UFL/COEL94/019
DEVELOPMENT OF A DIGITAL PARTICLE IMAGE
VELOCIMETRY SYSTEM WITH AN APPLICATION
TO A NUMERICAL MODEL OF THE BREAKING
WAVE TRANSITION REGION
by
Kenneth R. Craig
Thesis
1994
DEVELOPMENT OF A
DIGITAL PARTICLE IMAGE VELOCIMETRY SYSTEM
WITH AN APPLICATION TO A NUMERICAL MODEL
OF THE BREAKING WAVE TRANSITION REGION
By
KENNETH R. CRAIG
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF
FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA
1994
ACKNOWLEDGMENTS
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 saintlike 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.
TABLE OF CONTENTS
ACKNOWLEDGMENTS .................................................................ii
LIST O F TABLES .................................................................................. vi
LIST OF FIGURES ...............................................................................vii
LIST OF SYM BOLS ............................................................................ x
A B STR A C T ................................................ ........................................ xii
CHAPTERS
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
3 EXPERIMENTAL APPARATUS, PROCEDURES AND DATA
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
APPENDICES
A PLOTS OF TIME MEAN MASS FLUX AND TURBULENT
FLUCUTATION VELOCITY FIELD DATA .................... 73
B IMAGE DIGITIZING, FILTERING AND FILE
COMPRESSION PROGRAMS ...................................... 78
C IMAGE PROCESSING M FILES FOR MATLAB ............. 101
D WAVE DATA STATISTIC ANALYSIS M FILES
FOR M ATLAB .................................................................. 106
R E FER EN CE S .......................................................................................... 112
BIOGRAPHICAL SKETCH ................................................................. 115
LIST OF TABLES
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
LIST OF FIGURES
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
nonflow data included and b) only flow related data
included. ........................................................................... 51
Figure
5.5 Comparison of ensemble, timeaveraged 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
page
Figure
paMe
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
LIST OF SYMBOLS AND ABBREVIATIONS
a, P
T1
P
g, fg
*
AOI
b, t
CCD
DPIV
FFT
g
h
H
k
LSV
m,n,k,l,u,v
n
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
conditions
charge coupled device
digital particle velocimetry
fast Fourier transform
gravitational acceleration
water depth
wave height
wave number
laser speckle velocimetry
indices
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
DEVELOPMENT OF A
DIGITAL PARTICLE IMAGE VELOCIMETRY SYSTEM
WITH AN APPLICATION TO A NUMERICAL MODEL
OF THE BREAKING WAVE TRANSITION REGION
By
KENNETH R. CRAIG
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.
CHAPTER 1
INTRODUCTION
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 hotfilm anenometry, and hinders typical particle tracking
methods. It was thought that a method employing video analysis with its inherent filtering
2
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 inhouse. 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)
BREAK TRANSITION
POINT POINT
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.
CHAPTER 2
LITERATURE REVIEW
Introduction
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 DPIVlike 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 nonintrusive, 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 optomechanical 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 subsections 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)
(2.1)
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 crosscorrelation between the AOI's.
The crosscorrelation 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)
ke I,0 k~ = 1=
Applying equation 2.4 to equation 2.1 and neglecting noise, the following relationship is
found
/fg(m, n) = E[f(m, n),f(m, n) s(m, n)] (2.6)
or
/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
considered.
Willert and Gharib (1991) decreased the required processing time by using the
mathematical definition of crosscorrelation in the frequency domain
(fg(U, v) = F* (u, v) x G(u, v) (2.8)
11
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
crosscorrelation 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 subpixel 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
12
255
128
6e
s 21
2 24 tx1
9 g91
C)25
L20
r 6e
9%
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).
13
directions. The distances from the origin to the location of the maxima of these parabolas
determine the displacement vector to subpixel 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 crosscorrelation 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 mid1980's to determine fluid flow
characteristics. A quasidigital 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, nearbreaking 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 xdirection
+ 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.
18
Thieke (1992) has presented a onedimensional 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 depthvarying wave induced radiation stress and s', is the
depthvarying 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,
respectively
Sga2k gHk
S2aH 8a (2.13a)
ga2k gH2k
u2 2ahr 8ah (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.
CHAPTER 3
EXPERIMENTAL APPARATUS, PROCEDURES
AND DATA ANALYSIS TECHNIQUES
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 setup and wave height distributions. The
following will describe the experimental setup 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 6020 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.
Ninetyfive 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
point.
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 WV5470 high
resolution gray scale video monitor, a Panasonic AG1970 superVHS 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 superVHS 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
opened.
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 superVHS 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
SPARCLX 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
necessary.
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
frequency.
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 shutofffeature of
the Panasonic AG1970. 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 magnetooptical (MO) disk in
compressed format. The MO disk can store over 600 megabytes of data and currently
32
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
velocities.
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.
CHAPTER 4
TRANSITION REGION MODEL
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. LonguetHiggins (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,
36
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 )dztb (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,
respectively.
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 sa =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
39
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
form.
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
Hb
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]}
(4.9)
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)
h
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
(4.12)
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 =
(4.14)
H H+ +3+ *(a2 + 2ab+ b2) +Khb *A
I 4 hL 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
Tn/
II = p(u2 w2)dt for h
0
13 = p(u2 2)dt for << (4.15 b)
0
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)
H
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
(4.18)
Ih* 1 L( 2+ 12 h, ) (a 2 +2ab +b2)}
16 16h 128h ha)+ 8
2 i
Model 2
{~* i (28 )2] + H4
16 16128
(4.19)
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.
CHAPTER 5
RESULTS
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
employed.
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
0.5
0.4
0.3
0.2
0.1
0
11 12 13 14 1i 16 17 18 19 20
Distance from wavemaker (m)
b)
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)
(sec)
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 magnetooptical 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
49
... "
.7 ._ F 
I . Q 3 '_ P 
C I rt 1O Ii R
wir
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
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
51
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 nonflow 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) * .
25
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)
b)
   Z Z Z  
. . . . . .
10
5
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
measurements.
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
53
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
parameterizations.
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
7
 / / / / /
   
'sec
/ 5 I / l '/ l / s l / / I/
l \ I / l I' / J a / /I\\ /
 ////// //////
/  / / / / / / i 
111 / I /
~
I \ I I ia
/I / //
//// / /
  
a) 26
24
22
S20
e18
14
12
10
b) 26
24
22
S20
a is
IX16
14
12
10
0) 26
24
22
20
s18
14
12
10
0 5 10 15 20 25
AOI steps (16 pixels/step)
30 35
Figure 5.5 Comparison of ensemble, timeaveraged 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 . *. *.
r
*r
*,
i
I
SI I I I I I I
2.
'/
.1.
1'.
=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
22k
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
displacements
Sum of negative 6.217 6.195 5.279 6.116 6.512 6.384
displacements
Ratio ofneg to pos 1.126 1.128 0.948 1.141 1.253 1.117
Average ratio 1.119
I I
c

2.
2,
262 /
24
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
57
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.
2.5
2 .0 ...............
1.5
1 .0 .............................. ........
oTest
0 .5 ............... ........ 5.......... ......... .rest
aTest
Test
0.0
0.00 0.02 0.04 0.06 0.0f
rms//gqh
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.
0.105
0.100
0.095
0.090
0.085
0.080
0.075
0.0
20
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
................. ................... ..................................... .............................
y=0.2204x+0.07
. ...... ..
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 onedimensional 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
depth.
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
0.008
N
1,
en
0.002 . .....
0.000
0.000 0.002 0.004
0.014
r
0.010
0.008
0.004
0.002
0.006 0.008 0.010 0.012
H /gT2
b
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
(1979)
0.000 V
0.000
0.016
0.008
0.006
0.004
0.002
0.000
0.
0.006 0.008 0.010 0.012
H /gT2
b
0.012
0.006
0.004
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
(1979)
000 0.002 0.004
0.010 j A 1 ~
0.006
0.002
000 0.002 0.004 0. 00 0.008 0.010 0.012
H /gT2
b
0.014
0.010
0.008
0.004
0.002
0.000
0.0
00
0.004
0.008
0.012
0.016
h /gT2
b
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
(1979)
All 3 cases o
this line / 6 \
... .. .. .. .. .. . ..... . .... .o ...............
/ Oata of Hansen and
S/0 Svendsen (1979)
. ...... ..... ...
T
0.002 0.004 0.006 0.008 0.010 0.012
H /gT2
b
0.008 0.012
h /gT2
b
0.016
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.
0.010 
0.008
0.006
0.004
0.002
0.000
0.000
0.014
0.012
0.008
0.006
0.004
0.002
0.000 v
0.000
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
69
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.
Recommendations
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
displacements.
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
paper.
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.
Conclusions
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 higherorder wave representations and more complete
turbulence measurements within the same model framework will probably improve the
predictive capability.
APPENDIX A
PLOTS OF TIME MEAN MASS FLUX AND
TURBULENT FLUCUTATION VELOCITY FIELD DATA
Table A. 1 Horizontal scaling from pixels to centimeters
found by analyzing the videotaped grid.
Test number Horizontal scaling (pixels /
cm)
1B 16.8
2C 19.9
3C 19.1
4C 14.4
6A 14.3
Plots begin on next page
74
a)
25
20 ... ....... .......
,5
= 120 pixels/sec
I I I I l 1 /
5 10 15 20 25 30 35
AOI steps (16 pixels/step)
b)
25
( 20 . . . .
. / ^  .  ^ / / / / ^ 
n     '   r ^ 
<10
5
= 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.
20
I0
CD
 15
L1
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  .. .. ..
.__.,._._.
25
15
5 10
S= 120 pixels/sec
5 10 15 20 25 30 35
AOI steps (16 pixels/step)
b)
25
_0
. .. .. . . . . . . .
..) .. . . . . .
S10 . ..
5
= 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.
I I

  
  
 
I I I
I I I I I S I I
,,

    
I I I
'I
 
=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.
20
CL
0
x
T15
20
C)
.I
S15
10
Figure A.4
..  .. .. .o o. . o.
= 600 (pixels/sec)2
I I
APPENDIX B
IMAGE DIGITIZING, FILTERING AND
FILE COMPRESSION PROGRAMS
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)}
>DOSEscape
AClose/ReopenImagingBoard(s) NO
^Pause&PromptWhenDone NO
^Reset/RestorePCScreen NO
{!}IFSTREQ {@ans} {y} THEN
!ExecuteDOSCommand.Enter: init
{!}ENDIF
{!}MENUPROMPT dir {) {What directory should the UNFILTERED images be saved
in?}
{!}MENUPROMPT dirfil {} {What directory should the FILTERED images be saved
in?}
{!}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
>VideoDigitize/Display
!Digitize
;; this lets the user find the starting tc
>DOSEscape
"Reset/RestorePCScreen YES
!ExecuteDOSCommand.Enter: findtc
{!}ENDIF
{!}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}
{!}MESSAGE {DIGITIZING IMAGE } {@i}
>VideoDigitize/Display
!Digitize
;; {!}PAUSE 1
!Display
;; {!}PAUSE 1
!Digitize
;; {!}PAUSE 1
!Display
>ImageFileLoad/Save
>FileLoad/Save,TIFFFormatw.AOI
{!}IF {@i}<10 THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}0000{@i}.tif
{!}ENDIF
{!}IF (({@i}>=10)&({@i)<100)) THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir)\{@numpos}000 {@i}.tif
{!}ENDIF
{!}IF (({@i}>=100)&({@i}<1000)) THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}00{@i}.tif
{!}ENDIF
{!}IF (({@i}>=1000)&({@i}<10000)) THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}0{@i}.tif
{!}ENDIF
{!}IF {@i}>=10000 THEN
!SaveImagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos) {@i}.tif
{!}ENDIF
!ImageAreaofInterest:FullImage
{!}SET i {@i}+l
;; Have 50 images been saved?
{!}SET mod {@i)%50
{!}IF {@mod}=0 THEN
>DOSEscape
^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
{!}ENDIF
;; frame advance
>DOSEscape
^Reset/RestorePCScreen NO
!ExecuteDOSCommand.Enter: frame +{@hr) {@min} {@sec) {@frame}
{!}ENDWHILE
{!}EXIT
;; label "filter" which will filter the 50 previous images
{!}LABEL filter
{!}SETj ({@i}50)
>ImageFileLoad/Save
{!}WHILE {@j}<{@i}
{!}MESSAGE {FILTERING IMAGE }{@}
>FileLoad/Save,TIFFFormatw.AOI
{!}IF {@j}<10 THEN
!LoadlmagefromFile.Name: c:\research\unfilter\{@dir)\{@numpos}0000{@j}.tif
(!}ENDIF
{!}IF (({@j}>=10)&({@j}<100)) THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos}000{@j}.tif
{!}ENDIF
{!}IF (({@j}>=100)&({@j}<1000)) THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos}00 {@j.tif
{!}ENDIF
{!}IF (({@j}>=1000)&({@j}<10000)) THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos}0 {@j.tif
{!}ENDIF
{!}IF {@j}>=10000 THEN
!LoadImagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos} {@j}.tif
{!}ENDIF
!ImageAreaoflnterest:FullImage
>ImageProcessing
>SimplePixelOperations
^Enhance:LowPercentile 90
^Enhance:HighPercentile 99
!EnhanceContrast:GivenHistogramPercentiles
!ImageAreaofInterest:FullImage
>ImageFileLoad/Save
>FileLoad/Save,X/YFormatw.AOI
{!}IF {@j}<10 THEN
!SaveImage, 8BitBinary,toFile.Name:
c:\research\filter\{@dirfil)\{@numpos0000 {@j}.fil
{!}ENDIF
{!}IF (({@j}>=10)&({@j}<100)) THEN
!SaveImage,8BitBinary,toFile.Name:
c:\research\filter\{@dirfil)\{@numpos}000{@j}.fil
{!}ENDIF
(!}IF (({@j}>=100)&({@j}<1000)) THEN
!SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos}00{@j}. fil
{!}ENDIF
{!}IF (({@j}>=1000)&({@j}<10000)) THEN
!SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos}0{@j}.fil
{!}ENDIF
{!}IF {@j}>=10000 THEN
!SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos} {@j}.fil
{!}ENDIF
!ImageAreaofInterest:FullImage
{!}SETj {@j)+l
{!}ENDWHILE
{!}GOTO continued
;; end of filter
;; label del_tif deletes all *.tiffiles in the unfilter directory
{!}LABEL del_tif
{!}MESSAGE {DELETING *.tif}
>DOSEscape
!ExecuteDOSCommand.Enter: del c:\research\unfilter\{@dir}\*.tif
{!}GOTO continue
;; end of delete
;; label zip  zips the previous 50 filtered images
{!}LABEL zip
{!}MESSAGE {ZIPPING FILTERED IMAGES}
{!}SET k ({@i}50)
>DOSEscape
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
(!}MESSAGE {DELETING FILTERED IMAGES}
>DOSEscape
^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
{!}MESSAGE (COMPUTING NEXT TIMECODE POSITION}
;; 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
{!}ENDIF
{!}ENDIF
{!}ENDIF
;; 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
{!}ELSE
{!}SET pos 1
{!}ENDIF
{!}STRSUBSET min {@min} {@pos} {@len}
;; Convert sec back to a string
{!}SET sec {"0}{@sec}
{!}STRLENvv {@sec}
{!}IF ({@vv}=4) THEN
(!}SET pos 2
{!}ELSE
{!}SET pos 1
{!}ENDIF
{!}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
{!}ELSE
{!}SETpos 1
{!}ENDIF
{!}STRSUBSET frame {@frame} {@pos} {@len}
{!}GOTO continue
;; end of compute
;; label reset  calls c program to reset the VCR
{!}LABEL reset
>DOSEscape
^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
*
#include
#include
#include
#include
#define PORT
#define RESETT
#define MODE
#define COMMAND
#define INITFLAG
0x40
Ox4E
0x220
0x37
5
/* 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...");
if(!einitcom0)
/* this takes a few seconds */
/* initialize EditLink */
{ /* if error */
printf("Can't initialize EditLink\n");
exit(0);
}
exit(0);
} /* 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);
time_delay();
}
outp(PORT + 1,RESETT);
outp(PORT + 1,MODE);
outp(PORT + 1,COMMAND);
*/
time_delay0;
time_delay0;
time_delay0;
/* send internal reset */
/* send mode instruction */
/* send command instruction
inp(PORT);
return(inp(PORT + 1) = INIT_FLAG);
} /* end of einitcom */
/* 
/* get any waiting chars */
/* return 8251 status */
Name: time_delay
Purpose: 12 second time_delay
Parm: time_delay0
Return: none
void time_delay(void)
{
time_t x,y;
time(&x);
x += 2;
do { time(&y); } while(y <= x);
} /* end of timedelay */
/* get system time in seconds */
/* wait */

