic Engineering
The surf zone remains one of the least understood portions of the coastal engineering field. Previous attempts to quantify the fundamental properties of the surf zone have been made via the use of Hot Film Anemometry and Laser Doppler Anemometry. These, and other techniques, have not provided adequate spatial and temporal resolution in measurements of the surf zone. Particle Image Velocimetry, though able to yield good spatial and temporal resolution in the trough of the wave, fails to provide information in the aerated crest of the breaking wave due to its use of laser illumination. In the past seven years, the advancement in technology has led to the development of a Digital Particle Image Velocimetry (DPIV) system which uses a crosscorrelation technique between similar subsections of successive video frames to determine particle displacements. Ensemble and time averaging of these displacement




data allow for extraction of instantaneous and mean velocities, turbulence, and other properties of the flow studied.
Experiments were performed at the Coastal and Oceanographic Engineering Laboratory at the University of Florida, Gainesville, Florida. The measurements to be presented will include the instantaneous 2-D velocity fields in the surf zone, and also on time averaged quantities commonly used in modeling of surf zone dynamics, notably: 1) the spatial distributions of the horizontal and vertical root mean square wave fluctuating intensities, 2) the vertical profiles of the mean flow and integrated volume transport and 3) non-dimensional turbulent kinetic energy. Note that other measurement techniques (LDA, hot-film, etc.) have not permitted such measurements in the past; measurements of mass flux in the crest region of surf zone waves have only been inferred by assuming a balance with the seaward directed return flow below the trough level, and quantitative measurements of the turbulence in the upper surf zone have not been performed previously.




CHAPTER 1
INTRODUCTION
As a general understanding of many of the physical processes of the ocean is developed through scientific investigations and discoveries, one of the most accessible sections of the ocean, the surf zone, is perhaps one of the least understood. In recent years, it has been possible to predict wave generation due to wind. It has also been possible to predict transformations as waves propagate from deep water right up until the break point. In the surf zone, set-up and wave heights can be modeled reasonably well. However, many of the detailed flow characteristics including instantaneous and mean velocity fields, spatial variations of mass flux and turbulence, and turbulent kinetic energies are not nearly as well predicted, in large part due to a lack of supporting measurements in this region.
The surf zone is the area extending from the point at which the waves begin to break up to the still water shoreline. There are typically two distinct regions of the surf zone. The first is known as the transition region (or outer surf zone) which begins at the break point, and in which set-up is constant and wave height rapidly decays. The transition zone ends when set-up begins to increase and the rate of wave height decay decreases (Craig 1994). The second region is typically described as the bore region (or inner surf zone), extending from the transition point up to the beach/water interface. Global aspects of both of these areas have been modeled in the past with some success,




but detailed modeling of the entire surf zone has not been possible due to the general lack of accurate data for model comparison and development.
Various techniques have been applied to measuring velocities in these regions with notable difficulties. The largest problem occurring in the measurement techniques is determining an accurate way of measuring fluid velocities in the crest of the breaking wave. Previous measurement techniques such as Hot Film Anemometry (HFA) and Laser Doppler Anemometry (LDA) have failed because of the intense aeration of the water in the wave crests. Therefore, HFA and LDA have only been successful below the trough level of the wave, and are inherently point measurements of velocity only. Other techniques including Particle Image Velocimetry (PIV) have successfully determined instantaneous quantities over a large spatial domain with high resolution, though they are unable to measure data in the aerated portion of the broken wave. Digital Particle Image Velocimetry (DPIV) techniques show significant promise in quantifying many of the properties in the surf zone by applying similar techniques used in PIV averaged over many time intervals.
The technique of DPIV consists of videotaping illuminated neutrally buoyant particles suspended in the water column over many successive wave cycles. Each frame of the video is then converted into digital format. Subsections of successive frames are compared so that displacements of the particles can be determined. Ensemble averaging procedures over the many wave cycles filmed permit the separation of wave fluctuating velocities and turbulence, and subsequent quantification of integrated surf zone properties such as volumetric flow, turbulent kinetic energy, and radiation stresses.




The motivation for obtaining these measured quantities arises from need in several areas of nearshore process modeling. Perhaps most importantly, the data can be directly applied to numerical models of surf zone and coastal processes. As mentioned previously, waves in the surf zone have been modeled with limited success. The measurements obtained in these experiments are quantities which are essential to more accurate modeling of breaking waves in the surf zone, leading to more detailed crossshore and longshore current modeling. Sediment transport modeling is another area which would benefit from accurate measurements of fundamental surf zone quantities. The amount of suspended sediment in the water column is directly proportional to the amount of turbulence in the surf zone. In conjunction with wave generated currents, this combination impacts the amount of sediment transported in the longshore and cross shore directions, which in turn affects the erosional and accretional. processes occurring along the shoreline. Improved knowledge of the fundamental properties of turbulence and mean currents in the surf zone would, in principle, lead to substantial improvements of predictions of coastal sediment transport processes.
In the following pages, a review of the general features of the surf zone and the DPIV system will be presented. An application of the DPIV technique to measuring surf zone velocities, and the results of this application will also be introduced. Finally, several conclusions will be drawn concerning the DPIV technique, and recommendations for further advancement of this process will be discussed.




CHAPTER 2
LITERATURE REVIEW AND THEORETICAL BACKGROUND
The experiments and analysis presented in this thesis incorporate two somewhat independent fields of study. The first is the development of a Digital Particle Image Velocimetry (DPIV) system applicable to measurements inside the surf zone. An introduction to the theoretical background and the foundation of the DPIV technique will be presented, along with a description of a recent application upon which these experiments were based. Improvements to the technique made as a part of this study are also discussed. Secondly, this study employed the DPIV system to measure some of the fundamental properties within the surf zone (such as velocity measurements and turbulence). Similar measurements have been made by numerous investigators over the past 20 years. Previous experiments relevant to this study are reviewed, and significant contributions of each researcher noted.
Development of a Digital Particle Image Velocimetrv Technique
Willert and Gharib (1991) pioneered a system that determines particle displacements between successive video frames in a digital manner. They determined that the cross-correlation between the sub-sections of successive frames, referred to as Area's of Interest (AOI), produced a spatial shift equal to the displacement of the particles. Compilation of these smaller sub-sections produces a displacement field (or a velocity field when divided by the time interval between frames), over the area filmed.




The theory behind DPIV is conceptually simple: examine the same area on each of two successive images to determine the distance the particles have been displaced during that time. In the case of digital images, the particles are now represented by light intensities, and the displacements are determined via a cross-correlation process of the two images.
Craig (1994) summarizes the procedures of Willert and Gharib (1991), represented by:
g(m,n) = [f(m,n) s(m,n)] + d(m,n) (2.1)
where J(m,n) is the first AOI, s(m,n) is the spatial displacement function, d(m,n) is the system generated noise, and g(m,n) is the second AOL. The asterisk (*) represents a spatial convolution of the first AOI and the displacement function. The spatial displacement function, s(m,n), is the value sought.
A spatial auto-correlation of the first AOI yields a peak at the center of the AOL. The cross-correlation provides a maximum peak located a distance away from the origin equal to the average displacement of the particles within the AOL. The cross-correlation function, OIfg (m,n), is defined as:

: fg(m,n) = E[f (m,n),g(m,n)]

(2.2)




Applying equation 2.2 to equation 2.1, and neglecting the noise function d(m,n) yields :
(Dfg(mn) = Off (m,n) s(m,n) (2.3)
where (Dff(m,n) is the auto-correlation function of the first AOL. Rearrangement of equation 2.3 yields s(m,n). Modifications to these general equations have been developed to speed processing. However, because this method was used in application only, these modifications will not be discussed. For further details, see Willert and Gharib (1991) and Craig (1994).
Craig (1994) applied the process developed by Willert and Gharib (1991) to measuring fundamental quantities in the surf zone such as mean velocity and turbulence, specifically in the transition region of the surf zone. It was found from these experiments that the DPIV method was able to determine instantaneous, mean, and turbulent velocities both in the trough and in the crest of the wave. Craig (1994) also applied these data to calibrate a numerical model of the transition region presented by Thieke (1992) with the addition of conservation of angular momentum. Accomplishments stemming from Craig (1994) include the ability to measure velocities in the aerated portion of the broken wave due to gray-scale filtering methods employed, the ability to resolve turbulent fluctuations over the entire water column, and the use of Thieke's (1992) model to determine length of the transition region within the surf zone. Also noted were potential problems in the process, including the use of non-neutrally buoyant particles, the effects of low particle seeding densities, and the effects of significant aeration in the water column.




Huang and Fielder (1994) examined the effects of reducing the time interval between successive exposures in standard video PIV, (which is also known as DPIV). Their experiments consisted of a pulsed laser illumination system with video frames captured by a charge coupled device (CCD) video camera operating in interlaced scanning mode. They found that for an instantaneous velocity field of a fully developed flow downstream of a step structure, many velocities measured in the vortex region were false due to the large velocity gradients and large time interval (20 ins). Reduction of the time interval by 75%, achieved by pulsing the laser at 5 mns intervals within the 20 ms frame, allowed most velocities to be correctly detected. An example of their results is shown in Figure 2. 1. It should be noted that it was not possible to implement this technique due to the lack of a pulsed lighting system, however, this would be a significant advancement for future experiments.
Scale: 10cm/s
1.73.. ~
-Z
012
Scale: 10 cm/s
1.73. _ _ _ __ _ _
2 3
Figure 2.1 Comparison between Video PIV measurements with (a) time interval 2Oms and (b) time interval = 5 ins. Note that most velocities are correctly detected with shorter time interval of 5 ms in (b), Huang and Fiedler (1994).




Measurement of Velocity Components

Numerous surf zone quantities were determined throughout the experiment. It is necessary to develop a consistent set of definitions before any procedures or results can be discussed. In keeping with an Eulerian reference frame, the following schematic, Figure 2.2 illustrates the many physical definitions used.

Figure 2.2 Eulerian Averaging Definitions from Roebuck et al. (1997).
The definition of velocity according to the Eulerian reference, shown in Equations 2.4 and 2.5 for the horizontal direction, also applies to the vertical direction. Both the horizontal and vertical components of the velocity were determined for each test experiment. Note that the Eulerian mean velocity above the trough level requires special attention since a given point is submerged during only a portion of the wave period.




- 1 '(()
u = f udt
T,(Z)

if: 1,
if: -h
T
U=!f udt
0

(2.4)

(2.5)

A Reynolds decomposition of the instantaneous velocity can be employed to identify three major components: the Eulerian or time mean velocity, the wave fluctuating velocity, and the turbulent fluctuating velocity. This is represented by:

(2.6)

U=U+U +U

where:
u = Eulerian or time mean velocity
u" = wave fluctuating velocity = u
u' = turbulent fluctuating velocity = u = ensemble or phase averaged velocity

Instantaneous velocities, ensemble averaged velocities, wave fluctuating velocities, turbulent fluctuating velocities, and Eulerian mean velocities in both horizontal (U) and vertical (W) directions were calculated for all runs. From these velocity fields, values for mass flux, radiation stress, and turbulent kinetic energy were calculated.




Measurement of Surf Zone Ouantities
In the past, wave height, set-up, radiation stress, cross shore currents (undertow), and turbulence have been the major fundamental features studied in the surf zone. The previous studies reviewed herein examine all of these aspects of surf zone flow, however, surf zone turbulence will be the main focus of the discussion.
Svendsen (1987) discussed the direct measurements of turbulent energy by various investigators with the purpose of incorporating such measurements into surf zone models. Measurements generated inside the surf zone were made with Hot Film Anemometry (HFA) or with Laser Doppler Anemometry (LDA). These measurements were two-component point measurements, and because turbulence is inherently a threedimensional quantity, the transverse contribution to the turbulent kinetic energy (TKE) must be estimated and included. Svendsen proposed a ratio of three-dimensional turbulent kinetic energy (3-D TKE) to two-dimensional turbulent kinetic energy (2-D TKE), where the 3-D TKE is given by:
k = 2(U2 +VP2 +W') (2.7)
and the 2-D TKE is given by:
kI = 2(U12 +W12) (2.8)




In both of these equations, u2 and w'" are the time averaged horizontal and vertical squared turbulent fluctuating velocities. v'2 is the time averaged squared transversal turbulent fluctuating velocity.
Analyses by Svendsen (1987) show that surf zone waves can be modeled after a plane wake where the ratio of turbulent components, presented originally by Townsend (1976), is given by:
12 2 ,2
u :w :v = 0.42 : 0.32:0.26 (2.9)
Therefore, the ratio of two-dimensional TKE (k') to three-dimensional TKE (k) can be determined and is given by:
k = 1.33(k') (2.10)
Roebuck et al. (1997) provide support for this ratio by determining the experimental ratio of u 2 to w'2 to be 1.31 which identically agrees with the ratio 0.42 : 0.32 suggested in the two-dimensional definition of TKE according to Svendsen (1987).
Svendsen describes experiments by Stive and Wind (1982) who used LDA and ensemble averaging procedures to extract wave and turbulent components of the data. However, because LDA was used, they "could measure with confidence only below the wave trough level." It is also indicated that with the ensemble averaging process, "each sampling may not exactly come from the same phase in the wave relative to a characteristic point," a problem also encountered in DPIV and discussed in Chapter 4. A




result of this is that "patterns which occur regularly relative to characteristic points are recorded as turbulence. Another consequence is a general underestimate of the amplitude of the signals." Svendsen notes that all measurable data occur under the wave trough elevation, and concludes that although the ensemble averaging procedure still contains drawbacks, it is the most suitable method for determining quantities in the surf zone. Figures 2.3 (a-b) show results presented by Svendsen (1987) for both experimental data of Stive and Wind (1982) and model predictions of Deigaard et al. (1986). It is clearly seen that in Figure 2.3 (a), measured data is only present below C/h < 1 (i.e. below the trough level). Figure 2.3 (b) shows that the model by Deigaard et al. (1986) over-predicts the data generated, and is again only indicated for elevations below the wave trough level.
lh holho8
0 A 0.882
* 0.765 S&W T
4 X 0.647 Test Not
X o 0.529 //
0.5 + 0.412 0.5
A+
X 00-294
* 1 0.177
+ //
0 0.1
00.05 0.1 . .0.05 0.1 0.15
(a) (b)
Figure 2.3 Experimental Data and Model Predictions by (a) Stive and Wind (1982) and
(b) Deigaard et al. (1986) for dimensionless turbulent kinetic energy (TKE) in a surf zone, Svendsen (1987).




In a related review article of cross-shore currents in surf zone modeling, Svendsen and Hansen (1988) note that for a comprehensive model, such as the one discussed in their paper, there are several surf zone parameters which are not yet adequately described. These include the following:
a) A proper description is needed for the wave development in the outer region
of the surf zone, from the breaking point to the stage where the roller is
sufficiently developed.
b) A reliable prediction of the combined wave-height and set-up in the inner or
bore-region must be established.
c) A suitable prediction of the turbulent flow conditions in the region above the
bottom boundary layer is needed.
d) The mass flux in the breaking waves must be predicted more accurately.
It is hoped that through the present set of experiments, some light will be shed on these problems addressed by Svendsen and Hansen (1988).
More recent experiments by Ting and Kirby (1994) used a LDA system to measure velocities and turbulence in both spilling and breaking waves. There was an attempt to measure velocities above trough level, however, velocity measurements were made mainly below the trough level and above the bottom boundary layer. In areas above the trough level, the instruments experienced signal drop out when the water surface dropped below the measurement location. This resulted in inaccurate results measured in the crest portion of the wave, and subsequent results of these data were not presented. Ting and Kirby (1994) showed that below the trough elevation, the maximum water speeds were attained under the trough of the wave, as expected, and that the mean




flow velocity and turbulent intensity vary with distance from the surface in the spilling breaker.
Roebuck et al. (1997) extended the processing of velocity data generated by Craig (1994) to address many of the previous problems discussed by Svendsen and Hansen (1988), and Ting and Kirby (1994). Quantities generated from these data included instantaneous free surfaces for each phase of the wave covering a large spatial domain. This allowed for determination of wave height and set-up information. Like other data sets presented, ensemble averaging techniques were used to extract wave and turbulent velocities according to velocity decomposition shown in Equation 2.6. From this, vertical profiles of time-mean, ensemble averaged wave and turbulent fluctuating velocities for a large spatial domain were determined. Also, based on the relationships presented by Svendsen (1987), vertical profiles of non-dimensional turbulent kinetic energy were determined for the same spatial domain. From Eulerian mean velocity fields, volumetric transport was also determined, since the volume flow (or equivalently mass flux) is a needed quantity specified by Svendsen and Hansen (1988), and has been used as an essential boundary condition in all return flow (undertow) modeling in the surf zone.
Calculation of Two-Dimensional Volumetric Flow
The total volumetric flow is easily calculated given the Eulerian mean velocity. It is simply the integration of the velocity over the depth as follows:




VI ~r (2.11)
which can be decomposed into above and below trough volumetric flow given by:
V forward = 'r (2.12)
V return = udz (2.13)
It should be noted that in a closed flume, the total volume flux past a certain point over an entire wave period should equal zero. Flux measurements were analyzed to determine if conservation of mass was in fact verified by this measurement technique.
Calculation of Radiation Stress (due to waves and turbulence)
In the development of the radiation stress equations, the need for free surface elevations arises. In the area just outside the break point, the free surface is well defined and can be easily identified. Progressing inside the break point, the free surface becomes more difficult to distinguish due to the presence of the surface roller, and even further inside the surf zone, the wave resembles a moving bore with no clear continuous free surface. For these experiments, the free surface was always taken to be located at the vertical extent of the surface roller and bore. This was necessary to ensure relevant data was not removed during the free surface/bed filtering process. The radiation stress due to wave fluctuations is then given by:




S1 pui2_OWt2 _O (2.14)
where p is the density of water and g is gravity. The wave fluctuating velocities (u"2, w" 2 ) are ensemble averaged, time averaged quantities and are integrated from the bed to the crest of the wave. The mean square of free surface fluctuations, denoted by
7 was determined from digitized free surface information.
The equivalent "radiation stress" due to turbulent fluctuations is given by:
S' = J_7(p 7 Uw ) (2.15)
where mean square turbulent fluctuating velocities are integrated from the bed to the crest of the wave.




CHAPTER 3
EXPERIMENTAL SETUP ANT) PROCEDURES Experimental Summiay
Experiments were conducted at the University of Florida's Coastal and Oceanographic Engineering Laboratory located in Gainesville, Florida. Data was collected in a tilting wave flume, though the flume was horizontal throughout the experiments. A rigid sloping beach of 1 on 20 and piston type wavemaker were located at opposite ends of the flume. Wave data were collected with a capacitance type wave gauge, and videotaping was performed with a black and white video camera. Wave periods were varied from 1.3 to 1.7 seconds, deep water wave heights were varied from 2.6 to 5.5 cm and deep water depths were varied from 30 to 36 cm to make 10 separate and distinct experimental runs.
Wave Conditions
The wave conditions were varied as much as possible while still retaining monochromatic wave characteristics. The shortest period waves which could be consistently generated by the wavemaker were approximately 1.3 seconds. Over the course of the experiments, the wave periods were incremented from approximately 1.3 seconds to 2.0 seconds. However, periods greater than 1.4 seconds generated large reflections in the flume. Therefore, data collected for the longer wave periods were not processed. Consequently, the only wave periods examined were on the order of 1.3




seconds. The stroke length was adjusted to vary the wave height. Table 3.1 shows the test conditions run, though all data is only presented for those conditions fully processed (Tests D, G and J, with wave periods of approximately 1.3 seconds). All breaking waves were observed to be spilling breakers.

Table 3.1. Wave conditions positions 1, 2, and 3.

for experiments run.

H (1-3) represents Test H, film

Data Collection/Analysis Equipment

Two types of data were initially collected during the experiment: 1) videotape of the waves, still water, and grid; and 2) wave gauge data. A Vicon 2400 high resolution black and white video camera was used to film the experiments. Data was recorded with

Test ho (cm) Ho (cm) T(sec) hob(cm) Hb (cm) A(1-2) 33.0 5.35 1.65 N/A N/A
B(1-2) 34.1 5.41 1.36 N/A N/A
C(1-2) 34.1 5.35 1.48 N/A N/A
D(1-2) 35.0 4.21 1.35 11.40 11.90
E(1-2) 35.0 4.05 1.49 N/A N/A
F(1-2) 35.0 4.09 1.63 N/A N/A
G(1-2) 35.6 3.23 1.37 8.69 8.78
H(1-3) 35.6 3.03 1.48 N/A N/A
1(1-2) 35.6 2.90 1.63 N/A N/A
J(1-5) 30.8 2.67 1.35 7.87 8.06




a Panasonic AG1970 SVHS VCR onto Fuji H471S Double Coated SVHS video tape. Wave gauge data was collected through a capacitance type wave gauge, converted through a data acquisition board, and stored onto a PC.
The Vicon VC2400 high resolution black and white video camera provided 570 lines of horizontal resolution and required only 0.2 lux minimum illumination. Though film speed was fixed at 1/60Oh of a second, an internal shutter speed was set at 1/1000' of a second, indicating that the light could only enter the camera for 1 /1 1h of a second onto each frame representing 1/60"'~ of a second. This minimized blurring of particles, but still allowed for sufficient light to pass through the camera. Additionally, the camera aperture was adjusted for each run to ensure correct light level entering the camera. All experiments were run at night with exterior lights turned off to ensure that no ambient light could enter the camera.
The video tape was converted to TIF (Tagged Image Format) images through an EPIX Silicon Video Mux Frame Grabber and accompanying software. This software was capable of executing script files for automated digitization procedures. An Editlink 2200/TGC controller card was used to properly position the VCR at the correct frame to be converted into the digital image. A compilation of C programs written by Craig (1994), along with software internal to the Editlink card, aided in this process. The Editlink controller card and Silicon Video Mux Frame Grabber were run on a IBM compatible 486 DX2/66 PC. This computer was capable of storing approximately 2500 TWF images in zipped format which corresponded to one run of converted images.
Data was then transferred to a series of computers for analysis. The primary machine was a Dell Pentium Pro 150 with 16 MB Ram. This computer provided




sufficient speed to analyze the data, though another computer equivalent to this was needed to process lengthier analysis procedures.
Processing of the data was accomplished via MATLAB and FORTRAN programs. The majority of the processing involved image analysis and filtering in which MATLAB Image Processing Toolbox was used extensively, including reading of digitized images, gray scale filtering based on pixel intensity, and conversion of TIF to binary images. Subsequent development of instantaneous velocity fields, volumetric transport quantities, turbulent kinetic energies, and all plotting routines were also performed with MATLAB. Mean, root mean square, standard deviation, ensemble average quantities and their filtered values were all calculated by code written in FORTRAN.
Physical Setu
The tilting wave flume used in these experiments had dimensions of 18.3 m (60 ft) long, .61 m (2 ft) wide and .91 m (3 ft) deep. For these experiments, the tilting mechanism was not used and the tank was maintained level. The front glass wall extending the length of one side of the tank allowed for viewing of the waves. The other sides of the tank are constructed of steel, and the top is open. The fixed beach was positioned opposite to the wavemaker, covering a horizontal length of 7.3 m (24 ft) and vertical height of .365 m (1.2 ft) yielding a beach slope of 1/20. The beach was rendered stationary with the use of concrete blocks and lead weights. Waves were generated with a piston type wavemaker extending over the width and depth of the tank. This was controlled by a 110 VAC, .5 horsepower motor. Motor speed was controlled by an




expanding pulley and belt system located internally, allowing for generation of various wave periods.
A device was constructed to hold both the light box and cylindrical focusing lens. The light box used by Craig (1994) was employed again, though slightly altered to eliminate the charring problem previously experienced. The bottom of the box was modified such that two pieces of aluminum sheeting angled off each side of the bottom of the box to form a slit running the length of the box. Triangular sections of aluminum sheeting covered the ends. All joints on the aluminum sheeting were covered with black electrical tape to reduce the amount of light leaving other than through the slit at the bottom. The cylindrical focusing lens was suspended from the light box by small pieces of wood. This wood was clamped to the light box to allow for easy adjustment which ensured proper focusing of light into the tank. A 650 Watt FAD projection lamp bulb provided sufficient light to illuminate the particles in the water column. The entire light box apparatus was easily moved along the top of the tank to the desired location. One problem in previous experiments by Craig (1994) was the charring of the bottom of the light box due to immense amounts of heat generated by the bulb. With the modification to the box, a much stronger bulb could be left on for a sufficient amount of time with no damage. For a complete schematic, refer to Figure 3.1 (a-b).
A capacitance type wave gauge was attached to a movable carriage that ran along rails atop the flume. Deep water wave information, including wave height and period, was collected. The movable carriage allowed for measurements of the wave envelope to deter-mine wave reflections occurring within the tank. It was not necessary to measure set-up and other shallow water quantities, as these could be determined from the




videotape for the area filmed. Wave data information was converted through a data acquisition board and stored locally on a PC through Global Lab software.
it Box

L 'Cylindrical Le

-Focused Light
0
o o
W0
o a
0 0 00
0 0

- Neutrally Buoyant Particles

Capacitance Wave Gauge

Piston Wave Maker -

Figure 3.1 Wave Tank Schematic. (a) End View; (b) Front View.

VCR & Monitor

0 0
0 0
0 0 0 C
00 0
0:4




Videotaping was done through the glass wall on the front of the tank. The camera was normally positioned approximately 0.6-1.0 mn away from the tank, though magnification lenses on the camera allowed for zooming, fine adjustments, and focusing. The aim was to fill as much of the frame as possible with the breaking wave, thus ensuring maximum resolution of the water column for each run.
The particles used consisted of ground plastic, oval in shape, with an average length of 1.7 mmn and thickness of 1.0 mm. Because enough salt was added to the tank to make the particles neutrally buoyant, the particles did not have to be collected and redispersed after each run. A sufficient number of particles were introduced into the tank at the onset of the experiments. However, throughout the experiment, it was necessary to add more particles to the system when the particle seeding density became too low due to the particles becoming dispersed throughout the tank. All particles were collected at the end of the experiments.
The final piece of equipment used was a piece of Plexiglas with an electrical tape grid. This allowed for correct determination of scaling from pixels to centimeters in the post-processing of the data. Black electrical tape, 0.75 inch thick, was placed on 1.75 inch centers both horizontally and vertically, thus creating 1 inch by 1 inch squares of clear Plexiglas between the tape. The grid was recorded prior to each individual run.
Experimental Procedures
Initially, the camera was connected to the recorder and positioned in the approximate location of the desired filming. The wavemaker was then started and waves were allowed to come to their equilibrium condition, usually after about 2 minutes. The




breaking position was noted and camera was adjusted to capture the location. Also, the camera was leveled both left to right and front to back, to ensure the still water line would be horizontal in the film, and to minimize three-dimensional effects caused by filming at an angle to the water surface. The light and focusing lens were then positioned so particles in the area to be filmed were illuminated. The wavemaker was then shut off and the tank allowed to come to rest. Filming now began with a 10 second introduction to the run, i.e. a sign depicting the name of the run. The next 10 seconds of film consisted of the still water which would later be used to determine exact distances from the shoreline and other parameters in the data analysis. The Plexiglas grid was then inserted into the water column and recorded for 10 seconds. This was to be used to scale image distances in pixels to actual distances in centimeters.
The wavemaker was started and waves allowed to come into equilibrium once again. If it was determined that more particles needed to be added to the water column so that the particle seeding density was sufficient, more particles were added and allowed a short time to disperse to an equilibrium with the locally surrounding water. The waves were then recorded for 2.5 minutes. This length of time provided a more than adequate number of cycles to digitize and use for analysis. It also provided enough recorded data so that a section of the video record could be chosen to convert to TIF images, either at the beginning, middle, or end of the filming interval, depending on which section of film appeared to provide the optimum particle density. The filming was then stopped and the VCR advanced in preparation for the next run.
The waves continued to run while wave gauge information was collected. For each run, there were two or three sets of wave data. Two sets of data common to all runs




were the still and moving wave gauge data. First, the wave gauge remained stationary over the horizontal bottom of the flume and recorded water surface elevations with time. Data were collected for two minutes at a frequency of 60 Hz to analyze wave height and period. Secondly, the carriage which supported the wave gauge was slowly moved down the length of the deep water section of the tank. Moving the wave gauge slowly as the waves propagated past allowed for detection of reflected waves in the tank as described by Dean and Dalrymple (1991). The wave gauge was first slowly moved opposite the direction of wave propagation, and then back in the direction of wave propagation. Again, the data was collected for a length of two minutes at a frequency of 60 Hz. The third set of data collected by the wave gauge was not common to all runs. By slowly moving the wave gauge through the surf zone portion of the tank, the wave set-up could be determined. It was hoped to corroborate the wave set-up measured by DP11'V with the wave gauge set-up data. This was done for Tests A, B, C, D, E, and F. Preliminary analysis of this wave gauge data showed poor results as a consequence of not being able to traverse the shallow surf zone. Due to the configuration of the capacitance wave gauge used, measurements in extremely shallow water were inaccurate for two reasons. First, the wave gauge had to be positioned such that measurements could be taken throughout the surf zone region. This meant that the bottom of the wave gauge had to be positioned just under the trough level. However, signal drop out occurred and data was not recorded when the wave gauge was occasionally completely exposed to the air in presence of the trough of the wave. The wave gauge also returned inconsistent measurements due to the aeration of the water. Secondly, the bracket of the gauge came into contact with the sloping beach before the surf zone had been adequately measured. Therefore, this




information was not collected for the remaining runs. The period of the wave was changed and the experiments were repeated.
Data Processiniz
The data processing procedures are similar to those of Craig (1994). Identical procedures described by Craig (1994) are discussed briefly; modified and improved procedures are described in full.
Wave Gauge Data
Wave gauge data collected during the experiments were recorded as voltages from the capacitance wave gauge and stored in Global Lab. These were converted to ASCII text files and processed using MATLAB. Data from the fixed wave gauge was analyzed to determine wave height and period of the deep water waves generated for each run. The mean of these data were determined, recorded as the mean water levels for each run, and subsequently used in determining wave period. The interval between the zero upcrossings of the mean water level gave a number of samples for each period of the wave. Intervals for approximately 75 cycles were determined, and averaged. This was then divided by the sampling frequency of 60 Hz to determine the period in seconds.
Wave height was calculated by determining the maximum and minimum surface elevations within one period of data collected. The period interval determined previously was used. The wave heights were then converted from volts to centimeters by calibration data collected at still water before each run.




Image Digitization
Images recorded on the SVHS video tape were digitized with the SVIP Video Mux Frame Grabber and automated using the Editlink 2200 controller card. 30 frames were digitized at a time with a resolution of 640 X 480 pixels. Details of this procedure can be found in Craig (1994).
Image Filtering
A significant improvement in the analysis of the digitized frames arose in the filtering of the images. The gray scale filtering of the images essentially removed spurious light generated by water and entrained air in the water column, leaving only data generated by the illuminated particles. Previously, each image was filtered and stored as a separate file, generating massive amounts of data. This procedure was modified so that the filtering was done as the instantaneous velocity fields were being processed. MATLAB is able to read in a TIF image and convert it to matrix form based on pixel intensity. The matrix was then converted to a binary image based on a cut-off value assigned. It was determined that a value of 95% effectively eliminated the entrained air and water, leaving only the particles. All data below the 95% threshold were converted to values of 1 (or black), and the top 5% converted to values of 0 (or white).
Instantaneous Velocity Field
Filtered images were broken down into smaller areas of 32 X 32 pixels, or an "Area of Interest" (AOl). A two-dimensional auto-correlation was performed on the




image to yield a peak at the location of the center of the AOL A two-dimensional crosscorrelation was then performed with the same AOL in the following frame. The resulting shift of the peak intensity yields a net displacement of the particles for that AOL To speed processing, the cross-correlation is performed in the frequency domain (incorporating the Fast Fourier Transform (FFT) ) and an inverse transform is used to retrieve the displacement function in the spatial domain. Velocities were determined by dividing the displacements by the framing rate of 1/60Oh of a second. Complete details can be found in Craig (1994).
Ensemble Averaged Velocity Fields
Ensemble averaging of the Instantaneous Velocity Fields (IVFs) was performed in order to extract mean and turbulent fluctuations. Ensemble averaging consisted of averaging the data at the same phase of the wave over many cycles. Video images provided information for approximately 30 cycles of data for each run.
Previously, the wave period was multiplied by the filming frequency and rounded to the nearest whole number to determine the number of frames per period to use in the ensemble averaging. This was used as a starting point to determine the number of frames per period, however was not ultimately used in the ensemble averaging process for these experiments. Three factors influenced the number of frames per period to be used. First, the period rarely correlated directly with a whole number of frames. Secondly, the wave inside the surf zone was propagating on the steady return flow of the previous wave, altering the period slightly. And finally, the automated digitization process was accurate to /- 1 frame, skewing the data slightly. For these reasons, the IVFs were studied




directly, and a number of frames per period chosen such that the zero-uperossing in the IVFs remained fairly stationary throughout the total number of cycles.
In the ensemble averaging process, comparison of similar AOI's occasionally showed erratic results which were not physically consistent. These inconsistencies appear to be spurious data, generated in the presence of extremely low particle seeding densities or high aeration. The inconsistencies, or large incorrect velocities, were generated due to particles leaving through one side of the AOI and other particles entering through the other side of the AOL. Therefore, instead of a small positive displacement measured, a large negative displacement was measured as depicted in Figure 3.2. A filtering program was developed to try to eliminate these spurious effects. This process consisted of determining the uncorrected mean velocity and the standard deviation for each AOL. A cut off limit of 3 standard deviations was then applied to all velocity data at each AOl, eliminating the majority of the spurious data. The limit of 3 standard deviations was arbitrarily chosen to minimize any reduction in genuine turbulence, yet still eliminate most of the spurious data. Subsequent averaging was performed with the spurious points replaced by the ensemble mean velocity at that phase and spatial location.
Surf Zone Quantities
Time averaging the ensemble averaged velocities produced Eulerian Mean Velocities. In a closed flume, such as the one in which the experiments were conducted, this quantity should show conservation of mass within a two-dimensional plane. Eulerian




0 0 00
a)AOI @Time t-T b) AOI @Time t =T +At
Actual Displacement Vector:
Measured Displacement Vector:
Figure 3.2 Actual and measured displacements generated as a result of low particle seeding density.
mean velocities were determined for all runs. By taking the ensemble mean velocities and subtracting out the Eulerian mean velocities, velocities due to wave fluctuations were determined according to definitions in Chapter 2. Likewise, by taking the instantaneous velocity fields and subtracting out the ensemble averaged quantities, the turbulent fluctuating velocities were determined. These quantities were developed for both the horizontal (u) and vertical (w) velocities. Radiation stress, mass flux, and turbulent kinetic energy could all be calculated subsequently.
Free Surface/Bed Location
Determination of depth integrated quantities in the surf zone (such as radiation stress) sometimes required knowledge of the instantaneous free surface for each phase of the wave, the mean free surface level (z~,the bed location, and the still water level




information. To determine these quantities, images were displayed so that points depicting the free surface could be chosen. Points along the free surface were digitized and then connected using a cubic spline routine method to produce the location of the free surface as shown in Figure 3.3. This was done for the still water conditions and for each phase of the wave. Time averaging the free surface at each location yielded the wave setup, q7.
Previously, the instantaneous free surface information was not determined in this manner. Though it was possible to use wave gauge information to determine the mean water level, it was very difficult to correlate instantaneous wave gauge data with each frame of the video tape. Also, the wave gauge only provided a point measurement of a time history, whereas the videotape is a spatially varying measurement at a given time. This new technique allowed for digitization of the free surface over the entire filming area for each instantaneous phase of the wave.
Wave Height/Bed Filtering Method
Throughout all the experiments, extraneous light would appear both above the free surface of the water and below the bed. These spurious data were removed by the following approach. The digitized bed and each digitized instantaneous free surface, used to generate ri and q, were converted to their respective AOI locations in the X and Y direction. All ensemble averaged data above the free surface and below the bed were set equal to zero. This can be seen in Figure 3.4. Data filtered in this manner were used in further calculations of surf zone quantities.




Figure 3.3 Test G2, Image 38. Digitized free surface and bed information. Note that the lines depicting free surface and bed data have been enlarged for visual purposes.
Ensemble Averaged Velocity Field at phase 32 of 76, Test g2

E 25
'~20
0
-Z- 15 C.)
10
5

0 5 10 15 20 25 30 35

E25
20 0 15
10
15
10 0N

. ,. 5 .s .1 .
.. . . . -7 . .
. . . . . . . bm : 7 ,7 : :
.... .. .. ....... .. .... .. ..... .... .. .... .
0 5 10 15 20 25 30 35
X Direction (cm)

Figure 3.4 Unfiltered and filtered ensemble averaged velocity data determined through the use of digitized free surface and bed data.

. . . . .
. .. .. .. .. .
- 7 "-

U




CHAPTER 4
EXPERIMENTAL RESULTS
In the previous chapters, it has been noted that there are many surf zone quantities which can be extracted from laboratory measurements using Digital Particle Image Velocimetry. The following will present the quantities that were determined during these experiments, ranging from the free surface evolution (ri), to radiation stresses, and nondimensional turbulence intensities.
Image Processing
The development of all quantities using DPIV lies inherently in the Instantaneous Velocity Fields (IVFs). For each run, there were 2500 IVFs produced, though not all were used on every run. The actual number of IVFs used in the ensemble averaging process was equal to the product of the number of frames per period (fpp) and the number of cycles to produce the largest number less than 2500. For example, if the number of frames per period was 60, a one second wave, then 60 fpp 41 cycles equals 2460 frames used. It took approximately 10 hours to convert 2500 frames into TIF images, corresponding to approximately 15 seconds per frame. Generating the IVFs between successive frames, including filtering of the images, took approximately 23 hours for 2500 IVFs, corresponding to an average of 34 seconds per IVF. The generation of the IVFs was performed simultaneously on two computers, reducing processing time in half.




Free Surface Elevations/Bed Data
Digitization of the free surface was time consuming as well, approximately 1.5 minutes per wave phase. Each image, corresponding to each phase of the wave, had to be converted to binary form and digitized, as explained in Chapter 3, so that free surface information could be extracted. A typical example was previously shown in Figure 3.3, which shows the original image, the digitized free surface, and the digitized bed. This was done for each phase of the wave over one complete wave period or cycle. It was assumed that the waves were monochromatic, subsequent spectral analysis showed very little reflection for the tests processed, and therefore digitization only needed to be performed over one period of the wave. Compilation of the digitized free surfaces and bed information shows the wave evolution in time as in Figure 4. 1, though it should be noted that not all free surfaces for each phase of the wave are plotted. Still water level and mean free surface elevation ( q ) are shown depicting wave setup inside the surf zone. This free surface data were converted into their respective AOI's to be used in the filtering process.
Instantaneous Velocity Fields (IVFs)
Instantaneous Velocity Fields are the basic data generated from the processed images. From the IVFs, all other velocity and turbulence data could be extracted. Therefore, it was crucial to have reliable IVF information. Two factors which influenced the generation of IVFs were particle seeding density and video frame speed. The film speed, as described by Huang and Fiedler (1994) in Chapter 2, could not be varied due to




35
Wave Evolution in Time Test g2 24
22 20
18
C
L) 16
14
N
12 10
8.7 0.75 0.8 0.85 0 9 0.95
X Direction (cm)
Figure 4.1 Evolution of the free surface, digitized bed, q (-), and still water level (---), Test G2. Note that only every 5h instantaneous free surface is plotted corresponding to every 5/60tl or 1/12h of a second.
lack of faster filming apparatus and was designated by the standard video speed, 1/60th of a second. Particle seeding density, on the other hand, could be controlled throughout the experiment. Neutrally buoyant particles allowed for a higher seeding density in the crest of the wave, while sheer numbers of particles yielded an overall higher seeding density. IVFs with low seeding density, as shown in Figure 4.2 (a), did not produce reliable results due to the significant scatter in velocity measurements. The digitized free surface and bed locations, indicated by the black lines, bound the relevant data within the water column. Examining Figure 4.2 (a), AOI's 15-20 (x-direction) and AOI's 10-14 (ydirection), it can be seen that there are measured velocities in every direction, including zero measured data in AOI (17,12), represented by a single point. The actual images




making up this IVF are of the backside of the crest of a wave propagating to the left, and the beginning of the trough. Similarly, in Figure 4.2 (b), located closer to shore (X t 0.3) where a bore is nearly fully developed, the velocities are extremely varied as well. At this location, there is significant aeration, causing scattered velocity data and lack of measured velocities. Unlike these two examples, Tests with high particle seeding densities provided reliable data nearly all of the time. Examples of IVFs containing largely reliable data are presented in Figure 4.3 (a-d) which show a well defined trough, zero-upcrossing, crest, and zero-downcrossing respectively. In these IVFs, it can be seen that nearly all measured velocities follow the expected path lines of particles in the water column. Highly spurious data shown in these IVFs, along with data above and below the water column, are filtered out in post processing procedures.
An interesting note about Figure 4.3 (c) is the lack of measured velocities in the crest of the wave, and the spurious data just above the crest, AOI 20-23 (y-direction). The lack of measurements in the crest is due to a lower particle seeding density and higher crest velocities. Consistently lower seeding densities appear in the crest of the wave because of the slight negative buoyancy of some of the particles. Positively buoyant particles were used to try to resolve some of these crest velocities, however, they did not remain in the filming area. Because of their tendency to "surf' the breaking waves, they were quickly deposited on the beach above the run-up line. The spurious data above the crest of the wave is thought to be generated by light refracted through the bubbles on the leading free surface of the wave.




T TJ1 vF4 "1"J5- W22
. . .~~~ ~~ ~~~ .. . .. .. ... . . . . . . . .. . .
"~~ ~ ~~~ ." ... .l .... ... ..."-' .... :... ... '
2D
[] ....... ",' l '~ ~~ ~~~~ ~ .I' . .. .. . . ... , l- . ..
-7-:
._ -_ 7 i i i i i .--: I ,
i t [ [ .. . . . ,, [. . . . . . . .
'. '. .'.'
0 5 12015 2 3 Q 0 5 10 15 2
POa inX- D-recdw POa inX- Dredwi~
(a) (b)
Figure 4.2 Examples of low resolution IVFs due to (a) low particle seeding density and
(b) high aeration of the water column.
Filtered/Unfiltered Ensemble Averaged Velocity Fields
Ensemble averaging the IVFs significantly reduced the amount of data to be managed. This process reduced the data by a factor equal to the number of cycles used in the run and also eliminated many of the spurious effects through use of the filtering method discussed previously. As well, the filtering of ensemble averaged velocity fields using free surface and bed information eliminated the irrelevant data above the free surface and below the bed generated in the filming and image conversion processes. Figure 4.4 (a) shows the unfiltered velocity data, the free surface, and bed information converted to AOI values. The relevant data after being filtered is shown in Figure 4.4 (b).




TESIG2- IF4
30
10 --.....- --*! tt:7i2:! !!!.!

0 5 10 15 2 25 30 35 4
PQ inX- Orecim
(a)
Test G2 IF 41

'I, ''I----- -.- -

.1/ .
. //,/ / / /. .. / / l ; t /

.t.- . .

5 10 15 2 D 3 35
AOI inX- Direction

Test G2- IV 32

Ir I tI l \ 5,
- -. .- . . . . .
5
S 5 10 15 2D 25 30 35
AC in X Direction
(b)
Test (2 IVF 55
30
15
i iiii iii III '' -- "~ i i i .
15
" n ' . . . . . . . . ..
'1 1
0 5 10 15 2 2 AC in X Eirection

Figure 4.3 (a-d) Examples of IVFs with high resolution for Test G2, Ho=3.03 cm, T =
1.37 sec.




Ensemble Averaged Velocity Field at phase 32 of 76, Test g2
25 . . .
15- iiiiii K Z -Z Z Z Z= Z: L-r 7
')10 - - .- _- '5
0 7 ""
0 5 10 15 20 25 30 35
. . i : i.. . . . ..i J [ : l : =. .
25................................ -,............. ,--. "."" -- . . . . ...... . ..-.
25 ~ .
-- - -.~L N, A;-L0 -: -____
W 10--------- __Z___=
5 -7 : 5 C / 5 m s . . . . . .
N ....................................
0. ... .. .. .. ... I . .. A . . I . . I'
0 5 10 15 20 25 30 35
X Direction (cm)
Figure 4.4 (a-b) Unfiltered and filtered ensemble averaged velocities. Test G2 Phase 32 of 76. Ho = 3.03 cm, T = 1.37 sec.
Eulerian Mean Velocities
Theoretically, in a closed flume, the depth integrated Eulerian mean velocities should equal zero, as identified by conservation of mass. In previous experiments by Craig (1994), the Eulerian mean velocities needed to be corrected for a uniform fall velocity due to the particles having a specific gravity greater than unity. In these experiments, salt added to the water made the particles neutrally buoyant, and negated the need for this correction.
Unfortunately, for these experiments, none of the data represented the conservation of mass in this fashion. Velocities in the crest of the wave are shown to be




smaller than expected. One reason for this may be due to the temporal resolution in the crest of the wave where the velocities are the greatest. It is possible that all of the particles are exiting the AOI before the next frame is recorded. This would result in smaller measured velocities and an increase in spurious data in the crest. As well, because the Eulerian Mean Velocity fields are generated directly from averaging of the IVFs, Tests which have poor IVFs are expected to have Eulerian mean Velocity fields which do not necessarily conserve mass. This can be seen in Figure 4.5 which is the Eulerian Mean Velocity field for Test J5. Test J5 was filmed inside the surf zone where a bore had already formed. The significant aeration located in the bore of the wave caused for poor measurements (above approximately 7 cm), yet the trough of the wave (below 7 cm), which does not have appreciable aeration, still produces reliable data.
Volumetric Transport
The Eulerian Velocities were depth integrated over two regions in order to determine the volumetric transport in the water column. In accordance with Equations 3.8 and 3.9 provided in Chapter 3, the offshore transport was depth integrated from the bed to the trough, and the onshore transport was depth integrated from the trough to the crest of the wave. In keeping with conservation of mass, the net volume transport should equal zero.
Because the volumetric transport rate is just the result of the depth integrated Eulerian mean velocities, it follows that the quantities generated in the trough of the wave are more reliable than in the crest of the wave for the reasons mentioned previously. The volumetric transport rate show below in Figure 4.7 is for Test J5 and is the result of depth




41
Eulerian Mean Velocities Test g2
30 ...

25 '

5 10 15 20 25 30 35 40
X Direction (cm)

Figure 4.5 Eulerian Mean Velocity field, Test G2. The mean ratio of crest (shoreward) to trough (seaward) horizontal velocities is 0.3.

Eulerian Mean Velocities Test j5

2 . . . . . . . . . . . . . . . . . . .
0 ...........................................................
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
644
S . . . . . . . . . . . . . .
o I IIIII
0 2 4 6 8 10 12 14 16 18 X Direction (cm)

Figure 4.6 Eulerian Mean Velocity field, Test J5. Note the poor measurements obtained in the bore of the wave due to significant aeration, yet trough measurements still yield reliable data.

E 20
C t15
0
S10
N
5

.... .. . ... . .. .. .
. . . .. . . . . . ..s .

4

E
0
C a)
0
N

I

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

8

. . .

I




integrating Eulerian mean quantities in Figure 4.5. It would be expected that the volumetric transport would decrease as the wave shoals and dissipates energy, as can be seen in the measurements of volumetric transport below the trough of the wave. However, in contradiction to this, the volumetric transport for the crest of the wave is shown to be nearly constant. Because crest data has been shown to be less reliable in the inner surf zone, in the presence of significant aeration, the volumetric transport above the trough of the wave could be inferred as the mirror image of the volumetric transport in the trough about the horizontal axis. Determining the volumetric transport for the crest of the wave in this manner idealistically satisfies the conservation of mass equation.

Volumetric Transport Rate Test g2

L"
10
E
0 0.
CL M -10 I
.,
) .20
E
0
-30
N

0.8 0.85
X Direction (X/Xb)

Figure 4.7 Two-Dimensional volumetric transport showing conservation of mass, Test G2, Ho = 3.03 cm, T = 1.37 sec. Note the domination of seaward velocities due to better resolution in the trough.




Volumetric Transport Rate Test j5
0
00 06 0 0^ 0 0
0 00 0 O_00 00" 0 0 0 0
Crest Region (shoreward)
2
4 ,
+ + + + Net Transport
+ +
.,( w + + 4
Through Region (seawa.rd) + 4. *t.. .

0.2 0.22 0.24 0.26 0.28 0.3 0.32
X Direction (X/Xb)

0.34 0.36 0.38

Figure 4.8 Two-Dimensional volumetric transport, Test J5, H. = 2.67 cm, T = 1.35 sec. Note the expected decrease in transport below the trough level, and constant transport in the crest due to unreliable data caused by significant aeration.
Turbulence
Turbulence values were calculated and stored as root mean squared (r.m.s.) values according to Equation 3.6 in Chapter 3. In the most common description of turbulence, radiation stress, and turbulent kinetic energy (TKE), turbulence parameters occur as mean-squared terms as indicated in Equations 2.7 and 2.8. The turbulence intensities calculated are examined in several ways, including the ratio of horizontal to vertical turbulence in comparison with the Svendsen plane wake theory, the total turbulent kinetic energy in non-dimensional form and the evolution of turbulence induced radiation stress.

CO
E
0 0.
Cd)
.2
E
0
N

a

-4N I I I I I I I I




Ratio of u'/w'
Table 4.1 shows the ratio of horizontal to vertical turbulent mean square velocities and their relative locations in the surf zone, non-dimensionalized by the breaking distance from the shoreline (Xb). All turbulence data was used to determine the average ratio in Table 4. 1, Column 2. Column 3 shows the average ratio neglecting the rows which had extremely large ratio values due to extremely small or non-existent W' in the boundary layer. It can be seen that the data agrees well with Svendsen's (1987) plane wake assumption where the dimensionless position is outside of X = 0.72. This occurs for all tests, camera positions 1 and 2. For Tests J3, J4, and J5, inside of X = 0.71, the ratio increases to approximately 1.6. This could be a result of several various factors. Svendsen (1987) specifies the ratio of horizontal to vertical mean squared turbulence for a plane mixing layer to be approximately 1.75. In the filming regions of J3, J4, and J5, the wave transforms from the start of a bore in B3 to a fully developed bore in J5. The turbulence in this region is thus less consistent with the plane wake representation, and would be more characteristic of a plane mixing layer for which the ratio would be increasing and approaching the value of 1.75. However, it could also be a result of the DPIV measurement and accompanying ensemble averaging process in the inner surf zone region. Previously, it has been shown that velocity measurements are more scattered in the aerated bore region. Possible missing or spurious data could have serious effects on the mean, ensemble averaged, and subsequent turbulence values. It is difficult to speculate whether these calculated ratios are correct, or if they are heavily biased by the turbulent velocities measured in the bore of the wave.




Test All Data neglecting X-Xb %
boundary position difference
DI 1.40 1.35 0.83 0.74 3.0
D2 1.34 1.32 1.1 -0.90 0.8
G1 1.34 1.30 1.15 -0.95 0.8
G2 1.38 1.36 0.94 0.72 3.8
J1 1.29 1.27 1.06-0.95 0.0
J2 1.48 1.47 0.88 0.79 12.2
J3 1.61 1.58 0.71 0.62 20.6
J4 1.82 1.71 0.62 0.42 30.5
J5 1.51 1.50 0.40 0.27 14.5
Table 4.1 Comparing ratio of horizontal to vertical turbulence (u' / w'). % difference is based on the value of the ratio,1.31, for plane wake theory from Svendsen (1987).
Wave Fluctuating Velocities
The root mean square (r.m.s.) quantities of the wave fluctuating velocities for both horizontal and vertical components are shown in Figures 4.9 (a) and 4.9 (b) respectively. The evolution of these quantities is shown from non-dimensional horizontal distance X = 0.9 to X = 0.74. It can be seen that the horizontal wave fluctuations (u,'2 ) under the trough remain fairly constant at 14 cm/sec, while above the trough, which lies at a vertical height of Z _= 7.0 cm, the fluctuations are much larger. The fluctuations of the vertical velocity (w" 2 ) are observed to be smaller than the horizontal fluctuations (0.07.0 cm/sec) and is of course smallest at the bed where boundary effects dominate the vertical velocities.




X= 0.74
20
15
E
.10 8io I ***
S5 U"rms *
0 ,
20
15
10
5
'I 5 U"rms *
0 10 20 30
cm/s
X = 0.74 20
15
10
5 W"rms *
0
0 10 20 30
cm/s
X = 0.84 20
10
5 4. W"rms *
0 $
0 10 20 30
cm/s

X= 0.78

5
U"rms
0 *
0 10 20 30
cm/s
X= 0.87 20
15 *
O
10
* U"rms*
O I *
0 10 20 30
cm/s
X = 0.78
20
15
10 F
5 W"rms *
03
0 10 20 30
cm/s
X= 0.87 20
15.
10 ..).
5 W "rm s *
0
0 10 20 30
cm/s

X= 0.81
U"rms *
) 10 20 30
cm/s
X= 0.9

T **
U"rms *
), *
0 10 20 30
cm/s

X = 0.81 20
10 *
5
5 W"rms *
0
0 10 20 30
cm/s
X= 0.9
20

+
S W rms
0 10 20 30
cm/s

Figure 4.9 Vertical profiles of wave fluctuating velocities Test G2, Ho = 3.03 cm, T=1.37 sec. (a) U', ; (b) W",.




Non-Dimensional Turbulent Kinetic Energy
The non-dimensional turbulence was studied in greater detail. Previous experiments and data noted in Chapter 2 show that data has been acquired for turbulence, but only for the below trough region by using point measurement techniques such as LDA and HFA. In Figure 4.10 (a-d), the locations within the surf zone are indicated, in non-dimensional form, by the ratio of the local still water depth (ho) to the still water breaker depth (hob). The non-dimensionalized turbulence data shown as TKE, calculated by Equations 3.13 and 3.14, is measured over a large spatial domain (i.e. ho/hob ranges
from 0.88 to 0.27), and in the crest of the wave as well, (> 1). This crest data had not been previously measured. It is seen that the non-dimensionalized turbulent kinetic energy below the trough outside of ho/hob = 0.78, Figure 4.10 (a), is consistently at 0.8 0.9 while the crest experiences more turbulence, due to the wave breaking and water "spilling" down the wave face. The vertical profiles at each location under the trough of the wave are very consistent and well behaved. This data also fall between values measured by Stive and Wind (1982) and predicted values from modeling efforts of Deigaard et al. (1986) as shown in Chapter 2. Progressing shoreward, Figure 4.10 (b), the non-dimensional trough turbulence grows uniformly to a value of approximately 0.17. The vertical profiles at these locations are also self consistent, and below trough data fit within regions predicted by Deigaard et al. (1986). It also shows the turbulence in the crest of the wave approximately equal to that of Figure 4.10 (a). In this region, the wave is still "spilling" down the wave face, though closer to the bore region. Examining Figure 4.10 (c), it appears that the breaking wave turbulence has "reached" the bed, a bore has




begun to form and the turbulence from bed to crest is approximately between 0.16 and 0. 17. Here, the vertical profiles all exhibit a bulge near Al = 0.5, which is essentially at the "toe" of the "surface roller" in the breaking wave, and are all consistent from bed to trough. From h0,/hob between 0.4 and 0.27, Figure 4.10 (d), a complete bore has formed with significant aeration, showing large turbulence and significant scatter of data between 0.15 and 0.3. However, it is interesting to note that the bulge occurs in the profiles at the same vertical height as in Figure 4. 10 (c), near the vertical extent of the trough.
Tests G1 and G2 do not cover the same spatial range as Tests J2-J5, however, they do show the same trends exhibited by Tests J2-J5, and contain nearly the same nondimensional values. Figure 4.11 (a) shows Test G1. It can be seen that the data is very consistent in the trough of the wave, overlapping nearly perfectly between nondimensional TKE values of 0.8-1.0. These vertical profiles are nearly duplicated in Figure 4.11 (b) for Test G2, except for the innermost measurement which shows an increase in TKE under the trough of the wave. Also in Test G2, the turbulence in the crest of the wave is greater due to the water "spilling" down the face of the wave. In comparing the two Tests, G and J, it appears that the turbulence generated in Tests G I-G2 is greater than the turbulence generated in Tests J2-J5. It should be noted that the wave height used in Test G is larger than Test J, 3.23 cm vs. 2.67 cm respectively. Evolution of non-dimensional turbulent kinetic energy plots for Tests DI and D2 can be found in Appendices B and C.




E\dLicn dTutdert Ir~ic Enr -Test J2

+ + 078 0 o 079 + + Q8 081
o o 08 o o Q83

+t00 0"4 O5

0
0+ 4. 0
4o
o a

Q05 015 02 025 03 5 0.4 Q45 05
NmDrnisicr TutLiert nretic Emay
(a)

EdLin d Tutdert Nrelic BW Test J4

rduim fTutiert Krec r --Test J3

+ + 0*
o 0 0. + + 061
, 62 0
0 o 0.65 0, +
o o Q67 Vf
a 0 067 o+ 0 +
+ 00 10+ 0 O 0*
o 0. 000 41 0 0 ,
o 0
00 21 015 02 z 0.3 035 04
Nm.nicrda Tutdert N lrec Eral

(b)
E-cdian d Tutert Krefc ErcBj- Test J5

hh

o +
0 K

Nm-wrrad Tutdiet Kr9C E c

+ + 027 o 0.29 + + 32
, 0.34 0 0 Q37
o o Q4

+ Q
0
0+
O
o #0+
0 01, 0* 0 0 0 +
0 +
0 +
OD +

.5 Gl 015 02 G2 Q3 a35 04
N.r-Ontreal Tutdft Irec BraE
(d)

k2
Figure 4.10 Evolution of Non-Dimension Turbulent Kinetic Energy ( )."

2.67, T = 1.35, hob = 7.87 cm. Note that ho = still water depth and hob = the still water depth at the location of breaking. (a) Test J2; (b) Test J3; (c) Test J4; (d) Test J5.

I

I I I I I I I

i

Ho =




Bddiln d Tutdert Mnelic Bi Test G2

IolIsh
* a 94
o o Q97 + +1I S 1. 0 +
a a 1.OB + 0'+~
0 0 +
S+000
e0.
00
Q05 1 0115 02 02 03 035 4 045 Q5
NDrnarnsid Tutert Mer~icBa
(a)

4 + 074 o o a77
* + + 0.8
G83
0 8
Gag 0

+ 0
S o0
0 +
0 + '4
+ 0 O +
+0 .04

005 (1 015 02 0Z 03 0Q35 04 045 05
NOnDrrea -d TubJert MrdicEraf
(b)
1

k2
Figure 4.11 Evolution of Non-Dimension Turbulent Kinetic Energy ( ). H0 =
3.03 cm, T = 1.37 sec, hob =8.69 cm. (a) Test Gl; (b) Test G2.
Radiation Stress
The radiation stress was examined from two perspectives, the "classical" radiation stress due to waves, and the equivalent "radiation stress" due to turbulence, both of which are fundamental to the momentum balance in the surf zone. The equivalent "radiation stress" due to turbulence ( S ) should theoretically be close to zero near the break point where significant turbulence has yet to develop. It should increase steadily through the surf zone, to a point where it becomes a maximum, then decays. The radiation stress due to waves (S") progresses just the opposite. It should start off as a maximum near the break point and decrease to zero at the shoreline as the wave itself decays into turbulence

EddCin of TutUed Knelc Ereray Test G1




production. Figures 4.12 and 4.13 show these principles very well. In Figure 4.12, close to the non-dimensional breaker point (X = 0.85), the S x is essentially zero and builds from zero to approximately 1.5 through X = 0.45. At this point, S' remains fairly constant through the range of measurements, although one might expect decay further inshore.
Similar to what is to be expected, in Figure 4.13, S" is at a maximum closer to the break point and decreases to approximately 1 at a point where the bore has formed. At places, it appears that the data does not connect well between runs, i.e. between X = 0.78 and X = 0.73 (between Tests J2 and B). S" is highly dependent on the average free surface fluctuations (;7" ) as shown in Equation 2.14. In the digitization process, the areas close to the edge of the image may be miscalculated due to the cubic spline routine used. A small error in digitization is then squared and can effect the ends of S" data for each run. However, a best fit line through all of the data clearly shows the decomposition of the wave.




Turbulence Induced Radiation Stress Test J2, J3, J4
Test J4 Test J3 TestJ2
+
+
+
++
+
++
+ + + + + -i+ +
++ ++++ +t +-~
+ J, ++ -+
+ '+ -- + +- +- +++ ++
++ + + j + + + ++ ++ 4++ +++, .
+++.-t + 4+ ++ ++
++ + + +
-++
+
S r I I I I I

0.45 0.5 0.55 0.6 0.65 0.7
X- Direction (X/Xb)

0.75

0.8 0.85

Figure 4.12 Turbulence Induced Radiation Stress, Sxx' (N/m), from three under the same wave conditions. Tests J2, J3, J4

separate tests

Wave Induced Radiation Stress Test J2, J3, J4
4 ,I i i I 1

Test J4

2.51-

-*
+*+

Test J3

**
*
~ 4*
*
**
it

n i I I J I I -A-

0.4 0.45 0.5 0.55 0.6 0.65 0.7
X- Direction (X/Xb)

Test J2
+

0.8 0.85

Figure 4.13 Wave Induced Radiation Stress, Sxx" (N/m), the same wave conditions. Tests J2, J3 and J4.

from three separate tests under

15
1.5

0.5 -




CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
The primary goal of the present study was the measurement of mean and turbulent velocity fields in the surf zone. The experiments consisted of video taping breaking waves in a flume, and analyzing the video with the Digital Particle Image Velocimetry process. It was found that this process provides reasonable and consistent measurements of both the mean flow field quantities in the surf zone and the spatial variation of turbulence across the surf zone. The major findings from these experiments regarding the DPIV process and measured surf zone quantities are as follows:
1. The filtering process applied to the entire water column was particularly useful in
determining particle velocities in the aerated portion of the crest of the wave, although
the intense aeration in the inner surf zone still seems to be problematic.
2. The ensemble averaging process, though having its drawbacks, provided a reasonable,
and perhaps only, way to extract turbulence and wave fluctuating values from the
instantaneous velocity fields.
3. Eulerian mean velocities and volumetric transport for most cases had net values much
lower than zero. This shows that although higher particle seeding densities were used, crest velocities under most test conditions still remain unresolved. As well, for tests where crest velocities were affected by significant aeration, transport in the trough
dominated (presumably due to higher fidelity measurements).




4. Plots of the turbulence and wave induced radiation stress indicate that both of these
quantities are of the same order of magnitude and the momentum balance is influenced by both, especially in the inner surf zone where the magnitudes of these quantities are
approximately equal.
5. Total non-dimensional turbulent kinetic energies, though values were higher than
previously measured, were self consistent in each filming location, consistent between filming positions, and consistent between various wave conditions. More importantly, values were determined for the aerated crest of the broken wave, which had not been
measured previously.
Though these experiments provided many quantities previously unmeasured, it was found that the velocity measurements in the crest of the wave were largely unresolved. There are many areas in which the technique could be improved to help resolve these crest measuremnets. The first and most important would be a reduction in the time interval between successive frames. This reduction of the time interval would decrease the spurious data as explained by Huang and Fiedler (1994) in Chapter 2. The use of a digital camera and direct processing would also eliminate the conversion process from video tape images into TWF format, eliminating missing or duplicated frames generated by the 1 frame accuracy of the controller card used for these experiments. Finally, another technique consisting of padding the FFT's with zeros, as described by Lourenco and Krothapalli (1995) for PIV measurements, could be applied to the DPIV method. The typical AOI size used in the cross correlation process (32 x 32 pixels for these experiments) would be appended with zeros, enlarging it to a 64 x 64 matrix. This




55
would improve the measurements of displacements of the particles. However, it is computationally more intensive because the cross-correlation is now done on a much larger matrix. This technique would only need to be applied if the time interval between frames could be significantly reduced. Otherwise, the improvement in the cross correlation process would be insignificant compared to the accuracy obtained with the present time interval and conversion process.




APPENDIX A
POST PROCESSING INFORMATION

TEST FRAMES PER PERIOD CYCLES SCALING (pix/cm)
DI 76 19 16.0
D2 75 22 17.4
G1 76 22 17.7
G2 76 28 16.2
Ji 76 28 14.7
J2 78 30 25.5
J3 79 30 25.0
J4 78 31 26.0
J5 78 30 34.6

Table Al Processing information including number of frames per period of complete wave cycles, and scaling factor from pixels to cm.

(fpp), number




APPENDIX B
PLOTS OF MEASURED QUANTITIES FOR TEST D1

Wave Evolution in Time Test D1

E 20
C:
0
__ 15 10
N
5

0.72 074 0.76 0.78 0;8 0.82
X Direction (X / Xb)

0.84 0.86 0.88

Figure B1 Evolution of free surface, digitized, mean, and still water level. Test Dl. Note that free surfaces are at intervals of 5 frames (5/60' or 1/12t" sec).




58
Eulerian Mean Velocities Test dl
30 1 I 1
25 ....... ..... .. .......................................
C.) . .h. .u . a .
.~~X . .. ........ .... ..
0 / / aV 1, 1I t 'I t l a
.. a a a a a a . 5
E 0 .5 25 30 35 4.
15
X Direction (cm)
Figure B2 Eulerian Mean Velocity Field. Test DI.
Volumetric Transport Rate Test dl
20 i I i
Crest Region shorewardd)
0 -LL
-0 51 52 51 54
r"
Volme i Net Transport
E Trough Region (seward)
o -40 $
0
0 -50
CN
-60 I I I I I
0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 X Direction (XIXb)
Figure B3 Two Dimensional volumetric transport. Test D1




Turbulence Induced Radiation Stress Test D1
3 + + + +
++ + +
2 + ++ + + ++
+ + + +
+ +
1 + +
-+
+3
X -- Dieton(m
7 + + +
+
6.5 +
-2
-3
-41 I IIIII
07 0.72 074 076 0.78 08 0.82 084 0.86 X Direction (cm)
Figure B4 Turbulence Induced Radiation Stress, (N/r). Test D.
Wave Induced Radiation Stress Test D1
7.5, ,
* *4. 4
4.4
* 4
6.5 *-4
-x
X 4 ,
15.5 **
4
45
4 i I I I I III
0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 X Direction (cm)
Figure B5 Wave Induced Radiation Stress, (N/rn). Test D1.




X = 0.74

01 4 .4
0 10 20 30
cm/s
X= 0.8
20

*
*-1
* U"rms 10 20 30
cm/s

X= 0.76 20
15
10
5 1++
* U"rms *
0 *
0 10 20 30
cm/s
X = 0.81 20.
*
15 +
+
10
SU"rms *
0
0 10 20 30
cm/s

X = 0.78 20t

10
5 **
*4 U"rms *
0
0 10 20 30
cm/s
X = 0.83 20
15
*
5 -*
10
5
5 U"rms *
0
0 10 20 30
cm/s

Figure B6 Vertical Profiles of U",. Test DI.

X = 0.74

W"rms *
5
oi .,
0 10 20 30
cm/s X= 0.8
4
S *
4 *
+
W"rms *
0 10 20 30
cm/s

X = 0.76
4*4
W"rms *
0 10 20 30
cm/s
X = 0.81

10 20 30
cm/s

X = 0.78
4 W"rms*
*
0 10 20 30
cmis
X = 0.83
t
* W"rms
0 10 20 30
cm/s
X = 0 83
+
*4
5 *
*' W"rm s
0 10 20 30
cm/s

Figure B7 Vertical Profiles of Wr"s. Test D1.

15
0
1, O
10 N 5
0




61
Evolution of Turbulent Kinetic Energy Test D1
3
70
U)
O
2.5 ho / hob
O
.0 + + 0.74
<2 0 0 0.76 0
S + + 0.77 0 +0 x +
S x x 0.79 0 +
0 o 0.81 x 0o
- 1.5 0 O 0.83 + x 0x
C [] 0 x 0
.0 +[],x 0
to 0* 0
O- 1 0]GI0
E g
o
0
C o 0.5
0
z

0.1 0.15 0.2 0.25 0.3 0.35 0.4
Non-Dimensional Turbulent Kinetic Energy

0.45 0.5

Figure B8 Non Dimensional Turbulent Kinetic Energy. Test D1.




APPENDIX C
PLOTS OF MEASURED QUANTITIES FOR TEST D2
Wave Evolution in Time Test D2
25 ..

201-

0.9 0.92 0.94 0.96 0.98 1 1.02
X Direction (X / Xb)

Figure C1 Evolution of free surface, digitized, mean, and still water level. Test D2. Note that the free surfaces are at intervals of 5 frames (5/60 or 1/12th sec).

15
C) 1 ,i oI
N
5




Eulerian Mean Velocities Test d2

E
C)
0
C.)
N
N

0 5 10 15 20 25
X Direction (cm)

Figure C2 Eulerian Mean Velocity Field. Test D2.
Volumetric Transport Rate Test d2
20

101-

-40
-50
-60

30 35 40

0.9 0.92 0.94 0.96
X Direction (X/Xb)

Figure C3 Two Dimensional Volumetric Transport. Test D2.

Crest Region (shoreward)
^O0 0 00 Q V eo o

Net Transport Trough Region (seaward)

2 5 . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
.0 . . . . . . . . . . . . . . .
Jo I i I I
. . . . . . . . . . . . . . . . . . . .
15
20
15 io ** 4 /i 1 4 / iV V 411 /
5 I Z I NUS
- -

-10
-201




64
Turbulence Induced Radiation Stress Test D2

++ .+++- +++

+ +
+- +- +
+ + +- ++-

+ +.

-1U
0.88 0.9 0.92 0.94 0.96 0.98 1
X Direction (X / Xb)
Figure C4 Turbulence Induced Radiation Stress, (N/m). Test D2.
Wave Induced Radiation Stress Test D2
A ,

4.5 I-

0.9 0.92

0.94 0.96
X Direction (X / Xb)

0.98

Figure C5 Wave Induced Radiation Stress, (N/m). Test D2.

+ +
+
+

* *
4 *
* * -* *
* *4

8

0.8E




Z-Direction (cm)
****~,

3

Z-Direction (cm)
o4 4
**, + **
Z-Direction (cm)
S ***
* 4*4 ..
'"-e--..* *

XC

ii C

o

x
0 3C

Z-Direction (cm)
*4g4 "'$--...$ .$'"* $

4

Z-Direction (cm)
0a 0 o0 0

Z-Direction (cm)
o ol o o

o
+++*44so **,* *
0 C;
Z-Direction (cm)
0 01 0 0 C
0
c

Z-Direction (cm)
3 *** *
o Ol o *
4$..$ $

Z-Direction (cm)
00 C 0 0 4n

'C
X ii C

Z-Direction (cm)

*4r'
*3.
C+++ 1
4 I$
C).I

o8
0
0 0

** *
**** **
*
Z-Direction (cm)
++ + ,,4.*.*' *,.$ "
c

Z-Direction (cm) 0 ..

**




Evolution of Turbulent Kinetic Energy Test D2
3
ci)
m
2.5 ho / hob
.0 + + 0.9
< o o 0.91 +
2 + + 0.93 x
+
0) x 0.95 0 060
0 0 0.96 P
1.5 O o 0.98 ++0
0* +0 0 x +
E oo
0
- 0.5 o +
Z
00 z i

0.1 0.15 0.2 0.25 0.3 0.35 0.4
Non-Dimensional Turbulent Kinetic Energy

0.45 0.5

Figure C8 Non Dimensional Turbulent Kinetic Energy. Test D2.




APPENDIX D
PLOTS OF MEASURED QUANTITIES FOR TEST GI
Wave Evolution in Time Test G 1

22 [ 20

0.95

1 .0 5 1 1
X Direction (X / Xb)

Figure DI Evolution of free surface, digitized, mean, and still water level. Test G1. Note that the free surfaces are at intervals of 5 frames (5/60th or 1/12t sec).

-' 18
E
16
0
c 12
1
N lo

F I I II




Eulerian Mean Velocities Test gl
30 I 1
2 5 . . . . . . . . . . . . . . .
.= . . . . . . . . . . . . . . . . .
E 2 . .. . . . . .
.. . . . . . . . . . . .
, . . . . . . .
t . . . . . . . . . o .
25
2 0 . .- . . . . .- .. . .
15 "_ -- -1~c -] -[ : ] 2 2 2
N I : I I - :I --- -1------------------------------------------------------------* t i i o C ~. . . . . . . .
0 5 10 15 20 25 . .
. .

05 10 15 20 25
X Direction (cm)
Figure D2 Eulerian Mean Velocity Field. Test G1.

30 35 40

Volumetric Transport Rate Test g1
20 0 o
0
0
0
10 Net Transport
20
++
-30 + t
Trough Region (seaward)
4n I I

0.95

1 1.05
X Direction (X/Xb)

Figure D3 Two Dimensional Volumetric Transport. Test GI.

I
0
0.
Cn Cu
r
E
2
0
C>




69
Turbulence Induced Radiation Stress Test gl

0.9 0.95 1 1.05 1.1
X Direction (cm)

1.15 1.2

Figure D4 Turbulence Induced Radiation Stress, (N/m). Test G1.
Wave Induced Radiation Stress Test gl

5.5 I-

4.5-

3.5 P

2.5

1.05 1.1
X Direction (cm)

1.15

Figure D5 Wave Induced Radiation Stress, (N/m). Test G1.

4+
3 -++ ++ ++
++
2 -+ + + +
+
+
1 + + + + +
+ ++ +- ++,.
++ + O + ++
-I +
+
-2
-3
-4
+-

* *
*,_**$. "*-* *.
*
*
*
" .,.$. *
-,F*
4*$
*,




Z-Direction (cm)

Z-Direction (cm)
**
Z-Direction (cm)
t 0 .+ 8 1 1
+4 +
+*
.*
* *4

Z-Direction (cm)
* + +* o *** *
"$4$*.... $ $
4*$.$ $"

9
0 I oC
9

x
ii o,

Z Direction (cm)
oI I
% ** *
4
Z-Direction (cm)
+ ++0N'
4,+.. +.$.$.$ "".....
* 4+~*,

Z-Direction (cm)
o ..****'-$
0
**
Z-Direction (cm) o*
Z-Direction (cm)
o m 0 N 0
*44k.$..$.$..'"

e* +
** .,4

Z-Direction (cm)
** *. .
o .. ***

'C ii CV
9
0~

Xi C

0

m o
0

4

Z-Direction (cm) o ,
*

Z-Direction (cm) 0 0, 0 N
444




71
Evolution of Turbulent Kinetic Energy Test G 1
3
2.5 ho hob
o 0.94
.0
o 0.97
.,_, 2 + + 1 cx 1.03 + +
-- 103 +0x
0 0 1.05 + 0 o
1.5 0 0 1.08 + 0
-0 +1 x 0 +
0 x "$+ 0 [
U) 0+ & 03
c' 1 1
00.
E
0 .
z

0.1 0.15 0.2 0.25 0.3 0.35 0.4
Non-Dimensional Turbulent Kinetic Energy

Figure D8 Non Dimensional Turbulent Kinetic Energy. Test GI.

0.45 0.5




APPENDIX E
PLOTS OF MEASURED QUANTITIES FOR TEST G2
Wave Evolution in Time Test G2

0.8 0.85
X Direction (X / Xb)

Figure El Evolution of free surface, digitized, mean, and still water level. Test G2. Note that the free surfaces are at intervals of 5 frames (5/60' or 1/12'" sec).




25 -

Eulerian Mean Velocities Test g2
. . . . . . . . . . . . i . . . ., ., .
. . . . . . . I . . .
. ... .... ..,.... ... ,. ,o,...... ., ...
--- -os. ..----------------- ----
--------------------------------------------------........ .......... ................................

5 10 15 20 25
X Direction (cm)

30 35

Figure E2 Eulerian Mean Velocity Field. Test G2.
Volumetric Transport Rate Test g2
2en .-

0.75

0.8 0.85
X Direction (X/Xb)

Figure E3 Two Dimensional Volumetric Transport. Test G2.

15 10

U i

Crest Region shorewardd)
0 0000 0O<>O"-O
o0
+
Net Transport
T
+ + --+++ + -..
Trough Region (seaward) + 14 j 4
I-

to
10
o
0 o0
0

C.)
C
c
-20
E
0
0 -30 CI




Turbulence Induced Radiation Stress Test G2
4 -+ +
+ +++ ++ +++
2 +
++ + + +
+ +
2 + +
++ + +
+ +
++
1 +
+ + +
o + 4r
-1
+
-2 I III
0.7 0.75 0.8 0.85 0.9 0.9!
X Direction (cm)
Turbulence Induced Radiation Stress, (N/m). Test G2.
Wave Induced Radiation Stress Test G2
6 I

* *!
-*
*

* **** *
*

*
*
**
*

0.95

0.8 0.85
X Direction (cm)

Figure E5 Wave Induced Radiation Stress, (N/m). Test G2.

Figure E4

5.5
5
4,5
x
.)
3.5 3

** *




X = 0.74 20
15
0
10
5 *
SU"rms *
0 .
0 10 20 30
cm/s
X = 0.84 20
S15
10 +
s *
5 +
+ U"rms *
0
0 10 20 30
cm/s

X = 0.78
4*
U"rms ) ,
0 10 20 30
cm/s
X = 0.87
*
-*
5- 4
)0 . .
SU"rms *
0 10 20 30
cm/s

20 15
10
5
0
20 15'
0 10 N 5

X = 0.81
*
+ U"rms*
0 10 20 30
cm/s X= 0.9

cm/s

Figure E6 Vertical profiles of U",. Test G2.

X = 0.74
*
+
4
* W"rms *
0 10 20 30
cm/s
X = 0.84

0 10 20 30
cm/s

X = 0.78

1
0 10
o5
S 5t W"rms *
0
o//S
0 10 20 30
cm/s
X = 0.87
20
15
8 g o 4
0*
10
U 4
5 W"rms *
0 10 20 30
cm/s

X = 0.81
20
15
8+
0 4
SW"rms *
o *
0 10 20 30
cm/s X= 0.9
20
U 15
8 *
5r 5 W "rm s *
0*0
0 10 20 30
cm/s

Figure E7 Vertical Profiles of W",. Test G2.




Evolution of Turbulent Kinetic Energy Test G2
ho I hob

x 0
E3

- xO
'C 04
00 000
o x + eg + 0Ox 040

x 0
* +

X%
'C490

I I I

0.45 0.5

Figure E8 Non Dimensional Turbulent Kinetic Energy. Test G2.

1.5

0.51-

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Non-Dimensional Turbulent Kinetic Energy

x--I




APPENDIX F
PLOTS OF MEASURED QUANTITIES FOR TEST J2

Wave Evolution in Time Test J2

0.79 0.8 0.81 0.82
X Direction (X / Xb)

Figure F1 Evolution of free surface, digitized, mean, and still water level. Test J2. Note that the free surfaces are at intervals of 5 frames (5/60t or 1/12th sec).

14
E
C.) C 12
0
C
N_ 10
N




78
Eulerian Mean Velocities Test j2

14 -

E 12
0
0 10
0
8
6
N
4
2

U,
0 5 10 15 20
X Direction (cm)

Figure F2 Eulerian Mean Velocity Field. Test J2.

Volumetric Transport Rate Test j2

Jo
0
-5
o
CL ) -10
E
I
o -15
()
E_2
-20 0-25 025 C a

0.78 0.79 0.8 0.81 0.82
X Direction (X/Xb)

0.83 0.84 0 85

Figure F3 Two Dimensional Volumetric Transport. Test J2.

. . . . .
. . .
. . . .=.1.c. .

.........,,.,,o,,,.....
....#l...................
.........,,..............
. . . . . . . . . .~s
. ... .. .. ... ..l ~ t
-l-l---l-------------l--, - - - - -i -

Crest Region (shoreward

+ Net Transport

Trough Region (seawE

I-

I I I I I I n




Turbulence Induced Radiation Stress Test J2
2.5 iI + i i I i
+ +
2
1.5 ++ + +
+ +
1 + ++ ++ +
0.5 + + + ++
+ +
0 + +
+ ++ + + ++-0.5 +
+
-1
-1.5 +
-2

0.77 0.78 0.79 0.8 0.81 0.82
X Direction (X / Xb)

0.83 0.84 0.85

Figure F4 Turbulence Induced Radiation Stress, (N/m). Test J2.
Wave Induced Radiation Stress Test J2

0.85

X Direction (X / Xb)

Figure F5 Wave Induced Radiation Stress, (N/m). Test J2.

-2, L)IIII




X = 0.78

cm/s
X = 0.82
20
15
10
a *+q
N 5 + .rm S
0 *
0 5 10 15 20
cm/s

X = 0.8
20
S15
C
0
10
N 5 "rms *
0
0 5 10 15 20
cm/s
X = 0.83
20
15
. 10
N4 5r 0j*s* **
*frm s
0 5 10 15 20
cm/s

X = 0.81
20
15
,S
0
- 15 -10 +
N5 U"rms
0 $
0 5 10 15 20
cm/s
X =0.84
20
-15
E
0
~10
J5 4
0 U'rms
0 5 10 15 20
cm/s

Figure F6 Vertical profiles of U", Test J2.

20
15
.
-1
2 101
0

X = 0.78

S 5 10 15 20 cm/s
X = 0.82
.4
W"rms 0
0 5 10 15 20
cm/s

X= 0.8
20
. 10
N 5 *
- W"rms *
0
5 10 15 20
cm/s
X = 0.83
20
15
E
10
a W"rms
0 5 10 15 20
cm/s

X= 0,81
20
15
S
S10
5 W"rms *
0
0 5 10 15 20
cm/s
X = 0.84
20
- 15
E
.210 4
5 W"rms*
0
0 5 10 15 20
cm/s

Figure F7 Vertical Profiles of W" Test J2.




81
Evolution of Turbulent Kinetic Energy Test J2

2.5 ho hob
* + 0.78
o o 0.79
2 + + 0.8 x x 0.81
0 0.82
0 0 0.83
1.5
1 +0O
0.5
Ob+

0 x
o+# 0

0.45 0.5

Figure F8 Non Dimensional Turbulent Kinetic Energy. Test J2.

0.05 0.T 015 0.2 0.25 0.3 035 0.4
Non-Dimensional Turbulent Kinetic Energy

N I I I M I I I I I I I i

I I I




APPENDIX G
PLOTS OF MEASURED QUANTITIES FOR TEST B3
Wave Evolution in Time Test J3
16 1 1

14-k

0.58 0.6 0.62 0.64 0.66 0.68
X Direction (X / Xb)

0.7 0.72

Figure GI Evolution of free surface, digitized, mean, and still water level. Test B3. Note that the free surfaces are at intervals of 5 frames (5/60Oh or 1/12t" see).

E 12
C
0
8
N
6

0.74




Eulerian Mean Velocities Test j3
18 ..
16 . . . ..
14
. . . .
E12
N
4 .m .. I I'... '
. 2 .. .1. . .. ............ . . .. .... .
0 I
05 10 15 20 25
X Direction (cm)
Figure G2 Eulerian Mean Velocity Field. Test J3.
Volumetric Transport Rate Test j3
6- -5
N -10-4 -1 .
0 L0L L
X Direction (XIm)
Dvoluetric Transport. T ts j
0 Crest Reio (shrg e gio eawrd
U +
-5 .. . + -'
Fi Ur NeTo-Dmninl ouerctasot TraspJ3.




Turbulence Induced Radiation Stress Test J3

+
2.5
2
+
++ + +
+ + +
++ + +
+ + + +
-4 + + + +
+ + + -+ + ++ +
+1+++
+ +
0 5II I IIII

0 56

0.58 0.6 0.62 0.64 0.66 0.68
X Direction (X / Xb)

Figure G4 Turbulence Induced Radiation Stress, (N/m). Test J3.
Wave Induced Radiation Stress Test J3

0.58 0.6 0.62 0.64 0.66 0.68
X Direction (X / Xb)

0.7 0.72 0.74

Figure G5 Wave Induced Radiation Stress, (N/m). Test J3.

0.7 0.72 0.74

2.4 2.2

1.6
1.4

i i i= ,
*
*
**
*
* **
*@
4 *
*@
4
I *

i




X = 0.59

*4 *
N 5 4
SU"rms
0
0 5 10 15 20 25
cm/s
X = 0.63 20
15
E
10:
Ri 5 U"rms *
0
0 5 10 15 20 25
cm/s

X= 0.6 20
15
E
5 ./ U"rms*
0
10
o *j
0 Urms *
0 5 10 15 20 25
cm/s
X = 0.65 20
15
E
5 U"rms *
0
0 5 10 15 20 25
cm/s

X = 0.61
*
U"rms *
5 10 15 20 25
cm/s
X = 0.68

I 5 U"rms *
0 1
0 5 10 15 20 25
cm/s

Figure G6 Vertical profiles of U" ,. Test J3.

X = 0.59
Wrms *
5 10 15 20 25
cm/s X = 0.63

X= 0.6

-1
C
.1
0
ri

6
5
5 W"rms *
0
0 5 10 15 20 2
cm/s
X = 0.65

X = 0.61

lu
0!
5 W"rms *
0
5 0 5 10 15 20 25
cm/s
X = 0.68

20 20 20
15 15 -15
C Co
1Z 1010 .0 10
5 W"rms 5 W"rms 5 W"rms *
0 0 )
0 5 10 15 20 25 5 10 15 20 25 0 5 10 15 20 25
Figure G7 Vertical Profiles of Wcm/s. Test Figure G7 Vertical Profiles of W",. Test J3.




Evolution of Turbulent Kinetic Energy Test J3
3
CO
m
2.5 ho / hob
+ + 0.58
< o o 0.59
2 + + 0.61
+ +
.) x x 0.62 n +
D 0 o 0.65 O 0
15 0 0.67 +x 0 O+
= +
C 1 O -WO 0f
o 0o o.
S0 Ox Q' Do x-1
C 0.5 0 x
0 x 0+
Z [00. + -0
I C I I IIII I
0.05 0.1 0.15 0.2 0.25 0.3 0.35 04 0.45 0.5
Non-Dimensional Turbulent Kinetic Energy
Figure G8 Non Dimensional Turbulent Kinetic Energy. Test J3.




APPENDIX H
PLOTS OF MEASURED QUANTITIES FOR TEST J4
Wave Evolution in Time Test J4

14
E 12 C-,
0
8
N

0 4 0.42 0.44 0.46 0.48 0*5
X Direction (X / Xb)

0.52 0.54 0. 5 6

Figure Hi Evolution of free surface, digitized, mean, and still water level. Test J4. Note that the free surfaces are at intervals of 5 frames (5/60' or 1/12hb sec).
87

I I I




88
Eulerian Mean Velocities Test j4
1

141-

E 12
6 6
8
N
4 2

gi 1
0 5 10 15 20
X Direction (cm)
Figure H2 Eulerian Mean Velocity Field. Test J4.
Volumetric Transport Rate Test j4

X Direction (X/Xb)

Figure H3 Two Dimensional Volumetric Transport. Test J4.

. . . . . . . . . . . . . .t . . s o
. . . . . . . . . . . .. . . . . .
" . . . . . . . . . . . . . . . . . . .
,-.....
- . . . . . . . . . .
- . . . . . . . . . .
. . . . .10 ill. . . . . . . .
- . . . . .




89
Turbulence Induced Radiation Stress Test J4

0.4 0.5
X Direction (X / Xb)
Figure H4 Turbulence Induced Radiation Stress, (N/m). Test J4.
Wave Induced Radiation Stress Test J4
1.5
1.4
*4 4
1.3 -4
1.2 **
*-4 44 *
x
1.1 *
1*
0.9 +
0.8 1
0.4 0.5
X Direction (X / Xb)
Figure H5 Wave Induced Radiation Stress, (N/m). Test J4.


+
+ + +
+ ++ ++
+ + +
++ +
+ + +-+ + +
+ +
+ +- ++
+-++ +" + + + 4 +4- +