Front Cover
 Title Page
 Table of Contents
 Symbols and abbreviations
 Literature review
 Experimental apparatus, procedures...
 Transition regional model
 Appendix A. Plots of time mean...
 Appendix B. Image digitizing, filtering...
 Appendix C. Image processing M...
 Appendix D. Wave data statistic...
 Biographical sketch

Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 94/019
Title: Development of a digital particle image velocimetry system with an application to a numerical model of the breaking wave transition region
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00085009/00001
 Material Information
Title: Development of a digital particle image velocimetry system with an application to a numerical model of the breaking wave transition region
Series Title: UFLCOEL-94019
Physical Description: xiii, 115 leaves : ill. ; 29 cm.
Language: English
Creator: Craig, Kenneth R
University of Florida -- Coastal and Oceanographic Engineering Dept
Publication Date: 1994
Subject: Coastal and Oceanographic Engineering thesis, M.E   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (M.E.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 112-114).
Statement of Responsibility: by Kenneth R. Craig.
General Note: Typescript.
General Note: Vita.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00085009
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 32794833

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vi
        Page vii
        Page viii
        Page ix
    Symbols and abbreviations
        Page x
        Page xi
        Page xii
        Page xiii
        Page 1
        Page 2
        Page 3
        Page 4
    Literature review
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Experimental apparatus, procedures and data analysis techniques
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
    Transition regional model
        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
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
    Appendix A. Plots of time mean mass flux...
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
    Appendix B. Image digitizing, filtering and file compression...
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
    Appendix C. Image processing M files...
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
    Appendix D. Wave data statistic analysis
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
    Biographical sketch
        Page 115
Full Text




Kenneth R. Craig









I wish to express my sincere gratitude to my advisor and friend, Dr. Robert J.

Thieke. Despite his back breaking schedule, he consistently found time to answer each of

my questions, no matter how inane. Dr. Thieke's immense knowledge was a fully tapped

resource from which many of the ideas presented in this paper originated. Dr. Thieke's

wife, Adrienne, and his son, James, also have my thanks for their saint-like patience.

The other members of my committee, Dr. Robert G. Dean and Dr. Daniel M.

Hanes, provided both inspiration and technical assistance. Dr. Dean is without a doubt the

"Dean" of coastal engineering and I consider myself extremely fortunate to have had the

opportunity to interact with him. Dr. Hanes, in addition to being a solid left fielder,

allowed me to infiltrate his group and temporarily use an extensive amount of equipment.

My officemates, Eric Thosteson, Mark Gosselin and Tom Copps, aided me in

keeping my sanity. I would also like to thank Chris Jette for giving me a defense date to

shoot for. Paul Miselis and Al Browder accompanied me to Market Street on more than

one occasion to visit with Sam Adams.

The staff at the Coastal and Oceanographic Engineering Laboratory, especially Jim

Joiner, provided me the opportunity to get involved in the department during my

undergraduate years. The memories I have of the lab will remain with me forever.

My family, Ken Sr., Pam, Doug and Sandy, always was and is the bedrock of my

life. I could not have come close to achieving as much as I have and would not have such

an optimistic outlook to the future without them.

Finally, my bride Kimberly has been a rock. She has planned both a wedding and a

honeymoon while her groom was tucked away in Weil Hall, offering little help. For her

patience and love I am eternally grateful.


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

LIST O F TABLES .................................................................................. vi

LIST OF FIGURES ...............................................................................vii

LIST OF SYM BOLS ............................................................................ x

A B STR A C T ................................................ ........................................ xii


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

2 LITERATURE REVIEW ................................. ........ 5

Introduction ................................................................... 5
Evolution of Velocity Field Measuring Techniques ............. 5
Laser Speckle Velocimetry .......................................... 5
Particle Im age Velocim etry ................................................. 6
Digital Particle Image Velocimetry ................................... 7
Theory Development ......................................... ................ 8
Comparison of DPIV with Other Methods ........................ 14
Recent Applications of PIV and DPIV .............................. 15
Transition Region Modeling .......................................... 16

ANALYSIS TECHNIQUES ......................................... 21

Overview of Experiment ................................................... 21
Experimental Setup ..................................................... 22
Multifunctional Wave Flume ................................. 22
Data Analysis Equipment ..................................... 27
Experimental Procedures .................................................. 27

D ata Processing ............................................................. 29
W ave Gauge Data ................................................. 29
Image Digitization .................................. .... 30
Im age Filtering ................................................... 31
Velocity Field Processing ...................................... 32
Ensemble and Time Averaging ............................. 33

4 TRANSITION REGION MODEL .................................... 35

Linear Momentum Conservation Equation ........................ 36
Angular Momentum Conservation Equation .................... 41

5 RE SULTS .................................................. .................... 45

W ave D ata ....................................................................... 45
V elocity Field Results ...................................................... 47
Turbulence Parameterization .......................................... 52
Hansen and Svendsen Experimental Wave Data ................ 56
M odel Performance .......................................................... 60
Recomm endations ............................................................ 69
C conclusions ..................................................................... 72



COMPRESSION PROGRAMS ...................................... 78


FOR M ATLAB .................................................................. 106

R E FER EN CE S .......................................................................................... 112

BIOGRAPHICAL SKETCH ................................................................. 115


Table page

5.1 Experimental wave conditions ....................................... 47

5.2 Frames/cycle data for experiments .................... ............. 48

5.3 Comparison of mass flux components from Figure 5.6 ....... 55

5.4 Turbulence parameters determined from DPIV ................. 58

5.5 Hansen and Svendsen's wave data ..................................... 59

5.6 Model results for transition point wave height, 4 ............... 65

5.7 Model results for transition point water depth, h ................. 67

A. 1 Horizontal scaling from pixels to centimeters found by
analyzing the video taped grid .......................................... 73


Figure page

1.1 Definition sketch of the transition region .......................... 3

2.1 Graphical representation of pixel intensities within an area
of interest on a) image 1 and b) image 2 and c) the inverse
transformed correlation peak in the spatial domain. The
maximum peak in c) indicates a displacement of
approximately 4 pixels in the +y direction. ....................... 12

2.2 Partitioning of mass flux across the water depth at both the
break point and transition point. Technique used by Thieke
(1992) and employed in the models described in chapter 4. 20

3.1 Diagram of the multifunctional wave tank with enlargements
of the piston wavemaker and capacitance wave gauge. ........ 23

3.2 Experimental apparatus including video equipment location
and movable chassis arrangement. (Cross sectional view of
long axis of tank) ........................................................... 25

5.1 a) Mean water level and b) wave height distributions for test
6 found from analysis of capacitance wave gauge data. ....... 46

5.2 Comparison of a) an unfiltered digitized image and b) a
filtered digitized image from test 2. Gray scales have been
inverted for clarity. Note the removal of the aerated jet in
the filtered im age. .............................................................. 49

5.3 Example of an instantaneous velocity field found using the
DPIV process. (From test 6C, field number 536) ............... 50

5.4 A typical ensemble time averaged velocity field with a) all
non-flow data included and b) only flow related data
included. ........................................................................... 51


5.5 Comparison of ensemble, time-averaged velocity fields
using a) 30 cycles, b) 50 cycles, with c) the difference
between a and b. (Data from test 4C) ............................... 54

5.6 Enlargement of columns 15 through 20 of Figure 5.5b
indicating conservation of mass. .................... .............. 55

5.7 Typical turbulent velocity fluctuation field (data from test
4C). Note that the turbulence values are squared resulting
in all values oriented in the positive direction. ................. 56

5.8 Profiles of dimensionless u'r.,, with depth at the transition
point for four different test cases. Measurements obtained
with Digital Particle Image Velocimetry (DPIV).
Breaking wave height to water depth ratio and wave period
are noted. .......................................................................... 57

5.9 Empirical curve fit for dimensionless u'r., at the transition
point as a function of the surf similarity parameter.
(m=beach slope) ............................................................ 58

5.10 Comparison of predicted and measured a) wave height and
b) water depth at the transition point for various values of
the mass flux increase factor Q and turbulence model 1.
Measured data from Hansen and Svendsen (1979). ............. 61

5.11 Comparison of predicted and measured a) wave height and
b) water depth at the transition point for various values of
the mass flux increase factor Q and turbulence model 2.
Measured data from Hansen and Svendsen (1979). ............. 62

5.12 Comparison of predicted and measured a) wave height and
b) water depth at the transition point for various values of
the mass flux increase factor Q and turbulence model 3.
Measured data from Hansen and Svendsen (1979). ............. 63

5.13 Comparison of predicted and measured a) wave height and
b) water depth at the transition point for mass flux factor
Q=2.5 and the three turbulence models. ............................ 64

A. 1 Wave data from test IB. a) mass flux velocity and
b) turbulent velocity field ................................... ....... 74




A.2 Wave data from test 2C. a) mass flux velocity and
b) turbulent velocity field ................................................. 74

A.3 Wave data from test 3C. a) mass flux velocity and
b) turbulent velocity field ................................................. 74

A.4 Wave data from test 6A. a) mass flux velocity and
b) turbulent velocity field .................................................. 74


a, P



g, fg



b, t











component directions

mean water elevation

density of fluid

angular frequency

cross correlation

complex conjugate or spatial convolution

area of interest

indices indicating break point and transition point

charge coupled device

digital particle velocimetry

fast Fourier transform

gravitational acceleration

water depth

wave height

wave number

laser speckle velocimetry


ratio of wave group speed to wave celerity

PIV particle image velocimetry

PTV particle tracking velocimetry

S,, s, momentum flux

t time

i7 mean velocity

u" wave induced velocity

u' turbulent fluctuating velocity

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 Engineering




August 1994

Chairman: Dr. Robert J. Thieke
Major Department: Coastal and Oceanographic Engineering

Modem techniques for determining velocities in fluid flows have proven incapable

of adapting to the highly aerated flows present during wave breaking. Two widely used

techniques, Particle Image Velocimetry (PIV) and Laser Speckle Velocimetry (LSV), can

provide excellent spatial and temporal resolution in near breaking waves but have

difficulty resolving velocities when air bubbles are present after breaking. These methods

apply optical Fourier transformations to multiple exposed filmed images of the flow in

order to produce the phenomena known as "Young's fringes" which are proportional to

the displacement of the section of the image investigated. The availability of high

powered and low priced personal computers has facilitated the evolution of a digital

application of these transformations. A low cost Digital Particle Image Velocimetry

(DPIV) system has been developed and has been applied to the case of wave breaking.

The digital images used in DPIV (as opposed to filmed images used in PIV and LSV)

allow the aeration to be filtered out before processing of velocity fields is performed.

Video is currently the limiting factor in both the spatial and temporal resolution of

the resulting velocity fields but this is expected to improve as video technology improves.

A large time series of video taped images has been analyzed. The ensemble and time

averaged quantities of mean velocity and turbulent fluctuating velocity have been found

over the entire water column for shoaling and breaking waves. These data were used to

parameterize a numerical model of the wave breaking transition region. This is the area

bounded by the break point and the transition point in which waves undergo a rapid

transformation of wave height but the mean water level remains relatively constant. The

model conserves both linear and angular momentum by applying parameterizations for

mass flux, turbulent momentum flux and the wave induced radiation stress. Turbulent

velocity contributions were found to be substantial above mean water level. A linear

curve fit was performed that correlates the turbulent velocity with a surf similarity

parameter defining the break point conditions.

The model results indicate that transition point water depth (i.e., transition region

length) can be determined with a high degree of accuracy but it is very sensitive to the

details of the turbulence modeling. The transition point wave heights from the model

provide an effective upper boundary when compared to experimental data, with the results

being rather insensitive to the level of turbulence modeling.


Many of the mysteries of wave evolution have been explained by coastal engineers

over the past thirty years. Linear theory can accurately describe the behavior of offshore

waves, many shoaling models give good approximations of behavior as waves approach

shore and surf zone waves have been shown to be largely self similar and conducive to

modeling as moving bores. However, a noticeable deficiency in modeling capability

appears at the transition region, defined as the area from the onset of wave breaking (i.e.,

rapid wave height decay) to the point after which the mean water level begins to rise and

wave height decays less rapidly (inner surf zone). The purpose of this research is to

advance efforts to redress this deficiency.

Models are inherently based upon certain physical assumptions, therefore modeling

requires both a solid physical understanding and a strong foundation of experimental

support. Unfortunately, there exists a general lack of understanding of the physics of the

transition region. A method that better describes the processes occurring within this

region is required. Moreover, most present velocity measuring techniques are not capable

of accurately determining velocities in the aerated crest of a breaking wave. The aeration

in the crest precludes laser and hot-film anenometry, and hinders typical particle tracking

methods. It was thought that a method employing video analysis with its inherent filtering


capabilities might lead to success. This led to the development of a low cost digital

particle image velocimetry system that could be applied in this environment.

As a result, this research advanced on two parallel fronts. A velocity measurement

system employing video imaging of neutrally buoyant particles was developed which has

the flexibility to be adapted to other experimental situations. Also, a numerical model of

the breaking wave transition region was developed with the assumption that experimental

results of the above system would have certain empirical applications.

Digital Particle Image Velocimetry (DPIV), the analysis technique used to

determine velocity fields, uses standard super VHS video technology. Small, neutrally

buoyant particles are placed in a flow and videotaped. The tape is digitized frame by

frame to a 256 gray scale format. After applying a simple filtering process, the pixel

intensities of successive frames are compared via a frequency domain analysis technique,

yielding a field of displacement vectors describing the flow that occurred between the two

frames. The process will be discussed in detail in Chapter 2. The displacements can then

be converted to velocities by dividing by the known time between frames.

Implementation of this system required the development of equipment during each

stage of data gathering and processing. Budgeting constraints led to cost control

measures that were fairly effective. The equipment for the entire system cost under

$10,000. When possible, each piece of apparatus was constructed in-house. An injection

device was designed to evenly distribute the neutral particles over the field of view. A

shield to exclude ambient light combined with a light source capable of being focused into

a plane were constructed to enable appropriate lighting levels during taping. The

experimental setup is discussed in further detail in Chapter 3.

The video was then digitized by an automated computer program. Each pair of

frames was digitally analyzed through a series of programs that result in horizontal and

vertical displacement fields over the field of view. Ensemble averaging of these velocity

fields produced values for several derived quantities that have been applied to a model of

the transition region.

The transition region is defined as the location immediately after wave breaking

where setup is constant and wave height rapidly decays. The zone ends when setup begins

to increase and wave height decreases more slowly. Figure 1 shows a schematic of the

transition region.

Figure 1.1 Definition sketch of the transition region

Definition Sketch of Transition Zone

(Not to scale)


The model proposed by Thieke (1992), in which this region was modeled as a

shock, has been given "added dimension" by conserving both linear momentum and

moment of momentum. These equations may then be solved simultaneously. As a result,

both the final wave height and the transition region length can be determined.

Contributions of radiation stress, mass flux and turbulence production in the conservation

equations are also examined. The model is discussed in detail in Chapter 4.

Chapter 5 presents the results of both the data processing and the model. The data

processing has yielded mass flux and turbulence values that were obtained by ensemble

averaging. Model results will investigate the effect of these quantities upon predicted

transition point wave height and water depth. Several conclusions will be drawn and

recommendations for further study will be presented.



As indicated previously, the discussion of the literature will proceed on two fronts.

First, the evolution of velocity field measurement techniques that have led to the

development of digital particle image velocimetry (laser speckle velocimetry and particle

image velocimetry) will be discussed. The focus will be on the characteristics of each

technique that are relevant to the current process. Next, the actual theory behind DPIV

will be discussed. Present applications of DPIV-like processes are also addressed. The

second area of discussion will focus on past developments in transition region modeling.

The model proposed by Thieke (1992), which is the basis of the model presented in this

paper, is discussed in detail as are the limitations of current modeling techniques.

Evolution of Velocity Field Measuring Techniques

Laser Speckle Velocimetry

Complete representations of instantaneous velocity fields can be found by

analyzing images of markers in fluid flows. One such technique is laser speckle

velocimetry (LSV), which originated in the study of solid mechanics (Archbold and Ennos,

1972) and was first applied to fluid flows by Barker and Foumey (1977). Essentially, a

plane section of a flow containing particles is illuminated, typically by laser light. The light

reflected by these particles produces interference patterns called speckles which are

captured on film. The light is usually pulsed, leaving several exposures of the flow on the

film. The seeding density of the particles in LSV must be extremely high. The theory is

that because of this high density, individual particles cannot be resolved. The speckle

pattern is produced by interference of the reflected light caused by the overlapping of the

randomly spaced particles.

Processing occurs by interrogating a series of small sections of the photographic

negative with laser light. The light that passes the negative is optically Fourier

transformed with a special lens, producing "Young's fringes". The fringes are oriented

perpendicular to the flow in the section. Burch and Tokarski (1968) found that the

orientation and spacing of the fringes were proportional to the displacement of the speckle

pattern in the interrogated section. Unfortunately, direction cannot be resolved from this

method unless a complicated spatial shifting technique is employed during filming. This

represents a statistical approach to finding a representative displacement vector of a small

section of the flow. Both the Fourier transforms and the concept of a statistically

averaged representation of the displacement of a small section in a flow are incorporated

(although in a somewhat different manner) in DPIV.

Particle Image Velocimetry

Adrian (1984) and Pickering and Halliwell (1984) found that in practice the

particle density required for LSV is difficult to achieve. The more likely scenario is a

density in which individual particles are discernible. In this case a true speckle pattern is

not present. Instead, the particles themselves are tracked. In this case, the process is

called particle image velocimetry (PIV). Adrian (1989) further divided the class of PIV

into high and low density PIV modes.

In low density PIV, the probability of overlapping particles is quite low. In fact,

individual particles can be tracked by means of streak analysis. If the recording film is

exposed over a longer time interval (i.e., an extended pulse of the laser) the particles

produce streaks. The low particle density results in a low probability that the streaks will

cross. Displacements can be determined by manually establishing the endpoints of the

streaks. This method is often called. particle tracking velocimetry (PTV). The

complexities involved in tracking multiple particles make any automation of this process

quite difficult.

The particle densities designating high density PIV fall somewhere between PTV

and LSV. There is a high probability that several, individually identifiable particles will be

present in the small interrogated section. However, the higher density (compared to PTV)

makes tracking individual particles difficult. Once again the statistically determined

average displacement of an area is determined. The images are processed in a manner

similar to LSV by optically performing a two dimensional Fourier transform and

interpreting the Young's fringes. However, the fringes now identify the displacement of

the particles as a group instead of the speckle pattern interference displacement.

Digital Particle Image Velocimetry

Digital particle image velocimetry (DPIV) is a non-intrusive, velocity measuring

system that is based on the frequency domain analysis of pixel intensity distributions in

digital images of neutrally buoyant particles in a flow. It holds several strong advantages

over similar velocity field measurement techniques such as laser speckle velocimetry,

particle image velocimetry and point velocity measurements such as hot film and laser

doppler anemometry.

Theory Development

Willert and Gharib (1991) describe a system that digitally performs a process

similar to the opto-mechanical method employed in particle image velocimetry. Neutrally

buoyant particles are introduced into a fluid flow and video images are recorded and

digitized. Sequential digital images (each frame capturing a single instance in time) are

analyzed using frequency domain techniques. After digitizing, small sections of each

image, called areas of interest (AOI's), are compared. The AOIs are at identical locations

on each consecutive image.

A spatial shift caused by the fluid flow may be observed from one AOI to the next.

Considering the sub-sections together as a system, the first AOI, f(m,n,t=T), may be

considered the input and the second AOI, g(m,n,t=T+AT), the output. The transition

between them is caused by a spatial displacement function, s(m,n), as well as any signal

noise, d(m,n). The desired value is s(m,n) which will give the average displacement over

the area represented by the AOI's. The system may be stated mathematically as

g(m, n) = [f(m, n) s(m, n)] + d(m, n)


with indicating a spatial convolution of the first AOI with the displacement function.

Equation 2.1 may be written discretely as

g(m, n)= s(k- m, I n)f(k, 1) + d(m, n) (2.2)

where s(m,n) becomes a Dirac delta function which has moved from the origin by the

average displacement of the particles in the AOI's. If noise is neglected, the displacement

function could be found by first transforming equation 2.1 to the frequency domain

g(m, n) = f(m, n) s(m, n) <=> G(u, v) = F(u, v)S(u, v) (2.3)

where G(u,v), F(u,v) and S(u,v) are the Fourier transforms of g(m,n), f(m,n) and s(m,n)

respectively. Then S(u,v) is solved for and the result is inversely transformed back to the

spatial domain. Willert and Gharib found this method to be quite sensitive to noise effects

and sought a more effective technique.

Their alternative method employs a spatial cross-correlation between the AOI's.

The cross-correlation function, 4 fg, can be defined as

fgs(m, n) = E[fAm, n), g(m, n)] (2.4)

or discretely as

S f(k,l)g(k +m,l+n)
Ofg(m,n) = =-- (2.5)
1 f(kb ) Jg(k,b)
k---e I-,0 k~-- = 1=-

Applying equation 2.4 to equation 2.1 and neglecting noise, the following relationship is


/fg(m, n) = E[f(m, n),f(m, n) s(m, n)] (2.6)


/fg(m, n) = d(m, n) s(m, n) (2.7)

where 0 (m,n) is the autocorrelation function of f(m,n). The autocorrelation results in a

peak at the origin since the input function f(m,n) can be considered a stationary random

process and therefore perfectly correlates with itself at the origin. Application of the

displacement function may be interpreted as moving this peak away from the origin a

distance equal to the average displacement over the entire AOI for the time interval


Willert and Gharib (1991) decreased the required processing time by using the

mathematical definition of cross-correlation in the frequency domain

(fg(U, v) = F* (u, v) x G(u, v) (2.8)


where F* is the complex conjugate of the Fourier transform of f(m,n) and G(u,v) is the

Fourier transform of g(m,n). They employed fast Fourier transforms to further reduce

processing time. After D is found, an inverse FFT is performed, thus returning the data to

the spatial domain.

Essentially the process tries to match the pattern found in the first AOI with that in

the second after the pattern has been shifted. The location of the peak value of the

cross-correlation function represents the point that best correlates the particle positions in

each AOI. The shape of the peak value is dependent upon the level of noise present.

Large amounts of noise tend to broaden the peak. Smaller peaks are also present due to

some correlation between incorrect particle pairings. However, the maximum value found

in 4 ,, indicates the best correlated displacement over the AOI. Noise is generated by

particles moving out of the AOI laterally, vertically or normal to the plane of view. The

assumption is that the AOI is large enough that a majority of the particles in the first AOI

appear in the second. Figure 2.1 shows a typical example of the results of the application

of the correlation technique for particles settling downward.

Two different centroiding techniques may then be employed when examining the

peak. A center of mass method (Kimura and Takamori, 1986) provides one pixel

accuracy but is dependent upon the threshold value used to determine the limits of the

peak. The method used by Willert and Gharib provides sub-pixel accuracy. In controlled

experiments, they found a minimum uncertainty value of 0.01 pixels. However, in practice

the uncertainty may be an order of magnitude higher. Parabolic curves are fit through the

peak and each of the two neighboring data points in both the vertical and horizontal




s 21
2 24 tx1

9 g91



r 6e


Figure 2.1 Graphical representation of pixel intensities within an area of interest on
a) image 1 and b) image 2 and c) the inverse transformed correlation peak
in the spatial domain. The maximum peak in c) indicates a displacement
of approximately 4 pixels in the +y direction (downward).


directions. The distances from the origin to the location of the maxima of these parabolas

determine the displacement vector to sub-pixel accuracy. By dividing the displacement

vector by the known time difference between frames, the velocity vector is found.

The nature of the FFT limits the maximum displacement that can be determined by

this process. The Nyquist criterion, the largest discernible frequency due to discrete

sampling, limits this displacement to one half of the AOI in any direction. Willert and

Gharib (1991) found that even this limit was too large because signal to noise ratios

decrease for large spatial displacements. This results in noise becoming dominant before

the Nyquist limit is reached. They suggest limiting the maximum displacements to one

third of the AOI dimensions.

The optimal size of the AOI is thus a result of reconciling two conflicting goals.

First, the AOI must be large enough that one third of its size will sufficiently encompass

any expected displacements. If the AOI is too small, many displacements will be lost.

Second, the AOI must be small enough to limit any velocity gradients present within the

AOI. The calculated displacements are in fact average displacements over the area, so

areas with large velocity gradients will not be well represented.

The light reflected by the particles is assumed to have a Gaussian intensity profile.

The pixel intensity can be represented by the following

I(x) = loexp [ ] (2.9)

with radius o, peak pixel value location x and maximum intensity I0. The actual pixel

value recorded during digitization is the integral of equation 2.9 over the area represented

by each pixel. The pixel intensity distribution of each particle is therefore assumed to have

a Gaussian distribution.

After a displacement vector has been found for the original AOI using the complex

conjugate method described above, the interrogation area is spatially shifted along the

image. The method is repeated until the entire image has been processed. Willert and

Gharib (1991) suggested a minimum shift equal to the average particle spacing. The

resulting overlap of the AOI's causes neighboring velocity vectors to not be truly

independent of one another. However, Willert and Gharib state that the incorporation of

additional data in each AOI does "reflect individual measurements because each sample

incorporates a different set of particle images given a sufficiently high seeding density. In

analogy to time series analysis, the spatially shifted cross-correlation is similar to a moving

average." The application of this process to breaking waves used a 32 x 32 pixel AOI

(approximately 2 cm x 2 cm in a typical view) with a spatial shift of one half the

interrogation window, or 16 pixels (approximately 1 cm).

Comparison of DPIV with Other Methods

DPIV employs single exposure video images as a time series. The location of the

particles in each image of the time series is known and therefore, the direction of particle

displacements can be found. The seeding density of DPIV is lower than that for LSV and

comparable to PIV. This makes the introduction of the particles and clean up a

comparatively simple process. PIV and LSV also require the additional steps of film

development and optical processing using a special lens. DPIV is conducive to

automation to the extent that after video taping is complete, the processing of a large

number of images can begin almost immediately. The cost savings of DPIV are substantial

in that the use of a high power laser is unnecessary. The savings are enhanced by the fact

that in addition to removing the added cost of the laser itself (typically more expensive

than the entire DPIV system), the additional safety consideration inherent in laser

operations need not be addressed. There is also no need for any special lenses or

translation platforms needed to position an image negative for laser inspection.

However, DPIV does have some drawbacks. The spatial and temporal resolution

of the velocity fields are quite low when compared to PIV or LSV. These methods can

investigate tiny portions of the flow due to the high seeding densities and the fine

resolution available with film. The DPIV resolution is currently limited by the state of

video technology. Super VHS provides over 400 lines of resolution, yet this is dwarfed by

the capabilities of film. Images could be stored digitally directly from a CCD camera at a

higher spatial resolution but the storage requirements would be immense. The second

limiting factor of video is the relatively slow frame speed of 60 frames per second. PIV

and LSV can take advantage of the high speed at which a laser can be pulsed, providing

higher temporal resolution. Faster frame rates would allow smaller AOI's to be used since

the particles would move proportionally shorter distances. As video technology advances

in the future, these limitations will be addressed.

Recent Applications of PIV and DPIV

PIV has been used extensively since the mid-1980's to determine fluid flow

characteristics. A quasi-digital process involving optical Fourier transformations and

correlations in the frequency domain and digital inverse FFT's of the results has been

applied with good results (Powell et al., 1992; Greated et al., 1992; Morrison and

Greated, 1992). This process still includes the extra step of film processing which is

absent from DPIV.

Due to the recent development of DPIV there are a limited number of examples of

its use. Willert and Gharib (1992) directly applied this method to the investigation of time

dependent vortex ring evolution. Video, with its inherent capability to efficiently store

extensive quantities of data in the form of large time series, has been used in several other

investigations (Sakakibara et al., 1993 and Kimura and Takamori, 1986) which analyzed

statistically averaged flow quantities. However, the correlation process described above

has typically been replaced with a procedure that calculates correlation coefficients in the

spatial domain by artificially relocating the first AOI to different locations about the origin

of the second AOI.

Transition Region Modeling

The transition region can best be described as the area in which waves undergo a

rapid transformation in wave height while maintaining a nearly constant mean water level.

The region begins at the breakpoint and extends shoreward to the transition point, after

which the mean water level begins to rise and wave heights decrease less rapidly

(Svendsen, 1984). Within the transition region, a rapid reorganization of the wave motion

from an unsteady, asymmetric, near-breaking waveform to a flow resembling a moving

turbulent bore (Svendsen and Madsen, 1984) occurs. It has been suggested (Thieke,

1992) that this is analogous to jet flows, i.e., the transition region representing the "zone

of flow establishment" and the inner surf zone representing the "zone of established flow".

Svendsen (1984) and Basco and Yamashita (1986) have noted that a "paradox"

exists within the transition region. This can be seen when examining the simplified

horizontal momentum balance for waves propagating in the positive x-direction

+ pg(h + ) = 0 (2.10)

where S, is the radiation stress, p is fluid density, g is gravitational acceleration, h is still

water depth and I is the mean water level setup. The horizontal gradient of the radiation

stress (SJ should be balanced by the gradient of the setup (T). S, can be shown to be a

function of wave height and therefore, from the definition of the transition region, is

rapidly decreasing. Setup (fi) is nearly constant, so the equality is not satisfied and the

paradox is evident.

The effect of the paradox is notable when considering the influence it has on

similarity models used to describe the surf zone. Svendsen (1984) and Dally et al. (1985)

developed wave height decay models which did not yield good agreement with laboratory

experimental data when started at the breakpoint. Both investigators have noted that the

calculations give improved results if started at the transition point, i.e., within the inner

surf zone (where equation 2.10 is largely satisfied). This also justifies the need for further

investigation of the transition region.


Thieke (1992) has presented a one-dimensional model that compressed the

transition region to a "shock" to compensate for the rapidly varying flow present in the

transition region. Depth integrated momentum and mass flux were conserved. The

infinitesimally small horizontal length represented by the shock allows bottom friction to

be neglected. As a result, the horizontal linear momentum conservation can be reduced to

Spn2dz+ s+s dz p 2dz+ +s d (2.11)
-h -h b -h -h t

where s", is now the depth-varying wave induced radiation stress and s', is the

depth-varying fluctuating turbulent Reynolds stress. A Reynolds type decomposition of

the instantaneous velocity

u= u1 + u+ u/ (2.12)

where U is the mean velocity, u" is the wave orbital velocity and u' is the turbulent

fluctuating velocity was applied. Equation 2.11 can be further reduced by the assumption

that turbulent contributions in the Reynolds stress can be neglected relative to the wave

radiation stress.

The mean flow is partitioned by assuming an above trough shoreward directed

mean flow and a below trough offshore return flow (Thieke and Sobey, 1990; Svendsen

and Hansen, 1988; Stive and Wind, 1986) as shown in Figure 2.2. In the simple block

type representation of mass flux the above trough and below trough mean velocities are,


Sga2k gHk
S2aH 8-a (2.13a)
ga2k gH2k
u2 2ahr 8-ah (2.13b)

where H is wave height, k is the wave number, a is angular frequency, a is the wave

amplitude and h is the water depth at the wave trough. Linear theory has been shown to

poorly predict the large mass flux produced by breaking waves (Nadaoka and Kondoh,

1982). As a result, an empirical correction factor, Q, was applied to the mass flux term at

the transition point. Thieke applied the value of Q=2.5 suggested by the data of Nadaoka

and Kondoh.

By substituting the mass flux parameterization and the linear theory representation

of radiation stress into equation 2.11, the following equality can be found

[ Ik2 +- + (2n )] [ (- =Q)+L2 H(2n-)] (2.14)

where p is the fluid density, g is gravitational acceleration, n is the ratio of the wave group

velocity to wave celerity and the subscripts b and t represent break point and transition

point conditions, respectively.

Thieke solved this equation for the transition point wave height using the

laboratory wave data of Hansen and Svendsen (1979) as the input conditions. The

Figure 2.2 Partitioning of mass flux across the water depth at both the break point
and transition point. Technique used by Thieke (1992) and employed in
the models described in chapter 4.

calculated results indicate that the model output effectively yields an upper boundary for

the transition point wave height. Any reduction in wave height (and hence radiation

stress) is compensated for by an increase in the mass flux in the absence of a gradient in

setup. The ensuing deviation from the experimental results is attributed to the influence of

turbulence, which has been neglected throughout. Thieke stated, "the model indicates that

the majority of the wave height reduction in the transition region is associated with the

generation of the enhanced mean flow, with a smaller contribution toward the turbulent

momentum flux." This turbulent momentum flux will be addressed later in this paper.


Overview of Experiment

All experiments were carried out at the University of Florida's Coastal and

Oceanographic Engineering Laboratory in Gainesville, Florida. Waves were generated in

the multifunctional wave flume which is equipped with plate glass panels running the

entire length on both sides providing flexible access to camera and lighting positions.

Wave data were collected using a capacitance type wave gauge. Six separate tests were

run: tests 1 to 3 in approximately 30 centimeters of water and tests 4 to 6 in approximately

23 centimeters of water. For each test at a specific water depth, the wave periods were

varied from 0.85 to 2.13 seconds. The video tape and wave data were then analyzed to

determine velocity fields, mean water level set-up and wave height distributions. The

following will describe the experimental set-up and data analysis techniques.

All video imaging was done in black and white rather than color because of the

higher spatial resolution and tangibly greater light sensitivity that black and white

provides. The cost of black and white video equipment is also substantially lower than

similar quality color equipment. The advantage of black and white imaging is realized

during processing because DPIV relies on pixel intensity values to distinguish particles.

Color does not offer any advantages over black and white for this process. The theory

behind the DPIV method is discussed in detail in chapter 2.

Experimental Setup

Multifunctional Wave Flume
The internal wave flume is approximately 28 meters (90 feet) long, 0.58 meters (2

feet) wide and 1.4 meters (4.5 feet) deep. It is equipped with both a flap type and piston

type wave maker. Only the smaller Seasim RSP 60-20 Modular Piston Wavemaker was

used during the experiments. This unit is computer controlled through a central electronic

system with feedback loops to minimize reflections and generation of free second

harmonics. The wave maker was used to produce monochromatic waves propagating

towards a fixed beach with slope 1/20. The horizontal bottom portion of the flume

extends 15 meters from the wave maker. The fixed beach slope then extends for another

10 meters. The flume is also equipped with a remotely controlled carriage capable of

transiting its entire length.

Wave data were obtained using a capacitance type wave gauge. The gauge was

attached to the movable carriage and cabled to a data acquisition computer. Positioning

of the wave gauge was carried out by marking stations on the flume to which the chassis

could be relocated. The first station (A) was located over the flat bottom portion of the

flume and the second (B) approximately 0.5 meters after the beginning of the slope.

Ninety-five stations (C to SSSS) were then set up every 5 cm beginning 2.5 meters from

the beginning of the slope and extending shoreward beyond any expected data acquisition


Figure 3.1 Diagram of the multifunctional wave tank with enlargements of the piston
wavemaker and capacitance wave gauge.

Video equipment used at the experiment site included a Panasonic WV-5470 high

resolution gray scale video monitor, a Panasonic AG-1970 super-VHS recording VCR,

and a Vicon VC2400 high resolution black and white CCD video camera with variable

shutter speed. The camera provides 570 lines of horizontal resolution (which is actually

above super VHS quality) and requires only 0.2 lux minimum illumination. Shutter speeds

vary from continuously open to 1/10,000 of a second. A shutter speed of 1/1000th of a

second was used to minimize blurring of the particles while still allowing sufficient light to

pass through the camera lens for adequate videotaping. Both zoom and wide angle lenses

were available for use. The choice of lens magnification depended upon the wave

characteristics at each particular camera location. The goal was to fill the view with as

much of the flow field as possible to maximize resolution during processing. All video

was recorded on master quality double coated super-VHS video tapes. Ambient light was

controlled by placing a light shield made of flexible polyurethane coated nylon fabric

around the position of the video camera and flume. The light shield covered three panes

of glass and could be positioned anywhere along the flume. Removable side panels on the

light shield provided access to the camera when necessary.

The moveable chassis was equipped with the following items: a light source, a

cylindrical focusing lens and a dispenser for the neutrally buoyant particles. The light

source was a 500 watt electric bulb enclosed in a wooden box with a slit approximately 2

mm wide cut in the bottom. The slit was aligned with the long axis of the flume (i.e.,

direction of wave propagation) and allowed only a portion of the light from the bulb to

escape the box in the form of a quickly dispersing plane (see Figure 5.2 for a schematic of

the experimental apparatus). The light is then passed through the cylindrical lens and

focused into a tight plane perpendicular to the bottom of the flume. With the lens

approximately 1 meter above the flume bottom, the focused light diffused to a width of 1

centimeter at the flume bottom. It should be pointed out here that the light was only left

on for periods of a few minutes to minimize the chance of overheating caused by the high

power consumption of the light source and the wooden construction of the box. Despite

this safety precaution, the inside bottom of the box was charred by the end of the

experiment. It is recommended that a nonflammable material be used to construct the

light box for future applications.

Figure 3.2 Experimental apparatus including video equipment location and movable
chassis arrangement. (Cross sectional view of long axis of tank)

Pliolite, a granular material used as a road paint strengthening ingredient and

having a specific gravity of 1.04, was used for the neutrally buoyant particles. Pliolite is

bright white and therefore readily visible under the lighting conditions used during the

experiments. The pliolite has a highly irregular shape that traps a proportionally large

amount of air, causing it to remain on the water surface when first introduced. Therefore,

the pliolite was first washed in liquid soap and stored under water to facilitate breaking

the surface tension when the particles were introduced to the flume. The fines were

separated out of the pliolite, leaving particles ranging in size from 0.5 to 2 mm.

The pliolite dispenser was located next to the light source and was designed to

work like a hopper. A board was fixed diagonally across the inside of the dispenser to act

as a chute as the pliolite was released. A second hinged board was installed so that it

would form a "V" with the fixed board. Tension was maintained on the hinged board by

two elastic bands. The pliolite was placed along the intersection of these two boards and

held there until being dispensed. The chute was positioned to distribute the particles

linearly near the intersection of the plane of light and the water surface. The pliolite

release mechanism was designed to overcome the tension of the elastic bands and was

connected to the outside of the flume. Water from an elevated container located above

the chassis was fed along the top of the fixed board by plastic tubing and released through

a series of small holes directed down the chute. This water was used to wash any pliolite

out of the dispenser that was not removed by gravity when the dispenser was initially


A grid of 2 cm by 2 cm squares etched in clear Plexiglas was used to calibrate the

video, compensating for the magnification effects of filming through three types of media,

namely air, glass and water. Video of this grid was used to determine the number of pixels

per centimeter as recorded by the camera. The bottom of the grid was tapered to the

beach slope so that the grid lines could be read vertically and horizontally as the grid was

held firmly on the slope.

Data Analysis Equipment

All digitizing was carried out on a personal computer equipped with a 80486/66

MHz DX2 cpu. The computer also contained an EditLink 2200/TCG VCR controller

card and a one megabyte frame grabber board as accessories. An image processing

software package with macro language capabilities was used to digitize and filter the

images. Several C language programs were written to control the VCR through the VCR

controller card. The same super-VHS recording VCR and high resolution monitor were

used during the digitization process.

Processing of the velocity fields was carried out for the most part on a Sun

SPARC-LX workstation. The 486 microcomputer is capable of processing the velocity

fields at a speed about 33% slower than the Sun workstation, so it was used to process

only a small portion of the velocity fields. Matlab by the Math Works, a matrix

manipulation software package (also with macro language capabilities), was used to

process the images on both the 486 microcomputer and the Sun workstation. All analysis

of the velocity fields was done on the 486 microcomputer using this software package (see

appendices for the source code of the macros).

Experimental Procedures

The wave flume was filled to the appropriate water level and allowed to settle,

after which a water depth reading was recorded from the flat portion of the flume. The

wave maker was started, generating waves at the designated frequency. These waves

were observed to determine the break point position and initial camera location. Wave

gauge data were recorded at station A for a deep water reading, B for initial shoaling data,

and any appropriate stations outside and within the surf zone for setup and shoaling data.

The number of camera positions to be established for each test depended upon the

field of view that could be achieved. The area from just outside the breakpoint to inside of

the transition point needed to be taped for application to the transition region numerical

model. The camera was placed within the light shield at the proper location and the

position of the center of the field of view along the flume was recorded. Next, the

calibration grid was placed along the long axis of the flume in the field of view. The grid

was illuminated using the light source without the focusing lens. This allowed the grid to

be filmed while minimizing any shadows produced by the grid. It was found that if the

cylindrical lens was used, the shadows were too intense to provide any readings from the

grid. This also allowed the camera to be focused to the proper location at the tank

centerline. The pliolite was loaded into the dispenser and the flushing water source was

connected to the dispenser. At this point, the VCR began recording, the pliolite was

released into the flume, and the light source was turned on. To produce an adequate

ensemble average of flow characteristics, it was necessary to acquire a minimum of 30

cycles for each wave so taping lasted approximately two minutes for each test, at which

point the light was shut off and the recording stopped. The camera was then moved to a

location partially overlapping the field of view of the previous position and the process

repeated until the transition point had been recorded. The first camera position was

recorded as position A, the second as B, and for some tests a third position, C, was


When the taping was completed the wave maker was stopped and the flume water

surface allowed to settle in order to eliminate any residual low frequency activity. Wave

gauge data for still water levels were recorded for each station previously investigated. A

second water level reading was taken in the flat portion of the flume to determine if any

water was lost during the testing. The entire process was repeated for the next wave

Data Processing

Wave Gauge Data

Wave data recorded during the experiment were saved in Global Lab format

calibrated to convert the input from volts to centimeters. Two files were saved for each

station; the raw wave data when the waves were running and still water data after waves

were stopped and the water levels had stabilized. These files were then converted to

ASCII text format so that they could be imported into Matlab. The still water mean value

(mean used to remove instrument noise) was subtracted from the raw wave data. This

transformed the water surface displacement values of the raw wave data to displacements

about the still water level. In Matlab, period, setup and wave height were determined at

each station for each test by using various macro files.

Period was determined using standard spectral analysis techniques. Several

stations for each test were compared to assure agreement of the calculated periods. No

deviations were observed for any of the tests. The period values were used later in the

ensemble averaging of velocities. Values for setup/down of the mean water level were

calculated for each station of interest by subtracting the mean of the converted water

surface displacement data from the mean of the still water depth. The root mean square

wave height was determined directly from the time series data. A minimum wave height

criterion was applied to the data to filter out any high frequency instrument noise. Each

maximum value (i.e., wave height) is squared, summed and then averaged yielding rms

values. Plots of the rms wave height and setup/down can be seen in Figure 5.1 in Chapter

5. These plots were used to determine the breaking wave height and depth for each test.

Image Digitization

The Editlink 2200/TCG is capable of striping a video tape with longitudinal

Society of Motion Picture and Television Engineers (SMPTE) time code on one or both

audio tracks. This was done after initial taping, however it is suggested that the tape be

striped before taping to reduce the possibility of erasure. The Editlink manufacturers

claim that the time code can be used to locate any position on the video tape to an

accuracy of+/- 1 frame. Trials using various positions on the tape showed this to be true.

Actually, nearly every trial resulted in the Editlink finding the exact frame searched for.

Macro files were written to automate the process of digitizing the video images by

the frame grabber board. The images are processed in batches of 50. First, an image is

digitized at a resolution of 640 columns by 480 lines. The 480 lines is the maximum

allowable vertical resolution of the frame grabber card. A compiled C program is called

from the macro that instructs the VCR controller card to frame advance the tape. The

next image is digitized and the process repeated. After 50 images have been digitized, a C

program is called to stop the VCR. This is to circumvent the automatic shut-offfeature of

the Panasonic AG-1970. This feature will shut the VCR off if it does not detect any

"activity" for roughly three consecutive minutes: Unfortunately, frame advance is not

recognized as "activity". This 50 image limit actually provides an amount of data that

most current hard disk drives can reasonably handle, approximately 15 megabytes.

Image Filtering

Next, the fifty images are filtered. The filtering process is based on a histogram

analysis of the pixel values in each image. All pixel values lower than the 90th percentile

are set to black or 0. All remaining pixels from the 90th to 99th percentile are linearly

scaled from black to white (0 to 255). These filtered images are stored for later

processing. A C program then directs the Editlink to find the next frame to be digitized

and the process continues.

The filtering process produced one of the most important advances in this

research. Air bubbles entrained in the flow due to the impinging jet created by a breaking

wave can be filtered out of the image since, under the lighting conditions used in the

experiment, the bubbles have lower gray scale pixel intensities than do the pliolite. The

exact range of histogram percentiles for the air bubbles and pliolite was determined by a

trial and error method in which the author visually inspected the filtered images.

The filtered images were then transferred to the Sun (or occasionally the 486) for

DPIV processing. A series of M files were written to fully automate the process of

analyzing the images and returning velocity fields. All data (i.e., filtered images and

velocity field files) were stored on a high capacity magneto-optical (MO) disk in

compressed format. The MO disk can store over 600 megabytes of data and currently


contains over 200 MB of compressed velocity field data and over 300 MB of compressed

filtered images.

Velocity Field Processing

Video processing began by determining the calibration values to be used to convert

from pixels to centimeters for each camera position. This rather crude method consisted

of analyzing several frames from the grid video. Unfortunately, the grid lines were very

difficult to observe in a still frame. However, the outer edges of the grid were surrounded

by an opaque paper coating which gave a known distance of 12 centimeters. The values

of the pixel columns corresponding to the left and right edges were determined using a

screen pointer and mouse. The difference of these two values divided by the 12

centimeter distance gave the horizontal calibration for that camera position. The vertical

calibration was determined by multiplying the horizontal calibration by the pixel aspect

ratio. Several frames were compared to evaluate the accuracy of the results. Each test

showed slight variation from frame to frame due to slight movements of the grid on the

order of one pixel (generally less than millimeter order). An average value of the selected

frames was used.

All processing of velocity fields was done without converting from pixel

displacements to actual centimeters per second velocity values. This was done to reduce

the multiplicative effect of many calculations using the less accurate length conversion

from pixels to centimeters. Displacement vectors were found in pixels and only calculated

ensemble averages were then converted back to centimeters per second values using the

calibrations taken from the recorded grid frames. Vertical and horizontal displacements

were saved separately for each image pair processed. The two principle derived

quantities to be determined were the mean flow velocity and turbulence intensities.

Ensemble and Time Averaging

To accurately calculate ensemble values for both mean flow and turbulence, an

appropriate value for the number of frames per cycle (i.e., wave period) must be

determined. Standard video records at 60 frames per second. By multiplying this value

and the period and rounding to the nearest whole number, the frames per cycle is found.

The mean velocities at each 1/60th of a second interval of the wave period are then found

by taking an ensemble average over all of the cycles corresponding to that point in the

period. For example, if a one second wave is to be processed (corresponding to 60 frames

per cycle), the following frames are averaged: frame 1, frame 61, frame 121.... However,

due to the limiting effect of the Nyquist frequency criterion in the DPIV method, certain

sections of each velocity field are sometimes left without a value. In other words, there

may be holes in the data. This can occur if a displacement greater than 1/3 the size of the

area of interest is found. This is accounted for by keeping a running total of the number of

valid values for each position in the velocity fields during the ensemble averaging.

Therefore if 50 cycles are to be ensemble averaged, not every position in the resulting

velocity field is divided by a full 50 cycles. This may result in exaggerated values near free

surfaces where small variations in the wave height may produce a physical velocity value

during only a few of the cycles. Care must be taken when analyzing the data near

boundaries so as not to overstate the effect there. This method is used so that values

within the main part of the flow are not understated as they would be if the summed values

for say 48 cycles were actually averaged over 50 cycles. Both of the above effects

become more pronounced for the longer period waves which were processed using only

30 cycles.

The time averaging analysis consisted of summing the ensemble averaged

velocities over the entire period. Absent data are accounted for in the same manner as

above. Time averaging the ensemble averaged velocity fields gives the mean flow


Turbulence was found using the ensemble averaged data for each point during the

period. These values are subtracted from the instantaneous values of each velocity field

used to find the ensemble average. These differences are squared and summed. The sum

is then divided by a running total similar to that described above to account for the

nonexistent data. The turbulence values are then time averaged similar to the mean flow.

Turbulence values are returned as squared values because that is the form in which they

appear in the momentum conservation equations.


The numerical model of the transition region examined in this paper is an extension

of that presented by Thieke (1992). The details of Thieke's model are discussed in depth

in the literature review. While Thieke's model provides a good upper boundary for

transition point wave heights, a complete description of this area requires water depth data

as well, that is, the actual physical length of the transition region. A description of the

dimensions of the transition region will provide a bridge between the various wave

shoaling models and the similarity models typically used within the surf zone.

The extension to Thieke's model is the addition of a second equation, namely

conservation of angular momentum. Longuet-Higgins (1983) alluded to this development

when he stated that "a complete theoretical model of the flow (in the surf zone) will need

to balance both the mass flux, the momentum flux, and also the flux of angular

momentum." This equation is combined with the conservation of linear momentum

equation in a depth integrated, time averaged form and written across a finite control

volume (of unknown length) encompassing the transition region.. The two equations are

solved simultaneously for transition point water depth and wave height. Mass

conservation is implicit in the adopted mean flow velocity profiles. Inherent in the

definition of the transition region is that mean water level (MWL) is constant. This is the

key aspect that allows angular momentum conservation to be readily applied. Therefore,


moments may be taken about the same reference elevation (MWL) at both the break point

and transition point. Clockwise moments have been defined as positive around the mean

water level.
Linear Momentum Conservation Equation

Three components of instantaneous velocity can be identified as important in surf

zone processes. A Reynolds type decomposition is applied to the instantaneous velocity

(following Thieke, 1992) resulting in

u= T+u//+u/ (4.1)

where i is the mean flow velocity, u" is the wave orbital velocity and u' is the turbulent

fluctuating velocity (in this case generated by wave breaking).

The depth integrated, time averaged linear momentum equations expressed in

indicial notation are

) +a( +Sa ) = =-pg(h+ !) + Ta (4.2)

where ua and M" represent the total mass flux (incorporating the Stoke's drift in the

definition of ua), S1p is the wave induced radiation stress tensor, S / is the integrated

Reynolds stress tensor, p is the fluid density, g is gravity, h is water depth, T is the mean

water level, Ta is the net boundary shear stress and a & pare defined as the horizontal

component directions. By explicitly considering the depth integration, the vertical

structure of the horizontal components in equation 4.2 can be reinstated

d p2d =-pg(h+f) J f+s )dz-tb (4.3)
-h -h

where now s/ is now the depth varying wave induced radiation stress, s, is the depth

varying turbulent Reynolds stress and the mean flow (including Stokes drift) momentum

contribution has been separated from S, and is now represented by the first term.

Applying equation 4.3 to the transition region and neglecting bottom shear

stresses, it is observed that three components of momentum can be identified. The first

term on the right hand side of the equation drops out because the mean water level is

constant (i.e., 0) in the definition of the transition region. The terms within the

integral on the right hand side can be separated. Therefore, the total linear momentum at

a section is the summation of the mass flux component (first term) and the momentum

components of wave motion and turbulence. Since these remaining terms are exact

differentials, equation 4.4 represents the conservation of linear momentum from a section

at the break point to a section at the transition point

[ pu1dz+ s +s dz = : pu2dz+ s +s dz (4.4)
-h -h b -h -h

where the subscripts b and t indicate conditions at the break point and transition point,


Closure of this model requires a description of the wave kinematics and linear

wave theory has been used for simplicity. The suitability of linear theory will be discussed

in the results section (Chapter 5). Shallow water assumptions were applied to all terms in

the equations. Three components are represented in the momentum balance: mass flux,

radiation stress and turbulence.

The mass flux is represented by a crude block approximation above and below the

trough elevation similar to that employed by Thieke and Sobey (1990) as discussed in

Chapter 2 and shown in Figure 2.2. The corresponding mean velocities with shallow

water assumptions (applying the shallow water limit to wave celerity 2 = Jg ) are

ga2k gHk gH
2o H s-a -=8 s (4.5a)

ga2k gHk gH2
2= 8hr 8(h) (4.5b)

The mean velocity values above and below the wave trough are WT and Wi2, respectively.

The correction factor value, Q (see Chapter 2), was assigned values of 1.5, 2.0, 2.5 and

3.0 to assertain what effect this would have on model results. Note that the definitions in

equations 4.5a and 4.5b implicitly conserve mass.

In the linear momentum conservation equation, the depth integrated radiation

stress found from linear theory is

S p -(2 3H 2pgH2 (4.6)
S= = -8-(2n 1) = gH (.6

found by applying the shallow water assumption that n -- 1 (n = ve gp v y). Any

depth varying aspects of radiation stress are neglected by employing this depth integrated


Turbulence is represented in three models based on empirical data derived from

the DPIV experiments. Each successive model includes a more complete description of

turbulence than the previous model. It is assumed that all turbulence production occurs

after breaking, so this term is not included in the initial conditions at the break point. The

results of the DPIV analysis indicate that near the transition point, the largest area of

turbulence generation occurs above the still water level (SWL) (see chapter 5 for the

model calibrations).
Model 1 incorporates u2 values by modeling them as a block above SWL. All

turbulence below SWL is ignored in this model. The turbulence description found from an

empirical fit to the fluctuating velocity data derived from the DPIV analysis. The data are

normalized such that the dimensionless root mean square turbulent velocity is a function of

the surf similarity parameter

=a +b (4.7)

where u',,, is the turbulent velocity found from DPIV analysis, g is gravitational

acceleration, hb is the water depth at the break point, H1 is the wave height at the break

point, m is the beach slope, T is the wave period and a and b are coefficients to be

determined in chapter 5. The surf similarity parameter is defined as

mgTr (4.8)

Substituting equations 4.5, 4.6 and 4.7 into equation 4.4 and simplifying yields the linear

momentum conservation equation for Model 1

H2 *(H+H +J3]}

I* (H+L' +3+ *(a2 + 2ab+b b2)

Model 2 attempts to include vertical turbulence contributions by defining them as

wn 0.75un (4.10)

in accordance with the assumptions of similarity of breaking waves to a plane wake or

mixing layer (Svendsen, 1987). Within the depth integrated, time averaged momentum

conservation equation, the turbulence contribution appears as

S= f (p7'-pw;;2dz (4.11)

Therefore, the overall magnitude of S', in Model 2 is equal to only one quarter of the

Model 1 turbulence. Substituting equations 4.5, 4.6 and 4.11 into equation 4.4 and

simplifying yields the linear momentum conservation equation for Model 2

H\2 *[ L* (H+ i +3}=
-4h h-
2 f* H+ -+3+ + *(a (2 +2ab+b2)1

Model 3 adds the below SWL turbulence contribution, providing the "most

complete" description of the turbulent velocity field. This contribution is simply defined as

a block from SWL to the bottom and is calibrated using the following relationship found

from the DPIV data

u _-w = Khb (4.13)

The upper level parameterization used in Model 2 is again used in Model 3. Incorporating

equation 4.13 into equation 4.12 yields the linear momentum conservation equation for

Model 3

H .* (-,* ]+ +3 =

H H+ +3+ *(a2 + 2ab+ b2) +Khb *A
I 4 h-L 8 22y J

Angular Momentum Conservation Equation

The mass flux is partitioned in the same manner as in the linear momentum

conservation equation. The shoreward directed mass flux component is negated in the

angular momentum equation because it is symmetric about the mean water level. The

block representation of this component yields a moment arm of zero length. The below

trough, offshore directed return flow contributes a positive moment.

Radiation stress was partitioned over the water depth at both the break point and

transition point based on the work of Borecki (1982). The partitioning is based on linear

theory and is applied in the angular momentum equation by multiplying each radiation

stress component by the length of its moment arm from MWL to the respective

component's centroid. Fortuitously, the two pressure components (MWL to crest and

MWL to trough) are symmetric about the mean water level and therefore cancel. Thus,

only two of the components are included in the angular momentum equation. These are

the wave orbital velocity contributions above and below the trough level, defined by

Borecki as

II = p(u2 -w2)dt for -h 0

13 = p(u2 -2)dt for << (4.15 b)

where I is Jss(z)dz or the depth integrated value of each radiation stress component.

Applying shallow water asymptotic solutions to the above representations gives

I= -) (4.16 a)

13=EM (4.16 b)

where E is the energy per unit surface area of the wave. The applicable moment arms, z.

for each component are, respectively

zci = -h+2 (4.17 a)
zc3 = (4.17 b)

Turbulence is modeled as in the linear conservation equations. Models 1 and 2

produce a positive moment contribution in the angular momentum equation. Model 3 is

not so straightforward. The large magnitude of the turbulence in the upper part (above

SWL) is offset by the component's small moment arm. The opposite is true for the lower

part (below SWL) and yields a negative moment. The relative magnitude of the two

contributions will be dependent on the solution for the transition point wave height. A

large decrease in the wave height will give relatively greater importance to turbulence in

the lower part of the flow.

Multiplying each component of mass flux, radiation stress and turbulence by its

corresponding moment arm yields the following forms for the conservation of angular

momentum equations:

Model 1

[ I16h h2I8 + b
2 b


Ih* 1 --L( 2+ 12 h, ) (a 2 +2ab +b2)}
16 1-6h 128h h-a)+ 8
2 i

Model 2

{~* i (28 )2] + H4
16 16128


16 1)2+ +.) (a 2 +2ab+b2)

and Model 3

16L16 h h-

{HIh [iH4^ (1 242 2)'
6 +16 128 + t2 2+2ab+b )-Khb (4.20)

The complete parameterized conservation equations for linear and angular

momentum conservation (for each given turbulence model) are then solved simultaneously

by nonlinear shooting methods.


The results of this investigation are presented in this chapter. The wave data

obtained from the capacitance wave gauge are analyzed and discussed first, followed by

the processing of the digitized images to obtain velocity fields using the DPIV method.

The results of the ensemble and time averaging of the velocities are presented. Finally, the

transition region model performance is evaluated, including a discussion of the laboratory

data of Hansen and Svendsen (1979) used as input and the turbulence parameterizations


Wave Data

The data obtained from the capacitance type wave gauge have been analyzed as

described in chapter 3. Figure 5.1 is a typical representation of the mean water level

setup/down and wave height distributions as found for test 6. As can be seen in Figure

5.1, the mean water level is lowered (setdown) as the break point is approached from

offshore. At the breakpoint and for a short distance shoreward, the data fluctuate about a

nearly constant value indicating the extent of the transition region. Within the inner

surfzone, the mean water level rises again (setup). The inner surf zone measurements

contain large fluctuations due to limitations inherent in the wave gauges when sampling in

11 12 13 14 15 1i 17 18 19 20
Distance from wavemaker (m)

Figure 5.1 a) Mean water level and b) wave height distributions for test 6 found
from analysis of capacitance wave gauge data.

very shallow water and the effect of turbulence. However, these errors generally do not

effect any of the subsequent calculations because most of the flow quantities needed can

be found from the video record of the experiments. Derived properties based on the

instantaneous wave velocity data were not reported for test 4 because later analysis of the

video tape showed that the transition region had not been fully recorded. Test 5 values

also were not recorded because of results evident on the video and wave records

indicating that a significant level of low frequency wave activity was present in the wave

flume during this experiment. This manifested itself as a variably positioned breakpoint







11 12 13 14 1i 16 17 18 19 20
Distance from wavemaker (m)


which, if included in ensemble averaging calibrations, would smear the results of the

analysis and preclude any effective comparison to other monochromatic wave cases.

The values of h are the water elevations recorded over the flat portion of the wave

flume before and after each test. The tank did not lose sufficient water during the tests to

alter the initial readings. Hb and hb are breaking wave height and breaking water depth,

respectively. These data were found by determining the location at which the largest root

mean squared wave height value was measured (Figure 5.1). The water depths can be

found by multiplying the distance of the station from the onset of the fixed beach by the

slope of this beach (1/20). These wave heights and water depths are listed in Table 5.1.

Table 5.1 Experimental wave conditions

Test No. Period Hb (cm) hb (cm) ho (cm)
1B 0.85 4.85 4.7 31.2
2C 1.42 6.52 4.2 30.7
3C 2.13 6.42 4.5 31.2
4C 0.85 N/A N/A N/A
5* 1.42 N/A N/A N/A
6A 2.13 8.86 8.4 23.2

N/A = Not available, = invalid test case

Velocity Field Results

The raw velocity field data resulting from the DPIV method were analyzed using

ensemble averaging techniques in an effort to separate the wave and turbulent parts of the

motion. Consequently, the corresponding number of video frames per period for

monochromatic waves had to be determined. Table 5.2 shows a summary of the values

for the various tests.

A total of 21,162 velocity fields were incorporated in the ensemble averaging

during all of the tests. Actually, only 17,066 of these fields are completely independent

because the fields found during the 30 cycle ensemble averaging in tests 2C and 4C were

used as the first 30 cycles of the 50 cycle ensemble averaging. This allows a comparison

of the effectiveness of increasing the number of cycles included in the ensemble averaging.

Table 5.2 Frames/cycle data for experiments

Test No. Period Frames/ Total frames Total frames
(sec) cycle processed, 30 processed, 50
cycles cycles
1B 0.85 51 N/A 2560
2C 1.42 85 2560 4266
3C 2.13 128 3840 N/A
4C 0.85 51 1536 2560
6A 2.13 128 3840 N/A

Once the required number of digitized images was known, the digitization

process began. On average, it took fifteen seconds for an image to be digitized and fully

filtered. A comparison of an unfiltered and filtered gray scale image is shown in Figure

5.2. The filtering process has been described in chapter 3. The filtered images were then

stored in compressed format on a magneto-optical disk and also transferred to the

workstation for processing.

Image processing using the DPIV method to obtain instantaneous velocities can be

accomplished in one large data exchange if there is a sufficient data storage capacity

available at the processing computer. This was generally not the case. Data transfer was


... "
.7 ._ F -

I .-- Q 3 '_ P --
C- I -rt- 1O Ii R


rIr '.7 '
,C .- 3 ,' ...
*-"y .. .

q *-- '-

fc.- -l I L* O P 2a -

Figure 5.2 Comparison of a) an unfiltered digitized image and b) a filtered digitized
image from test 2. Gray scales have been inverted for clarity. Note the
removal of the aerated jet in the filtered image.

usually done by transferring 200 images to the workstation while removing the previously

processed velocity field files for the preceding 200 images. An example of a typical

instantaneous velocity field is shown in Figure 5.3 (recall 1 cm is approximately 16 pixels).

25 -
.- \\ \~.-\
1- -- z

-S20- -- -

?--- 600 pixels/sec

5 10 15 20 25 30 35
AOI steps (18 pixels/step)

Figure 5.3 Example of an instantaneous velocity field found using the DPIV process.
(From test 6C, field number 536)

After all of the required instantaneous velocity fields have been acquired, the

ensemble averaging process was undertaken according to the criteria of Table 5.2. As

described in chapter 3, an ensemble average of the corresponding velocity fields for each

1/60th of a second interval in the period is determined and saved. These ensemble

averages are then time averaged over the period, yielding results similar to Figure 5.4.

The first image in Figure 5.4 shows the resultant ensemble average velocity fields of the

entire field of view, including "velocities" that are outside of the flow. Most of these

extraneous velocities are the result of superimposing a digital stopwatch on the lower

portion of the screen during videotaping (Figure 5.2). The data in the bottom portion of

the field show the correlated motion of the stopwatch numerals. Some spurious data is


also present above the flow possibly due to splashing that occurs when the jet impinges

upon the front face of the breaking wave. Another possible source of nonflow velocities is

instrument noise associated with the video equipment that may occur during the

digitization process. All data other than the desired flow data have been removed from

the second image.

Figure 5.4

A typical ensemble time averaged velocity field with a) all non-flow data
included and b) only flow related data included.

Figure 5.5 shows a comparison of the 30 cycle and 50 cycle ensemble and time

averaged mean velocities for test 4C. Physically Figure 5.5 a and 5.5 b represent a

a) * .
S- \ \ -
I # / I I I I / / / / / / / / I I "I / / / / I 1 1.' -
i20 / .- l i / l / / / l / / / / / / / / ^/ "/ -

10 .......

120 plxels/sec .

5 10 1'5 20 25 30 35
AOI steps (16 pixele/step)

- - - Z Z Z - -
. . . . . .


120 pixels/sec
5 10 15 20 25 30 35
AOI steps (16 pixels/step)

synoptic view of the mean flow in the transition region. As seen in Figure 5.5 c, the actual

difference between the two cases is rather minor in the lower portions of the flow. The

larger differences in the upper portions are a result of large scale intermittent turbulence

and the effects of velocity measurements near a free surface which can introduce error

(chapter 3).

Figure 5.6 represents an enlarged section of the middle of the view for the 50

cycle case in test 4C. The profiles are typical examples of the expected form of this flow

except that in this case there are measurements above and below the wave trough

elevation. In principle, mass (volume) should be conserved across any given vertical

section (column) in this flow. Table 5.3 provides a summary of the vertical integration of

the velocity profiles of Figure 5.6, indicating that mass is largely conserved in the


Ensemble turbulent r.m.s. velocity fluctuations are then calculated as described in

chapter 3. Figure 5.7 shows the time averaged values of the turbulent fluctuations

associated with test 4C.

Turbulence Parameterization

The transition region model requires parameterization of the wave, mean flow and

turbulent contributions to the conservation equation. As previously discussed, linear wave

theory has been used to represent the wave and mean flow contributions. The mass flux

was partitioned using a block representation of the above trough and below trough

contributions (chapter 4). Figure 5.6 indicates that the vertical structure of the time

average mass flux actually varies substantially in the above and below trough regions. The


modeling of the mass flux is therefore a drastic oversimplification of the actual observed

mass flux. However, the block representation is actually consistent with the other


The turbulent contribution were parameterized using the measurements of the

turbulent velocity fields from the DPIV method. The original video record was observed

to determine the location of the relatively abrupt break in wave height change that signals

the end of the transition region (or the location of the transition point). This is a

somewhat subjective process, but it was determined that this technique would be more

accurate than relying on the wave gauge data because of the five centimeter gap between

wave gauge stations. After the general location of the transition point was determined, the

average of each row in the three columns of horizontal turbulent velocity data on the

offshore side of the transition point (toward the breakpoint) was found to develop a depth

varying profile of horizontal turbulent velocity fluctuations. The three column averaging

was used first to further minimize any effects that missing data may have had on the

ensemble averages (see chapter 3 for discussion of missing data) and second to increase

the likelihood that the data represent values not only near the transition point but within

the transition region. The depth varying values of the r.m.s. horizontal turbulent

fluctuations (normalized by the local wave speed) are presented in Figure 5.8.

Inspection of Figure 5.8 reveals that the below still water level (SWL) values of

u'rm.s are fairly consistent within each test as well as between tests. For each test, the

waves at the transition point are highly asymmetric about the SWL resulting in a majority

of the crest region appearing above the SWL. Mean values of the horizontal turbulent

S- =120 pixels/

- i i/ I I / I

--- / / / / -/

- --- --- -


/ 5 I / l '/ l / s l / / I/
l \ I / l I' / J a / /I\\ -/

- ////// //////-

/ - / / / / / / i -

111 / I- /

I \ I I ia
/I -/ //
//// / /

- - -

a) 26








b) 26




a is





0) 26








0 5 10 15 20 25
AOI steps (16 pixels/step)

30 35

Figure 5.5 Comparison of ensemble, time-averaged velocity fields using a) 30 cycles,

b) 50 cycles, with c) the difference between a and b. (Data from test 4C)

0 5 10 15 20 25 30 35
AOI steps (16 pixels/step)

I s I I I \ I I l / 1 11 l l / I l l / ^ / "-

/ /// / i l/ //// / ////1////////// / // /
/'/// // /////////////// // //////......

/ / / / / / / / / / / -

0 5 10 1i 20 25 30 35
AOI steps (16 pixels/step)

--120 pixels/sec

S0 . .

.. . . . . . . .
i . *. *.










=120 pixels/sec
I 1I

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5

Figure 5.6 Enlargement of columns 15 through 20 of Figure
conservation of mass.

Table 5.3

Comparison of mass flux comnonenta from FimireP 5

5.5 b indicating


Column Column Column Column Column Column
15 16 17 18 19 20

Sum of positive 5.523 5.491 5.572 5.361 5.195 5.714

Sum of negative -6.217 -6.195 -5.279 -6.116 -6.512 -6.384

Ratio ofneg to pos 1.126 1.128 0.948 1.141 1.253 1.117

Average ratio 1.119






262 /

2.4- / / /- / / / // // / / / / / -

20 -
s .,- . / / / .. / .I .. / /


12 . . . . . . . . .

1 400 (pixels/sec)^2
5 10 15 20 25 30 35
AOI steps (16 pixels/step)

Figure 5.7 Typical turbulent velocity fluctuation field (data from test 4C). Note that
the turbulence values are squared resulting in all values oriented in the
positive direction.

velocity results above SWL were found and then normalized by the known breakpoint

conditions. Figure 5.9 shows these values plotted against the breaking wave height

normalized by the surf similarity parameter under the assumption that the magnitude of

turbulent fluctuations at the transition point is a function of the conditions at the

breakpoint. The results are also presented in Table 5.4.

Hansen and Svendsen Experimental Wave Data

The best fit line presented in Figure 5.9 provides the simplest means of accounting

for the turbulent velocity fluctuations in the momentum conservation equations in the

model. The coefficients discussed in chapter 4 are determined from this best fit line. In

reality, the range of the corresponding surf similarity parameters is quite limited. Despite

this, the values have been extrapolated to apply to the conditions found in Hansen and

Svendsen's experimental wave data (1979). The below trough contributions of turbulent

fluctuations have been normalized by the water depth at the breakpoint since this is a


known condition and is expected to correlate with the total amount of turbulence that is

advected/diffused to the below SWL portion of the flow.


2 .0 ...............


1 .0 .............................. ........

0 .5 ............... ........ 5.........-. ......... -.-rest

0.00 0.02 0.04 0.06 0.0f

rnis swI

3 0.10 0.12 0.14

Figure 5.8 Profiles of dimensionless u'r,, with depth at the transition point for four
different test cases. Measurements obtained with Digital Particle Image
Velocimetry (DPIV). Breaking wave height to water depth ratio and
wave period are noted.









0.040 0.060 0.080 0.100 0.120 0.14e

H /mgT2

Figure 5.9 Empirical curve fit for dimensionless u'rm. at the transition point as a
function of the surf similarity parameter. (m = beach slope)

Table 5.4 Turbulence parameters determined from DPIV

Test 1

----.-------................ ................... .......................-----.-----------.-............ .............................


----------------. ...... .--------------.
o Test 2

-Test-- .... ... ............ .. ................. ......

0c Test 4

Test No. u'..,. Hb/mgT2 U'rm
(cm/sec) (ghb)12
1B 6.82 0.136 0.101
2C 5.35 0.066 0.083
3C 5.03 0.029 0.079
6A 6.99 0.039 0.077

The input and control conditions applied to the models were found from the

experimental wave data given by Hansen and Svendsen (1979). They present several

spatially varying wave parameters including water depth, wave height and mean water

level (MWL) for a series of tests covering a wide variety of wave conditions. To

determine the breaking wave height, a three point moving average was applied to the

wave height data, with the maximum value indicating Hb. The corresponding still water

depth for this location gives the breaking water depth, hb. The transition point conditions

are found by performing a series of linear regressions on the two successive sets of fifteen

MWL data points moving shoreward. The point corresponding to the maximum change in

slope of the two regressed lines provides the location of the transition point. The

appropriate wave heights and water depths at the laboratory transition points are listed in

Table 5.5 along with the break point conditions.

Table 5.5 Hansen and Svendsen's wave data

Test No. Period Hb (mm) hb (mm) H, (mm) h, (mm)
101101 1.0 105.8 143.9 62.9 110.8
A10112 1.0 75.8 97.4 64.0 85.5
081103 1.3 122.1 142.5 73.0 110.3
A08102 1.3 87.0 103.0 63.3 85.5
061102 1.7 139.2 151.9 87.8 119.3
061091 1.7 128.4 142.5 108.2 128.4
061082 1.7 116.5 138.7 85.7 114.5
061071 1.7 102.7 120.3 79.2 100.3
051071 2.0 108.2 115.0 79.4 98.1
051041 2.0 71.2 73.8 33.8 53.2
041071 2.5 128.7 134.5 64.3 107.3
041041 2.5 87.0 89.2 45.7 68.0
031041 3.3 92.9 94.7 50.8 66.5

Model Performance

Applying the input breakpoint conditions, the transition region model with

different turbulence parameterizations can now be evaluated. For each turbulence model,

the empirical correction factor for the increase in mass flux, Q, is varied to determine the

effect on the calculated values. Figures 5.10, 5.11 and 5.12 graphically illustrate the

resulting sensitivity of each model to the value of Q. Tables 5.6, 5.7 and 5.8 also present

the output. Figure 5.13 and Table 5.9 represent a comparison of the various turbulence

models for constant value of Q=2.5.

Figures 5.10, 5.11 and 5.12 imply that the transition point wave height is more

sensitive than the transition point water depth to the value of Q that is employed. The

results of the transition point wave height in model 1, for instance, give a range of the

overall mean error from the experimental data of approximately -1.0% to +13.6%. The

values of model 1 for Q=2.5 are actually quite similar to the results obtained by Thieke

(1992) for the same data set using the one-dimensional model that conserves only linear

momentum. This indicates that the wave height is fairly insensitive to the inclusion of the

angular momentum conservation equation. Also, the transition point wave height appears

quite insensitive to the level of turbulence modeled, as seen in Figure 5.13. The spread of

the data in the wave height plot (Figure 5.13a) is much more narrow than that of the water


A comparison of the results in Figure 5.13 indicate that as turbulence levels are

more completely described (i.e., progressing from model 1 to model 2 to model 3), the

prediction of the transition point water depth progressively departs from the measured



0.002 .- ....-.

0.000 0.002 0.004







0.006 0.008 0.010 0.012
H /gT2

0.004 0.008 0.012

h /gT2

Figure 5.10

Comparison of predicted and measured a) wave height and b) water depth
at the transition point for various values of the mass flux increase factor Q
and turbulence model 1. Measured data from Hansen and Svendsen

0.000 V-







0.006 0.008 0.010 0.012
H /gT2




0 000 V .. I I I I I . I . I
0.000 0.004 0.008 0.012 0.016
h /gT2
Figure 5.11 Comparison of predicted and measured a) wave height and b) water depth
at the transition point for various values of the mass flux increase factor Q
and turbulence model 2. Measured data from Hansen and Svendsen

000 0.002 0.004

0.010 j A 1 ~-



000 0.002 0.004 0. 00 0.008 0.010 0.012
H /gT2












h /gT2
Figure 5.12 Comparison of predicted and measured a) wave height and b) water depth
at the transition point for various values of the mass flux increase factor Q
and turbulence model 3. Measured data from Hansen and Svendsen

All 3 cases o
this line / 6 \
-... .. .. .. .. .. .-- ..... .- .... .o ...............
/ Oata of Hansen and
S/0 Svendsen (1979)

. ...... ..... ...-


0.002 0.004 0.006 0.008 0.010 0.012
H /gT2

0.008 0.012
h /gT2


Comparison of predicted and measured a) wave height and b) water depth
at the transition point for mass flux factor Q=2.5 and the three turbulence

0.010 -












0.000 v-

Figure 5.13

Table 5.6 Model Results for transition point wave height, H,

Q = 1.5 Q= 2.0

Test # Experimental Model I % Diff Model 2 % Diff Model 3 % Diff Model 1 % Diff Model 2 % Diff Model 3 % Diff
H, (mm) H, (mm) H, (mm) H, (mm) H, (mm) H, (mm) H, (mm)
101101 62.93 96.6 53.5 99.0 57.3 99.9 58.7 90.4 43.6 93.0 47.8 94.1 49.5

AI0112 64.03 68.7 7.3 71.3 11.3 71.3 11.3 63.9 0.2 65.8 2.8 67.0 4.6

081103 73.03 108.2 48.2 1 11.8 53.1 114.0 56.1 99.8 36.6 103.4 41.6 106.5 45.8

A08102 63.27 77.5 22.5 79.9 26.3 81.3 28.5 71.6 13.2 74.0 17.0 76.0 20.1

061102 87.77 121.2 38.1 125.8 43.3 129.1 47.1 111.1 26.6 115.5 31.6 119.4 36.0

061091 108.23 112.5 3.9 116.5 7.6 119.5 10.4 103.3 -4.6 107.2 -1.0 111.0 2.6

061082 85.67 104.1 21.5 107.1 25.0 109.0 27.2 96.2 12.3 99.3 15.9 101.9 18.9

061071 79.17 91.4 15.5 94.2 19.0 96.0 21.3 84.4 6.6 87.2 10.1 89.7 13.3

051071 79.37 93.5 17.8 97.2 22.5 100.3 26.4 85.5 7.7 88.9 12.0 92.9 17.1

051041 33.83 61.0 80.3 63.6 88.0 65.8 94.5 55.6 64.3 58.0 71.4 61.1 80.6

0411071 64.33 110.6 71.9 115.2 79.1 118.7 84.5 101.0 57.0 105.1 63.4 109.2 69.7

041041 45.67 74.2 62.5 77.4 69.5 80.4 76.1 67.7 48.2 70.5 54.4 74.6 63.4

031041 50.83 79.1 55.6 82.6 62.5 85.8 68.8 72.1 41.8 75.1 47.7 79.2 55.8

Mean %O Dirference 31.2 35.3 47.0 28.2 31.9 36.7

% Diff= (Model HI Experimental H) / Model H

N/S = No solution found

Table 5.6 (continued)

Q = 2.5 Q = 3.0

Test # Experimental Model 1 % Diff Model 2 % Diff Model 3 % Diff Model I % Diff Model 2 % Diff Model 3 % Diff
1IH (mm) H, (mm) H 11, (mm) H, (mm) H, (mm) H, (mm)
101101 62.93 85.4 35.7 87.9 39.7 88.8 41.1 81.4 29.4 83.7 33.0 83.9 33.3

AI0112 64.03 60.2 -6.0 62.0 -3.2 63.0 -1.6 57.3 -10.5 58.9 -8.0 59.5 -7.1

081103 73.03 93.7 28.3 96.9 32.7 99.9 36.8 89.1 22.0 91.9 25.8 N/S --

A08102 63.27 67.3 6.4 69.4 9.7 71.3 12.7 64.0 1.2 65.9 4.2 N/S

061102 87.77 104.1 18.6 107.9 22.9 111.9 27.5 99.0 12.8 102.2 16.4 N/S

061091 10823 96.8 -10.6 100.2 -7.4 104.2 -3.7 92.0 -15.0 94.9 -12.3 N/S

061082 85.67 90.4 5.5 93.2 8.8 N/S -- 85.9 0.3 88.4 3.2 N/S

061071 79.17 79.2 0.0 81.7 3.2 84.1 6.2 75.3 -4.9 77.5 -2.1 79.2 0.0

051071 79.37 80.1 0.9 83.0 4.6 87.0 9.6 76.2 -4.0 78.6 -1.0 N/S .-

051041 33.83 52.1 54.0 54.0 59.6 57.1 68.8 49.6 46.6 51.2 51.3 N/S --

041071 64.33 94.6 47.0 98.0 52.3 102.1 58.7 90.0 39.9 92.8 44.2 96.8 50.5

041041 45.67 63.4 38.8 65.7 43.9 N/S -- 60.3 32.0 62.3 36.4 N/S .-

031041 50.83 67.5 32.8 70.0 37.7 74.1 45.8 64.3 26.5 66.3 30.4 N/S --

Mean % Difference 19.3 23.4 27.4 13.6 17.0 19.2

% Diff= (Model H, Experimental H) / Model Ht

N/S = No solution found

Table 5.7 Model Results for transition point water depth, h,

Q = 1.5 Q = 2.0

Test # Experimental Model 1 % Diff Model 2 % Diff Model 3 % Diff Model 1 % Diff Model 2 % Diff Model 3 % Diff
h, (mm) h, (mm) h, (mm) h, (mm) h, (mm) h, (mm) h, (mm)
o10110 110.8 119.4 7.8 135.7 22.5 143.9 29.9 120.3 8.6 135.7 22.5 143.9 29.9

A10112 85.5 80.5 -5.8 97.4 13.9 97.4 13.9 80.6 -5.7 90.4 5.7 97.4 13.9

081103 110.3 114.0 3.4 130.1 18.0 142.5 29.2 112.9 2.4 127.4 15.5 142.5 29.2

A08102 85.5 83.4 -2.5 94.6 10.6 103.0 20.5 82.7 -3.3 92.8 8.5 103.0 20.5

061102 119.3 118.8 -0.4 135.7 13.7 150.7 26.3 116.9 -2.0 131.5 10.2 147.2 23.4

061091 128.4 112.5 -12.4 128.1 -0.2 142.5 11.0 110.8 -13.7 124.5 -3.0 140.8 9.7

061082 114.5 113.0 -1.3 127.6 11.4 138.7 21.1 112.0 -2.2 125.4 9.5 138.7 21.1

061071 100.3 97.5 -2.8 110.2 9.9 120.3 19.9 96.5 -3.8 108.0 7.7 120.3 19.9

051071 98.1 89.2 -9.1 101.8 3.8 115.0 17.2 87.5 -10.8 98.2 0.1 113.5 15.7

051041 53.2 56.5 6.2 64.6 21.4 73.8 38.7 55.4 4.1 62.1 16.7 73.8 38.7

041071 107.3 103.4 -3.6 118.2 10.2 132.3 23.3 101.4 -5.5 113.7 6.0 128.3 19.6

041041 680 67.9 -0.1 77.7 14.3 89.2 31.2 66.5 -2.2 74.6 9.7 89.2 31.2

031041 665 71.8 8.0 82.2 23.6 94.7 42.4 70.4 5.9 78.9 18.6 93.2 40.2

Mean % Difreence -1.0 13.3 25.0 -2.2 9.8 24.1

% Diff= (Model h, Experimental h) / Model h,

N/S = No solution found

Table 5.7 (continued)

Q = 2.5 Q =3.0

Test # Experimental Model 1 % Diff Model 2 % Diff Model 3 % Diff Model 1 % Diff Model 2 % Diff Model 3 % Diff
h, (mm) h, (mm) h, (mm) h, (mm) h, (mm) h, (mm) h, (mm)
o10ll0 110.8 123.6 11.6 137.9 24.5 143.9 29.9 81.4 29.3 142.0 28.2 143.8 29.8

A10112 85.5 82.6 -3.4 91.7 7.3 97.4 13.9 57.3 -10.5 94.3 10.3 97.4 13.9

081103 110.3 115.5 4.7 128.5 16.5 142.5 29.2 89.1 22.0 132.1 19.8 N/S

A08102 85.5 84.6 -1.1 93.7 9.6 103.0 20.5 64.0 1.2 96.3 12.6 N/S

061102 1193 119.6 0.3 132.4 11.0 148.6 24.6 99.0 12.8 136.3 14.2 N/S

061091 128.4 113.3 -11.8 125.4 -2.3 142.3 10.8 92.0 -15.0 129.0 0.5 N/S

061082 114.5 114.5 0.0 126.6 10.6 N/S -- 85.9 0.3 130.1 13.6 N/S

061071 1003 98.6 -1.7 108.9 8.6 120.3 19.9 75.3 -4.9 111.9 11.6 120.3 19.9

051071 98.1 89.6 -8.7 98.9 0.8 114.5 16.7 76.2 -4.0 101.8 3.8 N/S

051041 53.2 56.7 6.6 62.5 17.5 73.8 38.7 49.6 46.6 64.5 21.2 N/S

041071 107.3 103.8 -3.3 1 14.5 6.7 129.3 20.5 90.0 39.9 1 18.0 10.0 133.3 24.2

041041 68.0 68.2 0.3 75.1 10.4 N/S -- 60.3 32.0 77.5 14.0 N/S

031041 665 72.2 8.6 79.5 19.5 93.9 41.2 64.3 26.5 82.0 23.3 N/S --

Mean % Diference 0.2 10.8 24.2 13.6 14.1 22.0

% Diff = (Model h, Experimental h.) / Model h,

N/S = No solution found


value. This is rather curious in that the best description gives the poorest answer. This

result may be a consequence of the use of linear theory in the description of the radiation

stress for surf zone waves. Linear theory is based on symmetric sinusoidal waveforms

which do not adequately represent the waveforms found within the surf zone. Surf zone

waves are much more asymmetric about the MWL, resulting in the crest being present

above the trough level for a much shorter period than is assumed in linear theory. The

corresponding derived wave parameters such as radiation stress will be grossly

overestimated by the linear theory as a result. The effects of turbulence accordingly

appear unrealistically smaller. A higher order theory representation of the wave properties

would redress this deficiency. It should also be noted that the approximations to the mean

flow and turbulent velocities as block representations are crude at best. A more complete

description of the flow partitioning may produce better results.


Any future applications of DPIV need to address some concerns that arose during

this investigation. The neutrally buoyant particles used were not truly neutral; pliolite has

a specific gravity of 1.03. The settling velocity of the particles should be considered when

determining the instantaneous velocities of a flow. As can be seen from Figure 5.6, each

of the velocity vectors in the mean flow plot have a downward (-z) component, however

there should be an upward (+z) component within the transition region to account for the

increased mass flux that is observed at the transition point. Applying a fall velocity

correction to the velocities may yield the expected results.

Waves having a broader range of the surf similarity parameter should be examined

to evaluate how appropriate the linear fit is for the four test case data points (Figure 5.9).

The linear fit to such a narrow range of values is crude at best when such a large

extrapolation of the data that is needed to meet Hansen and Svendsen's data.

A concern existed in regards to the extent to which aeration of the crest of a

broken wave combined with the filtering process may affect the velocity field

determination in DPIV. It was possible that the bubbles produced during wave breaking

may distort the perceived location of particles due to refraction/diffraction of the reflected

light. To determine the net effect of this phenomenon, a mesh grid containing particles

glued to fixed positions was videotaped in the highly aerated section of flow centered on

the transition region. Velocity fields were then found for this video. In theory, the

particles were held stationary and should therefore produce zero motion in the velocity

fields. Analysis of the calculated velocity fields indicated that a mean error of 1.0 pixels in

the horizontal direction and 0.8 pixels in the vertical direction per velocity field can be

attributed to the distortional effects of the bubbles. Considering a typical scaling scenario

in the tests conducted, this can be converted to a 0.5 millimeter error in the calculated


There may be some difficulty in applying the same filtering technique to inner surf

zone waves in which the intensity of aeration may be quite high. The focal plane could be

effectively shielded from the camera by an excessive amount of aeration between the focal

plane and the camera. This did not occur for the waves and locations examined within this


A nearly endless list exists for future applications of DPIV to fluid flows and

analysis that can be done on the existing data set. The characteristic bidirectional flow

inherent in water waves results in simple particle seeding scenarios. Unidirectional flow

will carry particles away from the camera's field of view, thus requiring a high number of

particles during experimentation. Presently the techniques described herein are being

applied to the study of vortex development around cylinders in a unidirectional flow.

Other possible areas of current study in coastal engineering to which DPIV could be

applied are flow over a submerged breakwater, the effect of bars on two dimensional

circulation, flow patterns around modeled inlets and granular flow studies. Modifications

to the experimental approach must be made in each case, but the potential benefits (i.e.,

low cost velocity field determination) are substantial.

The current data set can be applied to determine the proper value of the mass flux

increase term, Q, used in the momentum conservation equations. The applicability of

higher order wave theories to surf zone flow can be found be analyzing the instantaneous

velocity field data. The ensemble and time averaged data could also be used to develop

empirical descriptions of surf zone waves if other representations are proved to be

inadequate. The turbulence data could be incorporated into a more complete description

of wave energy dissipation across the surf zone which may ultimately lead to better

predictive capabilities for sediment transport.


The following conclusions may be drawn from the work presented in this paper.

1) Velocity measurements are now possible in the aerated crest of a broken

wave within the transition region through the use of digital imaging and application of

appropriate filtering techniques. The spatial resolution of these velocities are somewhat

affected by the distortional characteristics of the bubbles produced during wave breaking.

However, the errors introduced are on the order of one millimeter per frame and,

considering the fairly coarse resolution of the velocities found with DPIV, are negligible.

2) Digital particle image velocimetry provides an effective alternative to

standard PIV techniques and is expected to improve as technology advances.

3) The use of video for examination of large temporal data sets by ensemble

averaging is the most efficient and economical method currently available for applications

in which the temporal and spatial resolution provided by video imaging are adequate.

4) Turbulent velocity fluctuations can be resolved over the entire water

column through the use of DPIV, although a high seeding density of particles in the crest

region is essential to maintain accuracy.

5) The extension of Thieke's one dimensional model (1992) to include

conservation of angular momentum has provided an effective means of determining the

length of the transition region, although it is still somewhat difficult to accurately predict

the wave height decay. Inclusion of higher-order wave representations and more complete

turbulence measurements within the same model framework will probably improve the

predictive capability.


Table A. 1 Horizontal scaling from pixels to centimeters
found by analyzing the videotaped grid.

Test number Horizontal scaling (pixels /
1B 16.8
2C 19.9
3C 19.1
4C 14.4
6A 14.3

Plots begin on next page



20- ... ....... .......


= 120 pixels/sec
I I I I l 1 /
5 10 15 20 25 30 35
AOI steps (16 pixels/step)


( 20 . . . .
-. / ^ -- -. -- -^ / -/ -/ -/ ^ -
-n - - - - -' - - -r ^- -



-= 600 (pixels/sec)^2
5 10 15 20 25 30 35
AOI steps (16 pixels/step)

Figure A. 1 Wave data from test lB. a) mass flux velocity field and b) turbulent
fluctuation velocity field.

5 10 15 20 25
AOI steps (16 pixels/step)

30 35

5 10 15 20 25 30 35
AOI steps (16 pixels/step)

Figure A.2 Wave data from test 2C. a) mass flux velocity field and b) turbulent

fluctuation velocity field.



| 15


Si* * * i l i

I I | I / I I I I I S I I S 5 -

S- -- / -

----------- -- 120 pixels/sec
-'^ - *' -- - -' -- p s- -
-- -* .- -* -* -' -- -' -^ -' - -* - - -

= 120 pixels/sec

a) . .
2 5. . . .

..* o > i i i ../ / /

20- -* *- - - -
S - .. .. ..




5 10
S= 120 pixels/sec

5 10 15 20 25 30 35
AOI steps (16 pixels/step)



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

..) .. . . . . .
S10 . ..


-= 600 (pixels/sec)A2

5 10 15 20 25 30 35
AOI steps (16 pixels/step)

Figure A.3 Wave data from test 3C. a) mass flux velocity field and b) turbulent

fluctuation velocity field.



- -- -
- ---- -

- -



- -- -- -- ---


- --

=120 pixels/sec

5 10 15 20 25 30 35
AOI steps (16 pixels/step)

5 10 15 20 25
AOI steps (16 pixels/step)

30 35

Wave data from test 6A. a) mass flux velocity field and b) turbulent

fluctuation velocity field.







Figure A.4

.. - .-.- --.. .o o. . o.

-= 600 (pixels/sec)2



B 1 IMGIN2 SVIP MIPX for multiple frame digitization

;; IMAGEIN.MPX -- MIPX for digitizing a series of images from ;;
;; video tape. Tape will be advanced by shelling to DOS and ;;
;; calling a program that informs the EDITLINK 2200/TCG VCR ;;
;; controller card to frame advance the tape.
;; Saves the unfiltered image in a user specified directory. ;;

;; Written by: Kenneth R. Craig ;;
;; Coastal and Oceanographic Engineering ;;
;; University of Florida ;;
;; Written 2/28/94

;; Last revision: 3/22/94

;; this initializes the EDITLINK 2200/TCG
{!}MENUPROMPT ans { {Initialize EDITLINK? (y/n)}

AClose/ReopenImagingBoard(s) NO
^Pause&PromptWhenDone NO
^Reset/RestorePCScreen NO
{!}IFSTREQ {@ans} {y} THEN
!ExecuteDOSCommand.Enter: init

{!}MENUPROMPT dir {) {What directory should the UNFILTERED images be saved
{!}MENUPROMPT dirfil {} {What directory should the FILTERED images be saved

{!}MENUPROMPT numpos { } What is the test number and camera position?}
{!}MENUPROMPT firstframe { } Enter the number of the first frame)
{!}MENUPROMPT lastframe {} {Enter the number of the last frame)

{!}MENUPROMPT ans { } Do you know the time code of the first frame? (y/n)}

{!}IFSTREQ {@ans} {n} THEN
;; this lets the user find the starting tc
"Reset/RestorePCScreen YES
!ExecuteDOSCommand.Enter: findtc

{!}MENUPROMPT hr {} {Time code values: HR }
{!}MENUPROMPT min {} Time code values: MIN }
{!}MENUPROMPT sec {} {Time code values: SEC }
{!}MENUPROMPT frame { } {Time code values: FRAME }

{!}SET i {@firstframe}

{!}WHILE {@i}<={@lastframe}


;; {!}PAUSE 1
;; {!}PAUSE 1
;; {!}PAUSE 1

{!}IF {@i}<10 THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}0000{@i}.tif
{!}IF (({@i}>=10)&({@i)<100)) THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir)\{@numpos}000 {@i}.tif

{!}IF (({@i}>=100)&({@i}<1000)) THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}00{@i}.tif
{!}IF (({@i}>=1000)&({@i}<10000)) THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}0{@i}.tif
{!}IF {@i}>=10000 THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos) {@i}.tif

{!}SET i {@i}+l

;; Have 50 images been saved?
{!}SET mod {@i)%50
{!}IF {@mod}=0 THEN
^Reset/RestorePCScreen NO
!ExecuteDOSCommand.Enter: stopvcr
{!}GOTO filter
{!}LABEL continue 1
{!}GOTO del_tif
{!}LABEL continue
{!}GOTO zip
{!}LABEL continue
{!}GOTO del_fil
{!}LABEL continue
{!}GOTO compute
{!)LABEL continue
{!}GOTO reset
{!}LABEL continue

;; frame advance
^Reset/RestorePCScreen NO
!ExecuteDOSCommand.Enter: frame +{@hr) {@min} {@sec) {@frame}


;; label "filter" which will filter the 50 previous images
{!}LABEL filter
{!}SETj ({@i}-50)


{!}WHILE {@j}<{@i}



{!}IF {@j}<10 THEN
!LoadlmagefromFile.Name: c:\research\unfilter\{@dir)\{@numpos}0000{@j}.tif
{!}IF (({@j}>=10)&({@j}<100)) THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos}000{@j}.tif
{!}IF (({@j}>=100)&({@j}<1000)) THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos}00 {@j.tif
{!}IF (({@j}>=1000)&({@j}<10000)) THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos}0 {@j.tif
{!}IF {@j}>=10000 THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos} {@j}.tif

^Enhance:LowPercentile 90
^Enhance:HighPercentile 99

{!}IF {@j}<10 THEN

!SaveImage, 8BitBinary,toFile.Name:
c:\research\filter\{@dirfil)\{@numpos0000 {@j}.fil

{!}IF (({@j}>=10)&({@j}<100)) THEN

(!}IF (({@j}>=100)&({@j}<1000)) THEN
!SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos}00{@j}. fil

{!}IF (({@j}>=1000)&({@j}<10000)) THEN
!SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos}0{@j}.fil

{!}IF {@j}>=10000 THEN
!SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos} {@j}.fil

{!}SETj {@j)+l

{!}GOTO continued
;; end of filter

;; label del_tif-- deletes all *.tiffiles in the unfilter directory
{!}LABEL del_tif
!ExecuteDOSCommand.Enter: del c:\research\unfilter\{@dir}\*.tif
{!}GOTO continue
;; end of delete

;; label zip -- zips the previous 50 filtered images
{!}LABEL zip
{!}SET k ({@i}-50)
AReset/RestorePCScreen YES

!ExecuteDOSCommand.Enter: zipfil {@dirfil} {@numpos} {@k}
{!}GOTO continue
;; end of zip
** ............. ,, ............................................. ... .
;; label del_fil -- delete the filtered images that have been zipped
{!}LABEL del_fil
^Reset/RestorePCScreen NO
!ExecuteDOSCommand.Enter: del c:\research\filter\{@dirfil}\*.fil
{!}GOTO continue
;; end ofdel fil

;; label compute -- find the new timecode position
{!}LABEL compute

;; Must convert hr min sec and frame from strings to numbers
{!}SET hr {@hr}
{!}SET min {@min)
{!}SET sec {@sec}
{!}SET frame {@frame}

{!}SET frame {@frame}+25

{!}IF {@frame}>=30 THEN
{!}SET num 30
{!}SET frame {@frame)%{@num}
{!}SET sec {@sec}+l

{!}IF {@sec)>=60 THEN
{!}SET num 60
{!}SET sec {@sec}%{@num}
{!}SET min {@min)+l

{!}IF {@min}>=60 THEN
{!}SET min {@min}%{@num}
{!}SET hr {@hr}+l



;; Convert hr back to a string
{!}SET hr {"}{@hr}
{!}SETpos 1
{!}SET len 1
{!}STRSUBSET hr {@hr} {@pos} {@len}

{!}SET len 2

;; Convert min back to a string
{!}SET min {"O}{@min)
{!}STRLENvv {@min}
{!}IF ({@vv}=4) THEN
{!}SET pos 2
{!}SET pos 1
{!}STRSUBSET min {@min} {@pos} {@len}

;; Convert sec back to a string
{!}SET sec {"0}{@sec}
{!}STRLENvv {@sec}
{!}IF ({@vv}=4) THEN
(!}SET pos 2
{!}SET pos 1
{!}STRSUBSET sec {@sec} {@pos} {@len}

;; Convert frame back to a string
{!}SET frame {"0) {@frame)
{!}STRLEN w {@frame}
{!}IF ({@vv}=4) THEN
{!}SET pos 2
{!}SETpos 1
{!}STRSUBSET frame {@frame} {@pos} {@len}

{!}GOTO continue
;; end of compute

;; label reset -- calls c program to reset the VCR
{!}LABEL reset
^Reset/RestorePCScreen YES

!ExecuteDOSCommand.Enter: reset +{@hr} {@min} {@sec} {@frame}
{!}GOTO continue
;; end of reset

B.2 init.c

C program to initialize the EDITLINK 2200/TCG

I --- - - - - - - - - -
Name: INIT.C
Purpose: Initialize the EDITLINK 2200/TCG for future use


#define PORT
#define RESETT
#define MODE
#define COMMAND
#define INITFLAG




/* port address */
/* reset byte */
/* mode byte */
/* command byte */
/* init flag */

int einitcom(void);
void time_delay(void);
Name: main
Purpose: main program module
Parm: "DEMO " at command line
Return: 0

void main()
int c;

puts("Initializing EditLink...");

/* this takes a few seconds */
/* initialize EditLink */

{ /* if error */
printf("Can't initialize EditLink\n");
} /* end of main */
/*-------------------------------- --........ ... .............
Name: einitcom
Purpose: initialize EditLink
Parm: stat = einitcom0

int stat; 0 = error, 1 = OK

Return: 0 = error, 1 = OK
int einitcom(void)
int i;

for(i= 0; i < 3; ++i)

/* send 3 dummy sync chars */

outp(PORT + 1,0);
outp(PORT + 1,RESETT);
outp(PORT + 1,MODE);
outp(PORT + 1,COMMAND);


/* send internal reset */
/* send mode instruction */
/* send command instruction

return(inp(PORT + 1) = INIT_FLAG);
} /* end of einitcom */
/*----- -----------------------

/* get any waiting chars */
/* return 8251 status */

Name: time_delay
Purpose: 1-2 second time_delay
Parm: time_delay0
Return: none

void time_delay(void)
time_t x,y;

x += 2;
do { time(&y); } while(y <= x);
} /* end of timedelay */

/* get system time in seconds */

/* wait */


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