Citation |

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

Full Text |

UFL/COEL-94/019
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 saint-like patience. The other members of my committee, Dr. Robert G. Dean and Dr. Daniel M. Hanes, provided both inspiration and technical assistance. Dr. Dean is without a doubt the "Dean" of coastal engineering and I consider myself extremely fortunate to have had the opportunity to interact with him. Dr. Hanes, in addition to being a solid left fielder, allowed me to infiltrate his group and temporarily use an extensive amount of equipment. My officemates, Eric Thosteson, Mark Gosselin and Tom Copps, aided me in keeping my sanity. I would also like to thank Chris Jette for giving me a defense date to shoot for. Paul Miselis and Al Browder accompanied me to Market Street on more than one occasion to visit with Sam Adams. The staff at the Coastal and Oceanographic Engineering Laboratory, especially Jim Joiner, provided me the opportunity to get involved in the department during my undergraduate years. The memories I have of the lab will remain with me forever. My family, Ken Sr., Pam, Doug and Sandy, always was and is the bedrock of my life. I could not have come close to achieving as much as I have and would not have such an optimistic outlook to the future without them. Finally, my bride Kimberly has been a rock. She has planned both a wedding and a honeymoon while her groom was tucked away in Weil Hall, offering little help. For her patience and love I am eternally grateful. TABLE OF CONTENTS ACKNOWLEDGMENTS .....................................................i LIST OF TABLES ................................................................. vi LIST OF FIGURES................................................................ vii LIST OF SYMBOLS............................................................... x ABSTRACT........................................................................ xii CHAPTERS 1 INTRODUCTION................................................. 1 2 LITERATURE REVIEW ......................................... 5 Introduction........................................................ 5 Evolution of Velocity Field Measuring Techniques .......5 Laser Speckle Velocimetry ...................................... 5 Particle Image Velocimetry ........................................ 6 Digital Particle Image Velocimetry.............................. 7 Theory Development................................................ 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 Data Processing.................................................... 29 Wave Gauge Data ......................................... 29 Image Digitization......................................... 30 Image 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 RESULTS........................................................... 45 Wave Data ......................................................... 45 Velocity Field Results ............................................. 47 Turbulence Parameterization..................................... 52 Hansen and Svendsen Experimental Wave Data................ 56 Model Performance................................................ 60 Recommendations ................................................. 69 Conclusions ........................................................ 72 APPENDICES A PLOTS OF TIME MEAN MASS FLUX AND TURBULENT FLUCUTATION VELOCITY FIELD DATA ................. 73 B IMAGE DIGITIZING, FILTERING AND FILE COMPRES SION PROGRAMS ................................. 78 C IMAGE PROCESSING M FILES FOR MATLAB ....... 101 D WAVE DATA STATISTIC ANALYSIS M FILES FOR MATLAB.................................................... 106 REFERENCES..................................................................... 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 wavemnaker 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 image................................................. 49 5.3 Example of an instantaneous velocity field found using the DPIV process. (From test 6C, field number 536) ........ 50 5.4 A typical ensemble time averaged velocity field with a) all non-flow data included and b) oniy flow related data included........................................................... 51 Figure pn 5.5 Comparison of ensemble, time-averaged velocity fields using a) 30 cycles, b) 50 cycles, with c) the difference between a and b. (Data from test 4C).......................... 54 5.6 Enlargement of columns 15 through 20 of Figure 5.5b indicating conservation of mass................................. 55 5.7 Typical turbulent velocity fluctuation field (data from test 4C). Note that the turbulence values are squared resulting in all values oriented in the positive direction .................. 56 5.8 Profiles of dimensionless u'rrms 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,. at the transition point as a function of the surf similarity parameter. (m--each 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 1B. a) mass flux velocity and b) turbulent velocity field ........................................ 74 p-ne Fip-ure Mae 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 T1 P Of, (Dfa 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 i 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 Velocimnetry (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 hot-film 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 in-house. An injection device was designed to evenly distribute the neutral particles over the field of view. A shield to exclude ambient light combined with a light source capable of being focused into a plane were constructed to enable appropriate lighting levels during taping. The experimental setup is discussed in further detail in Chapter 3. The video was then digitized by an automated computer program. Each pair of frames was digitally analyzed through a series of programs that result in horizontal and vertical displacement fields over the field of view. Ensemble averaging of these velocity fields produced values for several derived quantities that have been applied to a model of the transition region. The transition region is defined as the location immediately after wave breaking where setup is constant and wave height rapidly decays. The zone ends when setup begins to increase and wave height decreases more slowly. Figure I shows a schematic of the transition region. Definition Sketch of Transition Zone (Not to scale) BREAK TRANSITION POINT POINT Figure 1. 1 Definition sketch of the transition region 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 DPIV-like processes are also addressed. The second area of discussion will focus on past developments in transition region modeling. The model proposed by Thieke (1992), which is the basis of the model presented in this paper, is discussed in detail as are the limitations of current modeling techniques. Evolution of Velocity Field Measuring Techniques Laser Speckle Velocimetry Complete representations of instantaneous velocity fields can be found by analyzing images of markers in fluid flows. One such technique is laser speckle velocimetry (LSV), which originated in the study of solid mechanics (Archbold and Ennos, 1972) and was first applied to fluid flows by Barker and Foumey (1977). Essentially, a plane section of a flow containing particles is illuminated, typically by laser light. The light reflected by these particles produces interference patterns called speckles which are captured on film. The light is usually pulsed, leaving several exposures of the flow on the film. The seeding density of the particles in LSV must be extremely high. The theory is that because of this high density, individual particles cannot be resolved. The speckle pattern is produced by interference of the reflected light caused by the overlapping of the randomly spaced particles. Processing occurs by interrogating a series of small sections of the photographic negative with laser light. The light that passes the negative is optically Fourier transformed with a special lens, producing "Young's finges". 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 Veloci=mr Adrian (1984) and Pickering and Halliwell (1984) found that in practice the particle density required for LSV is difficult to achieve. The more likely scenario is a density in which individual particles are discernible. In this case a true speckle pattern is not present. Instead, the particles themselves are tracked. In this case, the process is called particle image velocimetry (PIV). Adrian (1989) further divided the class of PIV into high and low density PIV modes. In low density PIV, the probability of overlapping particles is quite low. In fact, individual particles can be tracked by means of streak analysis. If the recording film is exposed over a longer time interval (i.e., an extended pulse of the laser) the particles produce streaks. The low particle density results in a low probability that the streaks will cross. Displacements can be determined by manually establishing the endpoints of the streaks. This method is often called. particle tracking velocimetry (PTV). The complexities involved in tracking multiple particles make any automation of this process quite difficult. The particle densities designating high density PIV fall somewhere between PTV and LSV. There is a high probability that several, individually identifiable particles will be present in the small interrogated section. However, the higher density (compared to PTV) makes tracking individual particles difficult. Once again the statistically determined average displacement of an area is determined. The images are processed in a manner similar to LSV by optically performing a two dimensional Fourier transform and interpreting the Young's fringes. However, the fringes now identify the displacement of the particles as a group instead of the speckle pattern interference displacement. Digital Particle Image Velocimetry Digital particle image velocimetry (DPIV) is a non-intrusive, velocity measuring system that is based on the frequency domain analysis of pixel intensity distributions in digital images of neutrally buoyant particles in a flow. It holds several strong advantages over similar velocity field measurement techniques such as laser speckle velocimetry, particle image velocimetry and point velocity measurements such as hot film and laser doppler anemometry. Theory Development Willert and Gharib (1991) describe a system that digitally performs a process similar to the opto-mechanical method employed in particle image velocimetry. Neutrally buoyant particles are introduced into a fluid flow and video images are recorded and digitized. Sequential digital images (each frame capturing a single instance in time) are analyzed using frequency domain techniques. After digitizing, small sections of each image, called areas of interest (AOI's), are compared. The AOIs are at identical locations on each consecutive image. A spatial shift caused by the fluid flow may be observed from one AOI to the next. Considering the sub-sections together as a system, the first AOI, f(m,n,t=T), may be considered the input and the second AOI, g(m,n,t=T+AT), the output. The transition between them is caused by a spatial displacement function, s(m,n), as well as any signal noise, d(m,n). The desired value is s(m,n) which will give the average displacement over the area represented by the AOI's. The system may be stated mathematically as g(m, n) = [f(m, n) s(m, n)] + d(m, n) (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, 1- n)f(k, 1) + d(m, n) (2.2) where s(m,n) becomes a Dirac delta function which has moved from the origin by the average displacement of the particles in the AOI's. If noise is neglected, the displacement function could be found by first transforming equation 2.1 to the frequency domain g(m, n) = f(m, n) s(m, n) <= G(u, v) = F(u, v)S(u, v) (2.3) where G(u,v), F(u,v) and S(u,v) are the Fourier transforms of g(m,n), f(m,n) and s(m,n) respectively. Then S(u,v) is solved for and the result is inversely transformed back to the spatial domain. Willert and Gharib found this method to be quite sensitive to noise effects and sought a more effective technique. Their alternative method employs a spatial cross-correlation between the AOI's. The cross-correlation function, fg, can be defined as fg (m, n) = E[fm, n), g(m, n)] (2.4) or discretely as I f(k, )g(k + m, l+ n) Ofg(m,n) = (2.5) 1 1 f(kj 1) J1g(k, 1 l-- I- k---= 1Applying equation 2.4 to equation 2.1 and neglecting noise, the following relationship is found Ofg(m, n) = Ef(m, n),f(m, n) s(m, n)] (2.6) or Ofg(m, n) = df(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 cross-correlation in the frequency domain 4fg(u, v) = F* (u, v) x G(u, v) (2.8) 11 where F* is the complex conjugate of the Fourier transform of f(mn) and G(u,v) is the Fourier transform of g(mn). They employed fast Fourier transforms to further reduce processing time. After (D is found, an inverse FFT is performed, thus returning the data to the spatial domain. Essentially the process tries to match the pattern found in the first AOI with that in the second after the pattern has been shifted. The location of the peak value of the cross-correlation function represents the point that best correlates the particle positions in each AOI. The shape of the peak value is dependent upon the level of noise present. Large amounts of noise tend to broaden the peak. Smaller peaks are also present due to some correlation between incorrect particle pairings. However, the maximum value found in 0 ,, indicates the best correlated displacement over the AOI. Noise is generated by particles moving out of the AOI laterally, vertically or normal to the plane of view. The assumption is that the AOI is large enough that a majority of the particles in the first AOI appear in the second. Figure 2.1 shows a typical example of the results of the application of the correlation technique for particles settling downward. Two different centroiding techniques may then be employed when examining the peak. A center of mass method (Kimura and Takamori, 1986) provides one pixel accuracy but is dependent upon the threshold value used to determine the limits of the peak. The method used by Willert and Gharib provides sub-pixel accuracy. In controlled experiments, they found a minimum uncertainty value of 0.01 pixels. However, in practice the uncertainty may be an order of magnitude higher. Parabolic curves are fit through the peak and each of the two neighboring data points in both the vertical and horizontal 12 255 -fi 18 120 6 6 tx8 4222 el s i 2 24 x1 9 g4 1 9 8 X P t x t r9 121 6e6 a bt im 2 and 222 JLO c255 J18S r 60 1% in~~~ th spaia doai. The maxmu peki2)iniae22dslcmn oxe ls i % 191 98 Xe P et Figure 2.1 Graphical representation of pixel intensities within an area of interest on a) image I 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 sub-pixel accuracy. By dividing the displacement vector by the known time difference between frames, the velocity vector is found. The nature of the FFT limits the maximum displacement that can be determined by this process. The Nyquist criterion, the largest discernible frequency due to discrete sampling, limits this displacement to one half of the AOL 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 AOL dimensions. The optimal size of the AOL is thus a result of reconciling two conflicting goals. First, the AOL must be large enough that one third of its size will sufficiently encompass any expected displacements. If the AOL is too small, many displacements will be lost. Second, the AOL must be small enough to limit any velocity gradients present within the AOL 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 A(x) = Io exp [ 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 AO's causes neighboring velocity vectors to not be truly independent of one another. However, Willert and Gharib state that the incorporation of additional data in each AOI does "reflect- individual measurements because each sample incorporates a different set of particle images given a sufficiently high seeding density. In analogy to time series analysis, the spatially shifted cross-correlation is similar to a moving average." The application of this process to breaking waves used a 32 x 32 pixel AOI (approximately 2 cm x 2 cm in a typical view) with a spatial shift of one half the interrogation window, or 16 pixels (approximately 1 cm). Comparison of DPIV with Other Methods DPIV employs single exposure video images as a time series. The location of the particles in each image of the time series is known and therefore, the direction of particle displacements can be found. The seeding density of DPIV is lower than that for LSV and comparable to PIV. This makes the introduction of the particles and clean up a comparatively simple process. PIV and LSV also require the additional steps of film development and optical processing using a special lens. DPIV is conducive to automation to the extent that after video taping is complete, the processing of a large number of images can begin almost immediately. The cost savings of DPIV are substantial in that the use of a high power laser is unnecessary. The savings are enhanced by the fact that in addition to removing the added cost of the laser itself (typically more expensive than the entire DPIV system), the additional safety consideration inherent in laser operations need not be addressed. There is also no need for any special lenses or translation platforms needed to position an image negative for laser inspection. However, DPIV does have some drawbacks. The spatial and temporal resolution of the velocity fields are quite low when compared to PIV or LSV. These methods can investigate tiny portions of the flow due to the high seeding densities and the fine resolution available with film. The DPIV resolution is currently limited by the state of video technology. Super VHS provides over 400 lines of resolution, yet this is dwarfed by the capabilities of film. Images could be stored digitally directly from a CCD camera at a higher spatial resolution but the storage requirements would be immense. The -second limiting factor of video is the relatively slow frame speed of 60 frames per second. PIV and LSV can take advantage of the high speed at which a laser can be pulsed, providing higher temporal resolution. Faster frame rates would allow smaller AOI's to be used since the particles would move proportionally shorter distances. As video technology advances in the future, these limitations will be addressed. Recent Applications of PIV and DPIV Ply has been used extensively since the mid-1980's to determine fluid flow characteristics. A quasi-digital process involving optical Fourier transformations and correlations in the frequency domain and digital inverse FFT's of the results has been applied with good results (Powell et al., 1992; Greated et al., 1992; Morrison and Greated, 1992). This process still includes the extra step of film processing which is absent from DPIV. Due to the recent development of DPIV there are a limited number of examples of its use. Willert and Gharib (1992) directly applied this method to the investigation of time dependent vortex ring evolution. Video, with its inherent capability to efficiently store extensive quantities of data in the form of large time series, has been used in several other investigations (Sakakibara et al., 1993 and Kimura and Takamori, 1986) which analyzed statistically averaged flow quantities. However, the correlation process described above has typically been replaced with a procedure that calculates correlation coefficients in the spatial domain by artificially relocating the first AOI to different locations about the origin of the second AOL. Transition Region Modeling The transition region can best be described as the area in which waves undergo a rapid transformation in wave height while maintaining a nearly constant mean water level. The region begins at the breakpoint and extends shoreward to the transition point, after which the mean water level begins to rise and wave heights decrease less rapidly (Svendsen, 1984). Within the transition region, a rapid reorganization of the wave motion from an unsteady, asymmetric, near-breaking waveform to a flow resembling a moving turbulent bore (Svendsen and Madsen, 1984) occurs. It has been suggested (Thieke, 1992) that this is analogous to jet flows, i.e., the transition region representing the "zone of flow establishment" and the inner surf zone representing the "zone of established flow". Svendsen (1984) and Basco and Yamashita (1986) have noted that a "paradox" exists within the transition region. This can be seen when examining the simplified horizontal momentum balance for waves propagating in the positive x-direction ; pg(h + f) d 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 (SJc should be balanced by the gradient of the setup (ij). S.c can be shown to be a function of wave height and therefore, from the definition of the transition region, is rapidly decreasing. Setup (Ti) 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 one-dimensional model that compressed the transition region to a "shock" to compensate for the rapidly varying flow present in the transition region. Depth integrated momentum and mass flux were conserved. The infinitesimally small horizontal length represented by the shock allows bottom friction to be neglected. As a result, the horizontal linear momentum conservation can be reduced to pi2dz+ f f p,2dz+ (+sidz (2.11) 1h -h (S+ b -h (S+ (211 where s".x is now the depth-varying wave induced radiation stress and s'. is the depth-varying fluctuating turbulent Reynolds stress. A Reynolds type decomposition of the instantaneous velocity u = T1 + 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 - ga2k gHk 2rtH i- (2.13a) ga2k gH2k 2 2ah, 8ahr (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 IP + (2n- =)] [Q2( 3H'+ L(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 AM) 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 usin g a capacitance type wave gauge. Six separate tests were run: tests 1 to 3 in approximately 30 centimeters of water and tests 4 to 6 in approximately 23 centimeters of water. For each test at a specific water depth, the wave periods were varied from 0.85 to 2.13 seconds. The video tape and wave data were then analyzed to determine velocity fields, mean water level set-up and wave height distributions. The following will describe the experimental set-up and data analysis techniques. All video imaging was done in black and white rather than color because of the higher spatial resolution and tangibly greater light sensitivity that black and white provides. The cost of black and white video equipment is also substantially lower than similar quality color equipment. The advantage of black and white imaging is realized during processing because DPIV relies on pixel intensity values to distinguish particles. Color does not offer any advantages over black and white for this process. The theory behind the DPIV method is discussed in detail in chapter 2. Experimental Setup Multifunctional Wave Flume The internal wave flume is approximately 28 meters (90 feet) long, 0.58 meters (2 feet) wide and 1.4 meters (4.5 feet) deep. It is equipped with both a flap type and piston type wave maker. Only the smaller Seasim RSP 60-20 Modular Piston Wavemaker was used during the experiments. This unit is computer controlled through a central electronic system with feedback ioops 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 fiat bottom portion of the flume and the second (B) approximately 0.5 meters after the beginning of the slope. Ninety-five stations (C to SSSS) were then set up every 5 cm beginning 2.5 meters from the beginning of the slope and extending shoreward beyond any expected data acquisition point. Figure 3.1 Diagram of the multiflunctional wave tank with enlargements of the piston wavemaker and capacitance wave gauge. Video equipment used at the experiment site included a Panasonic W-5470 high resolution gray scale video monitor, a Panasonic AG- 1970 super-VHS recording VCR, and a Vicon VC2400 high resolution black and white CCD video camera with variable shutter speed. The camera provides 570 lines of horizontal resolution (which is actually above super VHS quality) and requires only 0.2 lux minimum illumination. Shutter speeds vary from continuously open to 1/10,000 of a second. A shutter speed of 1/1000th of a second was used to minimize blurring of the particles while still allowing sufficient light to pass through the camera lens for adequate videotaping. Both zoom and wide angle lenses were available for use. The choice of lens magnification depended upon the wave characteristics at each particular camera location. The goal was to fill the view with as much of the flow field as possible to maximize resolution during processing. All video was recorded on master quality double coated super-VHS video tapes. Ambient light was controlled by placing a light shield made of flexible polyurethane coated nylon fabric around the position of the video camera and flume. The light shield covered three panes of glass and could be positioned anywhere along the flume. Removable side panels on the light shield provided access to the camera when necessary. The moveable chassis was equipped with the following items: a light source, a cylindrical focusing lens and a dispenser for the neutrally buoyant particles. The light source was a 500 watt electric bulb enclosed in a wooden box with a slit approximately 2 mm wide cut in the bottom. The slit was aligned with the long axis of the flume (i.e., direction of wave propagation) and allowed only a portion of the light from the bulb to escape the box in the form of a quickly dispersing plane (see Figure 5.2 for a schematic of the experimental apparatus). The light is then passed through the cylindrical lens and focused into a tight plane perpendicular to the bottom of the flume. With the lens approximately I meter above the flume bottom, the focused light diffused to a width of I 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 MJ~z DX2 cpu. The computer also contained an EditLink 2200/TCG VCR controller card and a one megabyte frame grabber board as accessories. An image processing software package with macro language capabilities was used to digitize and filter the images. Several C language programs were written to control the VCR through the VCR controller card. The same super-VHS recording VCR and high resolution monitor were used during the digitization process. Processing of the velocity fields -was carried out for the most part on a Sun SPARC-LX workstation. The 486 microcomputer is capable of processing the velocity fields at a speed about 33% slower than the Sun workstation, so it was used to process only a small portion of the velocity fields. Matlab by the Math Works, a matrix manipulation software package (also with macro language capabilities), was used to process the images on both the 486 microcomputer and the Sun workstation. All analysis of the velocity fields was done on the 486 microcomputer using this software package (see appendices for the source code of the macros). Experimental Procedures The wave flume was filled to the appropriate water level and allowed to settle, after which a water depth reading was recorded from the flat portion of the flume. The wave maker was started, generating waves at the designated frequency. These waves were observed to determine the break point position and initial camera location. Wave gauge data were recorded at station A for a deep water reading, B for initial shoaling data, and any appropriate stations outside and within the surf zone for setup and shoaling data. The number of camera positions to be established for each test depended upon the field of view that could be achieved. The area from just outside the breakpoint to inside of the transition point needed to be taped for application to the transition region numerical model. The camera was placed within the light shield at the proper location and the position of the center of the field of view along the flume was recorded. Next, the calibration grid was placed along the long axis of the flume in the field of view. The grid was illuminated using the light source without the focusing lens. This allowed the grid to be filmed while minimizing any shadows produced by the grid. It was found that if the cylindrical lens was used, the shadows were too intense to provide any readings from the grid. This also allowed the camera to be focused to the proper location at the tank centerline. The pliolite was loaded into the dispenser and the flushing water source was connected to the dispenser. At this point, the VCR began recording, the pliolite was released into the flume, and the light source was turned on. To produce an adequate ensemble average of flow characteristics, it was necessary to acquire a minimum of 30 cycles for each wave so taping lasted approximately two minutes for each test, at which point the light was shut off and the recording stopped. The camera was then moved to a location partially overlapping the field of view of the previous position and the process repeated until the transition point had been recorded. The first camera position was recorded as position A, the second as B, and for some tests a third position, C, was 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 Gaugze 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 Diitization The Editlink 2200/TCG is capable of striping a video tape with longitudinal Society of Motion Picture and Television Engineers (SMPTE) time code on one or both audio tracks. This was done after initial taping, however it is suggested that the tape be striped before taping to reduce the possibility of erasure. The Editlink manufacturers claim that the time code can be used to locate any position on the video tape to an accuracy of +/- 1 frame. Trials using various positions on the tape showed this to be true. Actually, nearly every trial resulted in the Editlink finding the exact frame searched for. Macro files were written to automate the process of digitizing the video images by the frame grabber board. The images are processed in batches of 50. First, an image is digitized at a resolution of 640 columns by 480 lines. The 480 lines is the maximum allowable vertical resolution of the frame grabber card. A compiled C program is called from the macro that instructs the VCR controller card to frame advance the tape. The next image is digitized and the process repeated. After 50 images have been digitized, a C program is called to stop the VCR. This is to circumvent the automatic shut-off feature of the Panasonic AG-1970. This feature will shut the VCR off if it does not detect any "activity" for roughly three consecutive minutes, Unfortunately, frame advance is not recognized as "activity". This 50 image limit actually provides an amount of data that most current hard disk drives can reasonably handle, approximately 15 megabytes. Image Filtering Next, the fifty images are filtered. The filtering process is based on a histogram analysis of the pixel values in each image. All pixel values lower than the 90th percentile are set to black or 0. All remaining pixels from the 90th to 99th percentile are linearly scaled from black to white (0 to 255). These filtered images are stored for later processing. A C program then directs the Editlink to find the next frame to be digitized and the process continues. The filtering process produced one of the most important advances in this research. Air bubbles entrained in the flow due to the impinging jet created by a breaking wave can be filtered out of the image since, under the lighting conditions used in the experiment, the bubbles have lower gray scale pixel intensities than do the pliolite. The exact range of histogram percentiles for the air bubbles and pliolite was determined by a trial and error method in which the author visually inspected the filtered images. The filtered images were then transferred to the Sun (or occasionally the 486) for DPIV processing. A series of M files were written to fully automate the process of analyzing the images and returning velocity fields. All data (i.e., filtered images and velocity field files) were stored on a high capacity magneto-optical (MO) disk in compressed format. The MO disk can store over 600 megabytes of data and currently 32 contains over 200 N41B of compressed velocity field data and over 300 NM 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 Averap-ing 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 frill 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. Longuet-Hi-ggins (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 = + 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 V,+ + )a = -pg(h + !)- + Ta (4.2) where ua and MI" represent the total mass flux (incorporating the Stoke's drift in the definition of ua), S11 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 c & 3are 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 11c TIC d-J p2d =-(h+Td)'- (s +s ,)dz-tb (4.3) -h -h where now s/ is now the depth varying wave induced radiation stress, s= is the depth varying turbulent Reynolds stress and the mean flow (including Stokes drift) momentum contribution has been separated from S,, and is now represented by the first term. Applying equation 4.3 to the transition region and neglecting bottom shear stresses, it is observed that three components of momentum can be identified. The first term on the right hand side of the equation drops out because the mean water level is constant (i.e., 0) in the definition of the transition region. The terms within the integral on the right hand side can be separated. Therefore, the total linear momentum at a section is the summation of the mass flux component (first term) and the momentum components of wave motion and turbulence. Since these remaining terms are exact differentials, equation 4.4 represents the conservation of linear momentum from a section at the break point to a section at the transition point [J p 12dz+J + s) : p12dz + +s )dz] (4.4) -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 Fgh ) are - ga2k- gHk h (5) x-2" = g"=s (4.5a) ga2k gH k gH2 U2~j- 8afr ~f~(~~)(4.5b) The mean velocity values above and below the wave trough are W7 and W2-, respectively. The correction factor value, Q (see Chapter 2), was assigned values of 1.5, 2.0, 2.5 and 3.0 to assertaln 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= = -(2n 1) =IpgH2 (4.6) 39 found by applying the shallow water assumption that n~ -- 1 (n =Wave group velocity ). n Wave celerity An 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 ;71 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 U/= a Hb (47 ,F hb MgT2(47 where u'rms is the turbulent velocity found from DPIV analysis, g is gravitational acceleration, hb is the water depth at the break point, Hb 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 (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 H1 (H + H2J+3} (4.9) I2* 4h(H+ --L- *3+ *(a 22 + 2ab + b2) Model 2 attempts to include vertical turbulence contributions by defining them as w7 = 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- p;; dz (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 I2 *[-L*(H+ H)]+31}= 4h- 1 H2 (4.12) f ( + H2+3+"-*(a222+2ab4+b2) 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/2 = 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 .2 + H2]+3 = 2 b (4.14) H 2* Q2-* (H + H2 +--* (a 22 + 2ab4 + b 2) +Khb *A Anular 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 MvWL 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 Tn2 I1 =7 J P(U2-W2)dt for-hz-- (4.15 a) 0 13)t fr- Lr where I is fs (z)dz or the depth integrated value of each radiation stress component. Applying shallow water asymptotic solutions to the above representations gives 1, (4.16 a) 13= -M (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 =-2h 2 (4.17 a) H Zc3 =- 1 (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 [_3(ff)]214_( + H I16h h2I8 + b 2 b (4.18) Ih 1--L(E + Q2h 2) +(a2 2 +2ab +b2)} 16 16 h 128 h+ 8 Model 2 {~* [i~ h)2] + H fl 16 1 6 2 8 (4.19) 16 1- + 12h -,+ + + -(a 2 +2ab4+b2) and Model 3 S + 2 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 surfrone, 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 1 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 a) 0.5 0.4 0.3 0.2 0.1 0 - 1 2 1 3 1'4 is 1 9 1 ,7 1'9 9 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. H, 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) h" (cm) (sec) 1B 0.85 4.85 4.7 31.2 2C 1.42 6.52 4.2 30.7 3 C 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 1 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 IB 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 L__ A 2.13 1 128 3840 N/A Once the required number of digitized images was known, the digitization process began. On average, it took fifteen seconds for an image to be digitized and fully filtered. A comparison of an unfiltered and filtered gray scale image is shown in Figure 5.2. The filtering process has been described in chapter 3. The filtered images were then stored in compressed format on a magneto-optical disk and also transferred to the workstation for processing. Image processing using the DPIV method to obtain instantaneous velocities can be accomplished in one large data exchange if there is a sufficient data storage capacity available at the processing computer. This was generally not the case. Data transfer was 49 -- 7, - .. - Hf.* . .._,. 10 1 I . ~H ...- : .. .. -, -; r .. :: ,-U,..' ,. :- .. i i .,I ~ I.. *"'. ._. .- . cir U U~ LI F- I Y Vro w ~ X7!-iI l i I Simg fro test 2. Gra scale hav been:, invre for clriy Note the r-e of t e a t jt in .. .... ai, ,.-' '- H.. f ..; .$ . 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 20 15 ? 800 pixels/sec 5 5 10 15 20 25 30 3 5 ACl steps (18a 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 non-flow data included and b) only flow related data included. Figure 5.5 shows a comparison of the 30 cycle and 50 cycle ensemble and time averaged mean velocities for test 4C. Physically Figure 5.5 a and 5.5 b represent a a) . ..-. . 25 - I / I I I I I / / / // /. I / / I I I /d /E / / I..t 1 1.'l 20 ---,, i-' I / / / / / / / / 210 120 pfxels/sec . 5 10 15s 20 25 30 35 AOl steps (16 pixels/step) b) 25 .. .. -. . . . - -- I i I I/I/I iI// / d/ id/ | I// I I I//// I I s 10 5 - 120 pIxels/sec 5 10 15 20 25 30 35 AOI steps (15 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 111rams. 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 SWYL. Mean values of the horizontal turbulent K --120 pixels/ -, I j I j / I -- / / / / - - l l - sec / 5 /5 / 5'l/ J / I ti/ J", .* I' j J j a I // // - -/// / -/ /- - / / / / / / i - - l / 1/ /- / / a) 26 24 22 S20 .e18 ~16 14 12 10 b) 26 24 22 ~20 'is IX16 14 12 10 0) 26 24 22 ~20 18 14 12 10 0 5 10 15 20 25 AOI steps (16 pixels/step) 30 35 Figure 5.5 Comparison of ensemble, time-averaged velocity fields using a) 30 cycles, b) 50 cycles, with c) the difference between a and b. (Data from test 4C) 0 5 10 15 20 25 30 35 AOI steps (16 pixels/step) --120 pixels/sec ... .. - I I I-| I 1-/ / I I I / - /' / 'i 1 'iI/I I// 1//1/// / / / / 1 lS l/ /' / - - / / / / / / /- -/ / / -0 5 10 15 20 25 30 35 AOI steps (16 pixels/step) --120 pixels/sec . .. . . .. . I . .. . . . . . . . . . . . ..... .. ............. . S. .. ....... .. .. .. ... ...... . .. . ... . . . . .. . .. . . . I I I I I I I ./ '/ .1. 1' LLJ =120 pixels/sec '5 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 comnnnent. frnm Fimnir. S 5.5 b indicating 22L = . 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 226 2- T51 20 --............................. 10 400 (pixels/sec)-2 . . . . . . . . . a 5 10 15 20 25 30 35 AOl steps (16 pixels/step) Figure 5.7 Typical turbulent velocity fluctuation field (data from test 4Q). 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 .............. ................ ......... .. .. . . -- Test 0 .5 ................... ................... I---,- est -c-Test --Test 0.0 0.00 0.02 0.04 0.06 0.0f ii' rms/JI'qhSW1 3 0.10 0.12 0.14 Figure 5.8 Profiles of dimensionless u'rs 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 b/mgT2 Figure 5.9 Empirical curve fit for dimensionless U'r.m.. at the transition point as a function of the surf similarity parameter. (m = beach slope) Table 5.4 Turbulence parameters determined from DPIV Tes t 1 y=0. 2204x+0.0 ........ ...7......... o Test 2: 0 Test 4 Test No. u'...,. Hb/mgT' 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 (M4WL) 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 03 1041 3.3 92.9 94.7 150.8 166.5 Model Performance Applying the input breakpoint conditions, the transition region model with different turbulence parameterizations can now be evaluated. For each turbulence model, the empirical correction factor for the increase in mass flux, Q, is varied to determine the effect on the calculated values. Figures 5.10, 5.11 and 5.12 graphically illustrate the resulting sensitivity of each model to the value of Q. Tables 5.6, 5.7 and 5.8 also present the output. Figure 5.13 and Table 5.9 represent a comparison of the various turbulence models for constant value of Q=2.5. Figures 5.10, 5.11 and 5.12 imply that the transition point wave height is more sensitive than the transition point water depth to the value of Q that is employed. The results of the transition point wave height in model 1, for instance, give a range of the overall mean error from the experimental data of approximately -1.0% to +13.6%. The values of model 1 for Q=2.5 are actually quite similar to the results obtained by Thieke (1992) for the same data set using the one-dimensional model that conserves only linear momentum. This indicates that the wave height is fairly insensitive to the inclusion of the angular momentum conservation equation. Also, the transition point wave height appears quite insensitive to the level of turbulence modeled, as seen in Figure 5.13. The spread of the. data in the wave height plot (Figure 5.13 a) 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 I to model 2 to model 3), the prediction of the transition point water depth progressively departs from the measured 0.008 -r 0.002 -7. ..... 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 b/gT' 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 V0.000 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 0.008 0.004 0.000 V . .... . . .. .. . . . 0.000 0.004 0.008 0.012 0.016 h /gT2 b 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 . 0.006 0.002 000 0.002 0.004 0.006 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) -i / /o All 3 cases 0 .......... l~p -; ......... ........\ -i............. .... ... .................... - overlai along this line / o ............................ ...... ./'i~ ~ ~ t ........ ....... / Oata Of Hansen and S/o Sverdsen (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 L 0.000 Figure 5.13 Table 5.6 Model Results for transition point wave height, I-Jt 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 It, (mm) H-, (mm) 1, (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 A10112 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 48.2 111.8 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 -10 111.0 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 041071 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 % Difference 31.2 35.3 47.0 28.2 31.9 36.7 % Diff= (Model qI Experimental H) / Model q 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 % DifT 11 (mm) I, (mm) I 11, (mm) IH (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 Al0112 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 108.23 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 II Experimental H) / Model H1 N/S = No solution found Table 5.7 Model Results for transition point water depth, ht Q = 1.5 Q = 2.0 Test I 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) 101101 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 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 0A 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 68.0 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 66.5 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 %Difference -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) ki (mm) h, (mm) h (mm) h, (mm) 101101 110.8 123.6 116 137.9 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 -11 93.7 9.6 103.0 20.5 64.0 1.2 96.3 12.6 N/S 061102 119.3 119.6 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 100.3 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 -3.3 114.5 6.7 129.3 20.5 90.0 39.9 118.0 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 66.5 72.2 8.6 79.5 19.5 93.9 41.2 64.3 26.5 82.0 23.3 N/S Mean% Difference 0.2 10.8 24.2 13.6 14.1 22.0 % Diff'= (Model hN Experimental hi) / 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 DPJV. 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 higher-order 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 0. 0 ............. .............. - - - - - - - - - - -- -- --- -- -- <010 5 - = 120 pixels/sec I I IIl1/ 5 10 15 20 25 30 35 AOI steps (16 pixels/step) b) 25 - 2 0 . . . C's................................................... CI C, 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 0 CD CO CL, 10 . .' .' . - '- I I I I I I * 4 I *J I / S* .* I a ; a 1 I I I I S I I S I -------- --- -------*---- - - - = 120 pixels/sec a) . . . . . 2 5 . . . . . . . . . . . . . . . . . . . . .. . 20 . . . . . . . C) . s J . (0 0. .1 .... . .... ... .. CL 5 - 120 pixels/sec 5 10 15 20 30 35 AOI steps (16 pixels/step) b) 25 (C) _0 0.15 ........ .................................... CL .A .- .... .. .. .. .. .. ... ~10 . . 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 S I g ---,-------, - -- ------- --. * 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 C) (I. o15 C,, . 5=i -20 C) .i3 L 15 C). ~10 Figure A.4 - = 600 (pixels/secA2 . . 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 ;; SUniversity of Florida ;; Written 2/28/94 ;; Last revision: 3/22/94 .... ........... ..................................................... ;; this initializes the EDITLINK 2200/TCG {!}MENUPROMPT ans { } {Initialize EDITLINK? (y/n)} >DOSEscape ^Close/ReopenImagingBoard(s) NO ^Pause&PromptWhenDone NO ^Reset/RestorePCScreen NO {!}IFSTREQ {@ans} {y} THEN !ExecuteDOSCommand.Enter: init {!}ENDIF {!}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)} {!f}IFSTREQ {@ans} {n) THEN >VideoDigitize/Display !Digitize !ExecuteDOSCommand.Enter: findtc {!}MENUPROMPT hr {} {Time code values: HR } {!}MENUPROMPT min {} {Time code values: MIN } {!}MENUPROMPT sec {} {Time code values: SEC } {!}MENUPROMPT frame { } {Time code values: FRAME } {!}SET i {@firstframe} {!}WHILE {@i}<={@lastframe} {!}MESSAGE {DIGITIZING IMAGE }{@i} >VideoDigitize/Display !Digitize ;; {!}PAUSE 1 !Display ;; {!}PAUSE 1 !Digitize ;; {!}PAUSE 1 !Display {!}IF (({@i}>=10)&({@i)<100)) THEN !SavelmagetoFile.Name: c:\research\unfilter\{@dir)\{@numpos} 000 {@i}.tif {!}ENDIF {!}IF (({@i}>=100)&({@i}<1000)) THEN !SavelmagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}00 {@i}.tif {!}ENDIF {!}IF (({@i}>=1000)&({@i}<10000)) THEN !SavelmagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos}0 {@i}.tif {!}ENDIF {!}IF {@i}>=10000 THEN !SavelmagetoFile.Name: c:\research\unfilter\{@dir}\{@numpos} {@i}.tif {!}ENDIF !ImageAreaoflnterest:Fulllmage ;; Have 50 images been saved? {!}SET mod {@i)%50 {!}IF {@mod}=0 THEN >DOSEscape ^Reset/RestorePCScreen NO !ExecuteDOSCommand.Enter: stopvcr !ExecuteDOSCommand.Enter: frame +{@hr) {@min} {@sec) {@frame} ;; 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 !LoadlmagefromnFile.Name: c:\research\unfilter\{@dir}\{@numpos} 0000 {@j }.tif {!}ENDIF {!}IF (({@j}>=10)&({@j}<100)) THEN !LoadlmagefromFile.Name: c:\research\iunfilter\{@dir}\{@numpos}000 {@j}.tif {!}ENDIF {!}IF (({@j}>=100)&({@j}<1000)) THEN !LoadlmagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos} 00 { @j}.tif {!}ENDIF {!}IF (({@j}>=1000)&({@j}<10000)) THEN !LoadlmagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos }0 {@j }.tif {!}ENDIF {!}IF {@}>=10000 THEN !LoadlmagefromFile.Name: c:\research\unfilter\{@dir}\{@numpos} {@j}.tif {!}ENDIF !ImageAreaoflnterest:Fulllmage ^Enhance:LowPercentile 90 ^Enhance:HIighPercentile 99 !EnhanceContrast:GivenHistogramPercentiles !ImageAreaofInterest:Fulllmage >FileLoad/Save,X/YFormatw.AOI {!}IF {@j}<10 THEN !SaveImage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil)}\{@numpos} 0000 { @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 !Savelmage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos} 00 {@j }.fil {!}ENDIF {!}IF (({@j}>=1000)&({@j}<10000)) THEN !Savelmage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos } 0 {@j }.fil {!}ENDIF {!}IF {@j}>=10000 THEN !Savelmage,8BitBinary,toFile.Name: c:\research\filter\{@dirfil}\{@numpos} {@j}.fil {!}ENDIF !ImageAreaofInterest:Fulllmage {!)}ENDWHILE !ExecuteDOSCommand.Enter: zipfil {@dirfil} {@numpos} {@k} ;; label delfil -- 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 {!}MESSAGE {COMPUTING NEXT TIMECODE POSITION} ;; Must convert hr min see 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}+1 {!}IF {@sec)>=60 THEN {!}SET num 60 {!})SET sec {@sec}%{@num} {!}SET min {@min)+1 {!})IF {@min}>=60 THEN {!}SET min {@min}%{@num} {!}SET hr {@hr}+1 {!}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) {!} STRLENv 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 /* 3fU!T,!PE OZfTM!T! 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'.(,':$.,-.!E uizip !juI.,)sjnd { /* 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) { mt i; for(i= 0; i < 3; ++i) /* send 3 dummy sync chars */ outp(PORT + 1,0); timedelay(); } outp(PORT + 1,RESETT); outp(PORT + 1,MODE); outp(PORT + 1,COMMAND); */ timedelay0; timedelay0; timedelay0; /* 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: 1-2 second time_delay Parm: time_delay0 Return: none void timedelay(void) { timet x,y; time(&x); x += 2; do { time(&y); } while(y <= x); } /* end of time-delay */ /* get system time in seconds */ /* wait */ -------------------------------- |