• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Literature review and theoretical...
 Experimental setup and procedu...
 Experimental results
 Conclusions and recommendation...
 Appendix A. Post processing...
 Appendix B. Plots of measured quantities...
 Appendix C. Plots of measured quantities...
 Appendix D. Plots of measured quantities...
 Appendix E. Plots of measured quantities...
 Appendix F. Plots of measured quantities...
 Appendix G. Plots of measured quantities...
 Appendix H. Plots of measured quantities...
 Appendix I. Plots of measured quantities...
 Appendix J. Computer programs
 Reference
 Biographical sketch














Group Title: UFLCOEL-98008
Title: Quantification of surf zone velocities and turbulence using digital particle image velocimetry
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00091086/00001
 Material Information
Title: Quantification of surf zone velocities and turbulence using digital particle image velocimetry
Series Title: UFLCOEL-98008
Physical Description: x, 122 leaves : ill. ; 28 cm.
Language: English
Creator: Roebuck, Gregory J., 1973-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept.
Place of Publication: Gainesville Fla
Publication Date: 1998
 Subjects
Subject: Ocean waves -- Measurement   ( lcsh )
Fluid dynamic measurements   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1998.
Bibliography: Includes bibliographical references (leaves 120-121).
Statement of Responsibility: by Gregory J. Roebuck.
General Note: Typescript.
 Record Information
Bibliographic ID: UF00091086
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 41567277

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
    Abstract
        Page ix
        Page x
    Introduction
        Page 1
        Page 2
        Page 3
    Literature review and theoretical background
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
    Experimental setup and procedures
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
    Experimental results
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
    Conclusions and recommendations
        Page 53
        Page 54
        Page 55
    Appendix A. Post processing information
        Page 56
    Appendix B. Plots of measured quantities for test D1
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
    Appendix C. Plots of measured quantities for test D2
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
    Appendix D. Plots of measured quantities for test G1
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
    Appendix E. Plots of measured quantities for test G2
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
    Appendix F. Plots of measured quantities for test J2
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
    Appendix G. Plots of measured quantities for test J3
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
    Appendix H. Plots of measured quantities for test J4
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
    Appendix I. Plots of measured quantities for test J5
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
    Appendix J. Computer programs
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
    Reference
        Page 120
        Page 121
    Biographical sketch
        Page 122
Full Text




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


ACKNOWLEDGMENTS ........................................................ .................................. ii

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

LIST O F FIG U R E S .................................................................................................... vii

A B ST R A C T ...... ... ..................... ............................................................................................. ix

1 IN TR O D U CTION ................................................................................................... 1

2 LITERATURE REVIEW AND THEORETICAL BACKGROUND ...................... ....4
Development of a Digital Particle Image Velocimetry Technique......................4
Measurement of Velocity Components ..............................................................8
Measurement of Surf Zone Quantities............................................. .............. 10
Calculation of Two-Dimensional Volumetric Flow ............................................14
Calculation of Radiation Stress (due to waves and turbulence)............................15

3 EXPERIMENTAL SETUP AND PROCEDURES ................................................ 17
Experimental Summary .................................................................................17
W ave C onditions.......................................................................................... ......17
Data Collection/Analysis Equipment............................................................. 18
Physical Setup ..................................................................................................20
Experimental Procedures .................................................. ............................ 23
D ata Processing................................................................................................26

4 EXPERIMENTAL RESULTS................................................................................33
Im age Processing ................................................................................................ 33
Free Surface Elevations/Bed Data .......................................................................34
Instantaneous Velocity Fields (IVFs) ................................................................34
Filtered/Unfiltered Ensemble Averaged Velocity Fields .....................................37
Eulerian Mean Velocities.........................................................................39
Volumetric Transport..................................................................................40
T turbulence ............................................................................................ ........... 43
R radiation Stress .................................................................................... ...........50

5 CONCLUSIONS AND RECOMMENDATIONS ..............................................53









APPENDICES

A POST PROCESSING INFORMATION...........................................................56
B PLOTS OF MEASURED QUANTITIES FOR TEST D......................................57
C PLOTS OF MEASURED QUANTITIES FOR TEST D2....................................62
D PLOTS OF MEASURED QUANTITIES FOR TEST G .....................................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
I PLOTS OF MEASURED QUANTITIES FOR TEST J5 ......................................92
J COMPUTER PROGRAMS ............................................................................. 97


LIST OF REFEREN CES .................................................................................................120

BIOGRAPHICAL SKETCH ...................................................................................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, 1.31, for plane wake theory from
Svendsen (1987)..........................................................................................................45














LIST OF FIGURES


Figure page

2.1 Comparison between Video PIV measurements with (a) time interval = 20ms
and (b) time interval = 5 ms. 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 (1987). ................................................. .......................... 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 5/60t" or 1/12h 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 ofIVFs with high resolution for Test G2, Ho=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 shorewardd)
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, Ho = 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, Ho = 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) WI .....................................................46


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

Ho = 2.67, T = 1.35, hob= 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
J3; (c) T est J4; (d) T est J5..........................................................................................49

k2
4.11 Evolution of Non-Dimension Turbulent Kinetic Energy ( )

Ho = 3.03 cm, T = 1.37 sec, hob = 8.69 cm. (a) Test Gl; (b) Test G2.......................50

4.12 Turbulence Induced Radiation Stress, Sxx' (N/m), from three separate tests
under the same wave conditions. Tests J2, J3, J4 ...........................................52

4.13 Wave Induced Radiation Stress, Sxx" (N/m), from three separate tests
under the same wave conditions. Tests J2, J3 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 cross-

correlation 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 cross-

shore 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 f(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 AOI. 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 AOI.

The cross-correlation provides a maximum peak located a distance away from the origin

equal to the average displacement of the particles within the AOI. The cross-correlation

function, Ofg (m,n), is defined as:


Of(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 (m,n) = Of (m,n)* s(m,n) (2.3)



where (Dfm,n) is the auto-correlation function of the first AOI. 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 ms). Reduction of the

time interval by 75%, achieved by pulsing the laser at 5 ms 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.

Scote: -10cm/s
1.73 __ ___ \_ -_--__ _ _ _-.-.,'.,-'___ --___"







x/S
Scale: -- lOcm/s
1.73






0 1 2 3
x/s


Figure 2.1 Comparison between Video PIV measurements with (a) time interval = 20ms
and (b) time interval = 5 ms. 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 t2(z)
u- d
u=-- Judt


if: Tr

if: -h

T
u udt
0


(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.


(2.4)








Measurement of Surf Zone Quantities

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 three-

dimensional 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 t-u 2 +2 +w12) (2.7)




and the 2-D TKE is given by:




k'= 1( 2 2 (2.8)









In both of these equations, u'2 and w'2 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:



.2 .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.






1 Ih heg oI h
A 0.882
x .0.765 SW
Sx 0.57 Tt NO )iard
ax o 0.52/
0.5 + O.412 0.5 Z-
x+ 0.291.
m 0.177
+ /
Vi i 0 ;V2
01 ____ -, _____Ii. I
0 0.05 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 :









Vto = h ud z (2.11)



which can be decomposed into above and below trough volumetric flow given by :


V forward = udz (2.12)





Vretrn = udz (2.13)
return f-h



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:











I'l = u"2 _- 2z+ 2 pg"2 (2.14)



where p is the density of water and g is gravity. The wave fluctuating velocities

(u" 2, 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"2 was determined from digitized free surface information.

The equivalent "radiation stress" due to turbulent fluctuations is given by:



S f= pu 2 pw 2) (2.15)



where mean square turbulent fluctuating velocities are integrated from the bed to the crest

of the wave.














CHAPTER 3
EXPERIMENTAL SETUP AND PROCEDURES

Experimental Summary

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 1/60' 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 1/1000't 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

TIF 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 Setup

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

determine 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.

Light Box


IT Cylindrical Lel


- Focused Light



o
o0
0 0

0 0


L Neutrally Buoyant Particles


Capacitance Wave Gauge

I------- ---




Beach





Piston Wave Maker -

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
0 0
0o o
o o I
o
o








Videotaping was done through the glass wall on the front of the tank. The camera

was normally positioned approximately 0.6-1.0 m 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 mm 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 DPIV 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 Processing

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 up-

crossings 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" (AOI). A two-dimensional auto-correlation was performed on the








image to yield a peak at the location of the center of the AOI. A two-dimensional cross-

correlation was then performed with the same AOI in the following frame. The resulting

shift of the peak intensity yields a net displacement of the particles for that AOI. 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 1/60* 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-upcrossing 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 AOI. 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 AOI. A cut off limit of 3 standard deviations was then applied to all

velocity data at each AOI, 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


a) AOI @ Time t = T


Actual Displacement Vector:

Measured Displacement Vector: <


Figure 3.2 Actual and measured displacements
seeding density.


b) AOI @ Time t = T + At


generated as a result of low particle


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 (7), 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 set-

up, 7.

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






-.- --- - -. -"
p .,t. ~ -


5-
5 : : : : : : : : : : : : : : : : : : .: : : : : : : . : :;
0 5 10 15 20 25 30 35



5



.5 -. : :. : : : :,


5 i I= % A . . . .
0 . . . . . . I .. I . . . I . . I .. . I L .. ..

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.


!5

20

5

0


E 2
o
2
.











E 2
N





E2


0
"2
4-'

0



N


.r '~" -1."
'














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 (rl), to radiation stresses, and non-

dimensional 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 (7) 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 -




S16 -

14
N
12 -

10 -

g _______I-----------------------------------
0.7 0.75 0.8 0.85 0.9 0.95
X Direction (cm)



Figure 4.1 Evolution of the free surface, digitized bed, ; (-), and still water level (---),
Test G2. Note that only every 5t instantaneous free surface is plotted corresponding to
every 5/60" or 1/12h of a second.



lack of faster filming apparatus and was designated by the standard video speed, 1/60t 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 (y-

direction), 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 w 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.









TESJ1 F4 TESTJ5- NF22






S . . . . . . . . . . . . . *

5a inX- Ar-di \ :a inX- Dredim
-(b) high aeration of the water..... .

Ensemble averaging te IVFs signific ly r d te a t of da to
5 . . .. . . . .. . ,, -, ..-. . . .. . . . .. . .. . .
. . . .. .. .. .. .. . . . . .

method discussed previously. As well, the filtering of ensemble averaged velocity fields
0 5 30 15 2D 25 23 40 0 5 tO 15 23 2V 3 3 *
Aa inX- Dreicn PO inX- region


(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).













TEST2-INF4






30 --------- ---- ------------- -- '---





. 1 . . .



... .:: :::::::. ::::::::: : .. .








0 5 10 15 M M 3 36
aI inX- Dredin



(a)






TestG IF41


5 10 15 20 25 3 35
AO inX-Direction


TestG2- F 32


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


. . . . .. . . . . . . . F i . ... .






...^,1.(,-- ---,---'/ n\\\







I .n

0 5 10 1 20 25 3 3
AC inX- Direction



(b)






Test G2- I 55


I / llll . . .
/i / I l l I iI I b




. .. i.. .... .





5 10 15 2O 15 3 3
A linX-Direction


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

1.37 sec.


. . .
-.... .. .- ., -... .
iiii iii Ii

., ,11 .. / . 1 t,'l l111
- -'--

IIrrr r










Ensemble Averaged Velocity Field at phase 32 of 76, Test g2


25. . 1 I .. I . i . . . .



. . ... .. ...



0 5 10 15 20 25 30 35




0 . . Z - - 1 s.- -- - Z Z -Z=
) 10 II-
o3, !i i i.. i i i i -
015 ,t&' N--. -...---
S- -0 7 --









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 I 1 1 I


25



E 20

C
o
, 15
I,..


10
n 10
N


5


01
I I ---- I ---- I ----- i ----- i ------ i ---- ----- -----
0 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 shorewardd)

to trough (seaward) horizontal velocities is 0.3.


Eulerian Mean Velocities Test j5


E 10


0 8


1 6


N


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.


. . . . . . -
-.. .-,-.. . . . . . .


------------------ ------------------


r--C


'--'? --- .------ .
. . . . . . .


~~~~5C1~










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
20

Crest Region shorewardd)
S10 0 0 00
0 0
7 0.75 00000 00 0 o
"E
0 0 0
0
,.
C
CO -10
I-
Net Transport
W -20


-30 + ++++_ "
c+ + + + + + -
Trough Region (seaward)
-40 III
0.7 0.75 0.8 0.85 0.9 0.95
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
0 0 0 0 0
0 0 o 0 VO 00 O 0V Q v o 0 0
Crest Region shorewardd)



2 *


t+ + + Net Transport
++
6 T

Trough Region (seaward) + .


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, Ho = 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.


a,

E

0
C -

(-
I-


E
0
o
>


8


-101 ' ' ' '


~ Yc~2~ +








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 J3 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
D1 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 (0.0-

7.0 cm/sec) and is of course smallest at the bed where boundary effects dominate the

vertical velocities.















X= 0.74
20






10







0 10 20 30
cm/s

X= 0.84
20



15
lg


10. "



U"rms *



0 10 20 30
cm/s


X= 0.78







+



+ U"rms *



10 20 30
cm/s

X= 0.87


X= 0.81









*


U"rms



) 10 20 30
cm/s

X= 0.9


Szu







+ +l


SU"rms I* U"rms



10 20 30 0 10 20 30
cm/s cm/s


X = 0.74
20


15


10 +


5 +
+ W"rms *

0 10 20 30
cm/s
X 0.84
20









0 W"rms *

0 -
0 10 20 30
cm/s


X =0.78






0 .


S W"rms *


0 10 20 30
cm/s
X 0.87







5 *

W "rms *


0 10 20 30
cm/s


X 0.81
20





10 4

**

SW"rms *


0 10 20 30
cm/s
X= 0.9
20





10


5 +
5 W "rm s *


0 10 20 30
cm/s
Wrnis


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 (hb). 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/ho 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 h = 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 ho/hb 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 non-

dimensional 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 non-

dimensional 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 G1-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 D1 and D2 can be found in

Appendices B and C.












BcUionof Tubtert KIeicB c -TestJ2


4* a 78
0 o Q79
- + G+ Q
Q81
0 0 OM
a 0 Q83


0
0+ 0


o




GO5 a 15 02 OZ 03 G 04 045 05
NmO.rrenia Tubaeft NKeicBa Ee
~naneQiTraorl Turtiert ~nEi~icBEis


BEoloncofTubi ertKnelic r-Test J3


+ O
o o 5
+ + Q61
S* a2 ,

o 0 Q67 0
SD as7 o o*0


00 "X
04oO
040


0


005 1 0 15 02 O 03 035 04
NaeOners i TubJert Krebc Biaw


BdEcn dTutlert NreticB tBy-Test J4


hoIdb


0


NMnDmrsiac TuhJert reic Enwe


Bdilicno dTulertM nreicB W-TestJ5


S + 027
0 o 029
+ + 32
S 0a34
0 0 37
0 0Q4


+ O


t 0

0 0 04
0 0 o0 +
O 0 +
00
0a 0
00
am ~ ~ 01 00 02 O 3 t0
4o


Q05 01 015 02 025 03 035 04
NrODnwsieadel Tutert Ireic BraW



(d)


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


H =


2.67, T = 1.35, hob = 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 J3; (c) Test J4; (d) Test J5.










BdLlicnfTubtlert Ietic r ry-Test G1 EBdion ofTublert KNric Eeray-Test G
3 3


25 Ihhbt 25 h)/tl b
S* Qa94 + + 074
o o 097 o 77
+ + 1 2 + + 08 +

0 0 1.5 0 o o 1 o 0
a a 1.08 0 + 5 a 89 .0
+ 0 + 0o +
0 + 0 +


5. 0 0


Qo6 01 02 .s 03 0. 04 04 .5 05 01 015 02 025 03 35 04 04 05
NMDanersiad Tutert KMreicB Ery N.OrrensiatrTubJet KMricEBay


(a) (b)

1
k2
Figure 4.11 Evolution of Non-Dimension Turbulent Kinetic Energy ( ). Ho =

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








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'^ is essentially zero and builds

from zero to approximately 1.5 through X = 0.45. At this point, Sj 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 J3). S"x is highly dependent on the average

free surface fluctuations (17") 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"x 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


++ ++ +

S+
+ + +
+ +++ + + +


Test J3


+




4++ +
+~ ++++ +

++

+ +


Test J2



-++
++


+ 4-
t+

+ -4-


r+ +
.8 ---------------------------
1


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


0.75 0.8 0.85 I


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


separate tests


Test J4


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


Test J2


+*I



+s


*


rL I I I j I


*+*+

**
4*

rt*


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


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


2.5 -


0.5 -


Test J3














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 TIF 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)
D1 76 19 16.0
D2 75 22 17.4
G1 76 22 17.7
G2 76 28 16.2
J1 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 Dl
























Wave Evolution in Time Test D1
An-


E 20
o

0
15
a,

10
, 10
N


5



0


0.72 0.74 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).


~-------





1 I I I I I













Eulerian Mean Velocities Test dl
in .


25




E 20


t-s

0 15


S10
N


0 . 10 15 20 25.3


0 5 10 15 20 25 30 35 40
X Direction (cm)




Figure B2 Eulerian Mean Velocity Field. Test Dl.


Volumetric Transport Rate Test dl


0 10
) 0


0
o o




C
L. -20
I-
o
0
b -30

E
-40



-50


X Direction (X/Xb)


Figure B3 Two Dimensional volumetric transport. Test D1


. . . . . . . . . .


I V / I / 0 0 1 1 0 1
/ i/ I V t / I V/ i l i t .
l\ ^ \S \ \\ \ ^\


- - S '- S '- - -


= 0 cmIs


>.* ~ ~ - ------.-.>--------*


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


: : : : : :


Iiirl


111111


: :


i i












Turbulence Induced Radiation Stress Test D1



3 + + + +
+ +

+ + + +
2 ++ +
+

+ ++ +
1 + +
+ + + +

S++

U) + +

-1
+
+
-2


-3


-4 IIII I I
0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86
X Direction (cm)




Figure B4 Turbulence Induced Radiation Stress, (N/m). Test D1.





Wave Induced Radiation Stress Test D1
7.5 -,







.5 + *



6 ++ *+
'X
X -$






441
++
4.5 *+



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/m). Test D1.














X= 0.74
20


15
+

10


5 +
5 U"rms *

0
0 10 20 30
cm/s

X= 0.8
20


15


10


5 1
5 U"rms *

0
0 10 20 30
cm/s


X= 0.76


cm/s

X = 0.81
20,,

1 *
15


10



5 U"rms *

0
0 10 20 30
cm/s


X = 0.78
20-


10


5 *

















5 *
U"rms
0 -
0 10 20 30
cm/s

X= 0.83
20

*
15





5 f U"rms *



0 10 20 30
cm/s


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


X= 0.74





o **




W"rms *


0 10 20 30
cm/s

X= 0.8





+*




i W"rms



0 10 20 30
cm/s


X= 0.76










S W"rms *


0 10 20 30
cm/s


0 10 20 30
cm/s


X= 0.78


5r *










0 10 20 30
cmls

X = 0.83
*










W"rms *


0 10 20 30
cm/s


Figure B7 Vertical Profiles of W",. Test Dl.







61



Evolution of Turbulent Kinetic Energy Test D1
3-


m

O
25 ho / hob

0
0 + + 0.74 0
< o 0.76 0
2 +0
M + + 0.77 0 x +
2) x x 0.79 x +
0 0 0.81 x C
15- O 0.83 + o o. o

o +aox 0
C[ O" 0
c- D oaO

E q_
0 Q
1c 0.5
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.
X Direction (X / Xb)


Figure Cl 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 1/12t sec).


E
o


O
15
0

L.

0

N

5


98 1 1.02


I "'I


v








63




Eulerian Mean Velocities Test d2
30.


E 20
O
Co

0
G15-




10
N


0 5 10 15 20 25
X Direction (cm)


30 35


Figure C2 Eulerian Mean Velocity Field. Test D2.






Volumetric Transport Rate Test d2
20 .


101


-40 -


-50 -


-60 -


0.9 0.92 0.94 0.96
X Direction (X/Xb)


Figure C3 Two Dimensional Volumetric Transport. Test D2.


S. Vt V V .. J
. t . . .
. . -. . . .


i I I-------------------------------------
--------------------------------------

--------------------------------------,


40


Crest Region shorewardd)
0O 0_0-
OO 0


Net Transport


Trough Region (s ar
e+ + ++

Trough Region (seaward)


~~~~~~~~~-----+----H~~-CC~~~-~-CCCH~-C~


I


-10


-20







64




Turbulence Induced Radiation Stress Test D2


0.94 0.96
X Direction (X / Xb)


Figure C4 Turbulence Induced Radiation Stress, (N/m). Test D2.





Wave Induced Radiation Stress Test D2
a _______________-. ----.- -- .-- ----- i 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.


8


6


4


2

x
x

-2


-4


-6


-8


*+


* *+ *
*

**
*






++*


3.5

3L
0.8


8














X= 0.9
201, --- --- --- -


15


10 *


5 U"rms *


0
0 10 20 30
cm/s

X= 0.95
20

**
15 ++


10



5 U"rms *

0
0 10 20 30
cm/s


X= 0.92
20,


15

S
2 10


5 Urms


0
0 10 20 30
cm/s

X= 0.97
20 --- -, --,-
20

**

E *
+* +
2 10 +



5 U"rms *

o
0 10 20 30
cm/s


X = 0.93
20


15 1;
*o



*
15








0
5 W U"rms *



0 10 20 30
cm/s

X= 0.99
20
.*

15 +.


10 +



5 t U"rms *

0
0 10 20 30
cm/s


Figure C6 Vertical Profiles of U",. Test D2.


X= 0.9










W"rms "


0 10 20 30
cm/s

X= 0.95
*










W"rms *


0 10 20 30
cm/s


X = 0.92









W"r*s **








#i W"rms *



10 20 30
cm/s
X= 0.97















cm*s


X= 0.93










SW"rms *

*
0 10 20 30
cm/s

X = 0.99










' W"rms *


0 10 20 30
cm/s


Figure C7 Vertical Profiles of W",. Test D2.







66



Evolution of Turbulent Kinetic Energy Test D2
3-

n0

2.5 ho / hob

0
+ + 0.9
< o o 0.91 +
2 + + 0.93 +
o x 0.95 + x
0 o 0.96 O+
S1.5 0 0.98 r ++0
c 0 o+
O- In i +0 O
-o



C 0.5 x
E o



0 1 I I
z


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



Figure C8 Non Dimensional Turbulent Kinetic Energy. Test D2.


0.45 0.5

















APPENDIX D
PLOTS OF MEASURED QUANTITIES FOR TEST G1


















Wave Evolution in Time Test G1


22 -


1.05 1.1
X Direction (X /Xb)


Figure D1 Evolution of free surface, digitized, mean, and still water level. Test Gl.
Note that the free surfaces are at intervals of 5 frames (5/60"' or 1/12th sec).


20

18 -
E
o
16
C
t14
0


Q 12

N 10


6-
F


0.95








68




Eulerian Mean Velocities Test gl
30 1 I




25

25 .. ....... ................. .......... . ...





15------------------------------------------------------------------------


10







05 -5 = 1015202



C I I
- -ii^ ^ ^ - i--- -- -- ----- --- -
0 -. - - - I - - I - -- - - - - - -
L-
---------------------------------~----



5 -* = o / ------- ------ [ .. J J
. . .

5 . 10' dh/i~/

t


0 5 10 15 20 25
X Direction (cm)




Figure D2 Eulerian Mean Velocity Field. Test Gl.


U)
-


0
0.
cn
t.
C
I-




r-
CO)
-4-.
0)
EC
Z3


30 35 40


Volumetric Transport Rate Test g1
20 1 1


Crest Region shorewardd)


10-
0 0


0



++
10 Net Transport




20 -++



.30 -. + + + +++
Trough Region (seaward)


.dn I I


0.95


1 1.05
X Direction (X/Xb)


Figure D3 Two Dimensional Volumetric Transport. Test Gl.







69



Turbulence Induced Radiation Stress Test gl


1.05 1.1
X Direction (cm)


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


Wave Induced Radiation Stress Test gl
ft ,


4.5 -


3.5 -


1.05 1.1
X Direction (cm)


1.15


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


***

*
4**r ++*,
*
* *
*++
+

++4


1.25














X= 0.94
20


15









10 10 20 30
Ie + *
o *








20 ---- ---- ---- -



C +





0 W"rms
o









0 10 20 30
cm/s
cm/s


X = 0.98


0 10 20 30
cm/s

X = 1.06
20


15
S *+

. 10 +



W"rms


0
0 10 20 30
cm/s


X= 1











W"rms *


10 20 30
cm/s

X = 1.08


SW"rms *



0 10 20 30
cm/s


Figure D6 Vertical profiles of U" Test Gl.


X= 0.94
20


15


10



5 W"rms *


0 10 20 30
cm/s

X= 1.03
20


15


10
1" **


5 W"rms *


0
0 10 20 30
cm/s


X= 0.98
20


15



S *

0 5 W"rms


0
0 10 20 30
cm/s

X= 1.06
20


15


I10


5 W"rms *



0 10 20 30
cm/s


X= 1
20


15


S +
0







20 *
N 5
5 W"rms *



0 10 20 30
cm/s

X= 1.08
20






.210 *

* *
SW"rms


0
0 10 20 30
cm/s


Figure D7 Vertical Profiles of W",. Test G1.







71



Evolution of Turbulent Kinetic Energy Test G 1
3-

-0
(D
m
2.5 ho I hob

0 + + 0.94
-0
S o o 0.97
2 + + 1
Sx x 1.03 +
S) o 1.05 o +
I 0 0 1.08 0 +
- 5 o o 1.08 +o +
1.5
C 0 +x0 0 +
o x *++ oo

0)
E -0. -

C 0.5 -
Z r TS- A


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 G1.


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 (5/60g" or 1/12h sec).


E
)18

0

4)

S14
N



















25 -


Eulerian Mean Velocities Test g2







. . . . . . . . . . . . . . . . . . .. .
. . . . . . . . I . . . . . .







- - --c-s . : :-- - 2
~~~~~-------=~' ~~-~-------
- ---------------------
-------------------------------a
-------------------------



--------------- ---------


5 10 15 20 25
X Direction (cm)


30 35


Figure E2 Eulerian Mean Velocity Field. Test G2.






Volumetric Transport Rate Test g2
in .


10


o


0
"E o
0
,Q.
-0


C(
L -10


-20
0





Q -30

CI


0.75


0.8 0.85
X Direction (X/Xb)


Figure E3 Two Dimensional Volumetric Transport. Test G2.


15




10


Crest Region shorewardd)
O 0 < > 0 o -000 0
^ 0000 O


00




t


Net Transport









Trough Region (seaward) +


U III ---,












Turbulence Induced Radiation Stress Test G2

+


4 + +
+


3 -+
3+ + + ++ + + ++

+ +++ + +
+ +
++ +


++
S+ ++


0 + +



-1

+
-2 I I I I
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 i 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 4-
x


3.5


3


2.5


2
0.7














X= 0.74
20


i
10
15





N 5UU"rms *


0
0 10 20 30
cm/s

X = 0.84
20


15

S *+
o10


5 ++
+ U"rms *

0 .
0 10 20 30
cm/s


X = 0.78





4/.




S U"rms *




cm/s

X= 0.87






*



U"rms


0 10 20 30
cm/s


20


15


. 10


5


0


X 0.81











S U"rms *



) 10 20 30
cm/s

X= 0.9


S U"rms *



0 10 20 30
cm/s


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


X 0.74
20


15


10 4



5 W"rms *


0 10 20 30
cm/s

X = 0.84


0 10 20 30
cm/s


X= 0.78
20




10





W.rms *


0 10 20 30
cm/s

X= 0.87
20


15

10



5 W"rms


0 -
0 10 20 30
cm/s


X= 0.81
20


15,


10 *



5 W"rms *

0
0 10 20 30
cm/s

X= 0.9
20






10 "*
*


5 W"rms *


0 10 20 30
cm/s


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












Evolution of Turbulent Kinetic Energy Test G2




ho I hob


-P


x 0
O x + O1
+0 x O4
+0


x
00


xx


no +


oCHo
'%
w0+


0.45 0.5


Figure E8 Non Dimensional Turbulent Kinetic Energy. Test G2.


2.5 -


1.51-


0.5 -


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


I 1 I ....


= I II I















APPENDIX F
PLOTS OF MEASURED QUANTITIES FOR TEST J2















Wave Evolution in Time Test J2


1.79 0.8 0.81 0.82
X Direction (X / Xb)


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

















16


14


E 12


.4--
O 10
C-

0
8


6
N

4


2


78




Eulerian Mean Velocities Test j2





. . . . . . . . . . . . f . . . . . .


4ll4I 4 4 I I 4 4lI ll lI I

. . . .. . . .'. .. / '.Il .I











S= 10 cm/.


0 5 10 15 20
X Direction (cm)




Figure F2 Eulerian Mean Velocity Field. Test J2.





Volumetric Transport Rate Test j2
C ______-------


0 0

0
C.o
v -5

o


0-
V) -10

R-
I-
0 -15


E
| -20
0

Q -25
IN


-30 L
0.7


7


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.


Crest Region shorewardd? ""jv~C V


+ Net Transport


I-


I I I I I I













Turbulence Induced Radiation Stress Test J2
2.5 I I

+ +
2


1.5 + +
++ +
+ +
1 + ++ ++ +


0.5+ + + + +


0- + + +
0-
+ + + +
+ ++ ++
-0.5 -+
+

-1


-1.5 -


-2
-2. iii


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


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





Wave Induced Radiation Stress Test J2


X Direction (X/Xb)


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


-2.t L


0.83 0.84 0.85


2.6


X 2.4
U)


0.85














X= 0.78
20


15


S10



5 t U"rms *


0
0 10 15 20
cm/s

X = 0.82
20


I15
E
0
10


r 5 *$1J"rms


0 4,
0 5 10 15 20
cm/s


20 20


S15 i 15
o : 1o) :

0 10 10
lO 0



N5 (5 5
+ U"rms "rms *

0 10 2
0 5 10 15 20 0 5 10 15 20
cm/s cm/s

X = 0.83 X= 0.84
20, 20


S15


2 10

oE
5


0
5 "rms *



0 5 10 15 20
cm/s


E

10
15
io -

0 5 U"rms *


0 5 10 15 20
cm/s


Figure F6 Vertical profiles of U' Test J2.


X = 0.78
20


15


. 10 *
10



W"rms *


5 10 15 20
cm/s

X = 0.82
20




S~ +

S10 1
* +

SW"rms *


0
0 5 10 15 20
cm/s


X= 0.8











W"rms *


5 10 15 20
cm/s

X = 0.83


X = 0.81










W"rms *



5 10 15 20
cm/s

X = 0.84


,u 1.


S15 15

C
2 10 o 10


N 5 W W"rms W"rms*


0 0
0 5 10 15 20 0 5 10 15 20
cm/s cm/s


Figure F7 Vertical Profiles of W",. Test J2.


X= 0.8


X = 0.81







81



Evolution of Turbulent Kinetic Energy Test J2


ho I hob

+ + 0.78
o o 0.79
+ + 0.8
x x 0.81
0 0 0.82
S El 0.83







O (o
4$0

Wo-
fo

4 3,


0
+ 0+-
0o+ +. 0 13
o+o 4 13
OS tp;~


Figure F8 Non Dimensional Turbulent Kinetic Energy. Test J2.


2.5k


1.5


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


0.45 0.5


u s : 1 gr si



















APPENDIX G
PLOTS OF MEASURED QUANTITIES FOR TEST J3





















Wave Evolution in Time Test J3
16I I I I II


14-


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


0.7 0.72


Figure Gl Evolution of free surface, digitized, mean, and still water level. Test J3. Note
that the free surfaces are at intervals of 5 frames (5/60t1 or 1/12th sec).


E 12
O


10

' a

8
N


6


0.74


4 1 i


I


------------_
I '











Eulerian Mean Velocities Testj3
18 1




14
S. . . . .. .-- |. . ... . ..-- . . .--- . . .



E 12 -

C--

S- -- - - - -





2 -





0 5 10 15 20 25
X Direction (cm)




Figure G2 Eulerian Mean Velocity Field. Test J3.





Volumetric Transport Rate Test j3

0 5- 0 15 o 2

0 -X Crest Region shorewardd)

o
t- -5


~C Net Transport
I- -10 -


b + + + ++ +
) -s+


SC Trough Region (seward))
> + Tl
9-20- +
-25





0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74
X Direction (X/Xb)



Figure G3 Two Dimensional volumetric transport. Test J3.








84




Turbulence Induced Radiation Stress Test J3
3
+



2.5





2
+
++ + +

+ + +
+ +
5++ + +
1.5
S + + + +
++ + + +
+ + + + + + +
+ + +

10 +




0.5I +r" I I __- I I---I-I


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


0.7 0.72


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





Wave Induced Radiation Stress Test J3
A -,


2.4


2.2


1.6


1.4


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.


*
*
*
*
*





*
*

*




**


*++*

**
i4 =i .














X = 0.59


N' *4 *

N 5 U"rms


0.
0 10 15 20 25
cm/s

X = 0.63
20


15


. 10



N 5 U"rms*


0
0 5 10 15 20 25
cm/s


X= 0.6
20


15
U

1


N 5 U"rms *


0
0 5 10 15 20 ;
cm/s

X= 0.65
20,


20


15




S1 5
S

o|





0
5 I



S 20


X = 0.61











SU"rms *


5 10 15 20 2
cm/s

X = 0.68


5 U"rms I 5 U"rms


0 0 *
0 5 10 15 20 25 0 5 10 15 20 25
cm/s cm/s


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


X = 0.59










W"rms *


5 10 15 20 25
cmls

X = 0.63


1

S
0


X= 0.6



15






5 t W"rms '



0 5 10 15 20 2
cm/s
X = 0.65


X = 0.61
20


15

0

. *

1 5 f W"rms *



5 0 5 10 15 20 25
cm/s

X= 0.68


20 20 20


15 15 15








o 0 0
10 2 1 0 10


5 W"rms 5 Wrms *5 Wrms


0 -0 J -- 0
0 5 10 15 20 25 5 10 15 20 25 0 5 10 15 20 25
cm/s cm/s cm/s





Figure G7 Vertical Profiles of W",. Test J3.











Evolution of Turbulent Kinetic Energy Test J3
3-

()
CD
S2.5 ho / hob

0
.* + + 0.58
< o o 0.59
2 + + 0.61
) x x 0.62 o + +
00 o o 0.65 EO 0 *
1.5- 0 0.67 -'X o 0+
o +
0o 0 *0 c


E 0o-

S0.5- o0
z 00


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 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


0.4 0.42 0.44 0.46 0.48 0.5
X Direction (X / Xb)


0.52 0.54 0.56


Figure H1 Evolution of free surface, digitized, mean, and still water level. Test J4. Note
that the free surfaces are at intervals of 5 frames (5/60t or 1/12th sec).









87


E


0





N


16



14



12



10



8



6



A_


-











Eulerian Mean Velocities Testj4
1i


16


14


E 12
0
C-
10

Q)

, 6
N

4


2


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.


,, - , - --- -- - - - - -
-----------





, i0 .....







89



Turbulence Induced Radiation Stress Test J4


2.5-


1.5 -


+ +



+ +
++ + +
S+ + +
+ + ++
+ + ++ + +

+ + ++ +


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 .


*++

4
4 ,+ *

**

++

+ *


+ *


U.t ---
0.4 0.5
X Direction (X/Xb)




Figure H5 Wave Induced Radiation Stress, (N/m). Test J4.




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Last updated October 10, 2010 - - mvs