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Bedform ripple model evaluation and the design of an acoustic ripple profiler

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Title:
Bedform ripple model evaluation and the design of an acoustic ripple profiler
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UFLCOEL 94008
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Jetté, Christopher D., 1969-
University of Florida -- Coastal and Oceanographic Engineering Dept
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English
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x, 99 leaves : ill. ; 29 cm.

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Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
Coastal and Oceanographic Engineering thesis, M.E ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (M.E.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 97-98).
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Typescript.
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Vita.
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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.
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by Christopher D. Jetté.

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University of Florida
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UFL/COEL-94/008

BEDFORM RIPPLE MODEL EVALUATION AND THE DESIGN OF AN ACOUSTIC RIPPLE PROFILER by
Christopher D. Jett6 Thesis

1994




BEDFORM RIPPLE MODEL EVALUATION AND THE DESIGN OF AN ACOUSTIC RIPPLE PROFILER
By
CHRISTOPHER D. JE'IE

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 a great deal of thanks to my advisor and supervisory committee chairman, Dr. Daniel M. Hanes, for his support and guidance during my master research. I would also like to thank the members of my supervisory committee, Dr. Robert G. Dean and Dr. Robert I Theike. Also my thanks go to Dr. Peter Thorne, Dr. Chris Vincent, and Mr. Van Holiday for help with the design and potting techniques of the multi-element transducer.
I would like to thank my parents, Sandie and Bill Kline and Don Jett6, for their love and support over the years. I would also like to recognize my grandparents, Alma and Leon Jette, for their unending encouragement. Thanks go to Monica for proof-reading help as well as for making my life wonderful. Thanks go to Eric Thosteson for the collection of the supertank data set, for the supertank camera set-up figure, and for being a great friend. Thanks also go to Tae-Hwon for helping me with some of my thesis formatting problems.
Thanks go to everyone at the Coastal Engineering Lab, without their help this research never would have been possible. Thanks go to Vic, Sidney, Chuck, Vernon, Danny, and J.J.. Thanks also go to the clerical staff; Becky, Sandra, Sonya, Cynthia, and Lucy, for having patience with my general failure to meet deadlines.
Thanks also go to my friends for the great times and sanity checks, especially to Paul, Phil, Darwin, Kenny, Mark, Tim, Tom, Al, and Christina. Thanks for entertainment go to Market Street Pub, Plaza Triple Theatre, Butler Beach, S. R. 441 bike rides, and Rock and Roll. I would like to thank God for my family, friends, and health, and also for giving us yeast. Much thanks go to King Neptune for the awesome waves he has sent my way.




TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS...................................................................... ii
LIST OF TABLES.............................................................................v
LIST OF FIGURES............................................................................vi
LIST OF SYMBOLS ........................................................................viii
CHAPTER 1: INTRODUCTION.............................................................. 1
CHAPTER 2: PREVIOUS WORK ............................................................ 4
Mechanics of Ripple Formation.............................................................. 4
Rolling Grain Ripples ...................................................................... 5
Vortex Ripples.............................................................................. 6
Classification Schemes........................................................................ 6
Bagnold (1946)............................................................................. 6
Dingier and Inman (1976).................................................................. 7
Clifton (1976) .............................................................................. 7
Nielsen (1981) .............................................................................. 9
Osbourne and Vincent (1993) ............................................................. 9
Predictive Models ........................................................................... 10
Nielsen (1981)............................................................................. 10
Wiberg and Harris (1994)................................................................. 15
Wikramanayake (1993)................................................................... 18
CHAPTER 3: SUPERTANK EXPERIMENT .............................................. 21
Site Description.............................................................................. 21
Supertank Project ......................................................................... 21
Equipment and Measuring Techniques..................................................... 22
Camera Setup ............... ....... ....................22
Determining Measured Ripple Heights and Lengths .................................... 23
Supertank Data Analysis .................................................................... 26
Comparison to Previous Data Sets....................................................... 26
Nielsen (1981) Model Comparison ...................................................... 26
Wiberg and Harris (1994) Model Comparison.......................................... 35




Wikramanayake (1993) Model Comparison............................................. 39
CHAPTER 4: RIPPLE MEASUREMENT TECHNIQUES AND DESIGN OF RIPPLE
PROFILER ................................................................................ 44
Ripple Measurement Techniques........................................................... 44
SCUBA Diver Observations.............................................................. 44
Video ...................................................................................4
Stereo Video! Photography .............................................................. 46
Video with Image Processor ............................................................. 47
Hollywood Deployment Example........................................................ 47
Acoustic ................................................................................. 49
Transducer with Stepper Motor.......................................................... 52
Side-scan Transducer..................................................................... 53
Stationary Multi-element Transducer Array............................................. 53
Design and Construction of an Acoustic Ripple Measurer................................ 54
Determination of Frequency.............................................................. 54
Selection of Materials..................................................................... 57
Geometry of Transducer.................................................................. 59
Potting of Transducer..................................................................... 60
Testing of Transducer..................................................................... 65
Design of Electronics..................................................................... 67
CHAPTER 5: CONCLUSIONS.............................................................. 69
APPENDIX A: SUPERTANK RIPPLE PROFILE DATA AND PLOTS ................ 71
APPENDIX B:MANUFACTURER SPECIFICATIONS FOR CRYSTALS AND
POTTING RESIN ......................................................................... 86
APPENDIX C: MAThAB PROGRAMS USED FOR DATA ANALYSIS.............. 88
REFERENCES ............................................................................... 97
BIOGRAPHICAL SKETCH ................................................................. 99




LIST OF TABLES

Table Page
2.1 Wiberg and Harris (1994) ripple classification........................................ 15
3.1 Values of relative error (A) between measured and predicted values............... 43
5.1 Values of relative error (A) between measured and predicted ripple values ....... 70




LIST OF FIGURES

Figure Page
2.1 Relative field ripple length vs. Mobility Number with Nielsen (1981) curves ......... 12
2.2 Ripple Steepness vs. Shield's Parameter with Nielsen (1981) curves ................. 13
2.3 Relative ripple height (Ti/a) vs. Mobility Number with Nielsen (1981) curves ........ 14 2.4 Ripple Steepness vs. (do/ri) with Wiberg-Harris (1994) model curves .............. 17
3.1 Supertank underwater video setup ................................................................... 22
3.2 Supertank ripple pattern with mean subtracted for run # 63 .............................. 25
3.3 Supertank detrended ripple pattern for run # 63 ............................................... 25
3.4 Measured versus Nielsen (1981) predicted ripple lengths (lab and field) ........... 27
3.5 Measured (2,/a) vs. V for supertank data with spectral types ............................. 28
3.6 Measured (,/a) vs. V for supertank data with ripple types ................. 29
3.7 Measured versus Nielsen (1981) predicted ripple heights (lab and field) ............ 30
3.8 Measured (Tl/a) vs. V for supertank data with spectral types ............................. 31
3.9 Measured (l/a) vs. AV for supertank data with ripple types ................................ 32
3.10 Measured versus Nielsen (1981) predicted ripple steepness (lab and field) ..... 33 3.11 Measured ('q/X) vs. 02.5 for supertank data with spectral types ....................... 33
3.13 Measured versus Wiberg and Harris (1994) predicted ripple lengths .............. 36
3.14 Measured versus Wiberg and Harris (1994) predicted ripple heights .............. 37




3.15 Measured versus Wiberg and Harris (1994) predicted ripple steepness ........... 38
3.16 Steepness (Ti/,) versus (di/n) for supertank data ........................................... 38
3.17 Measured versus Wikramanayake (1993) predicted ripple lengths .................. 40
3.18 Measured versus Wikramanayake (1993) predicted ripple heights .................. 40
3.19 (nl/a) vs. Z for supertank data with Wikramanayake (1993) model curve ...... 41 3.20 Measured versus Wikramanayake (1993) predicted ripple steepnesses ........... 42
3.21 Steepness versus Z with Wikramanayake (1993) model curve ....................... 42
4.1 Hollywood underwater video set-up with rod array ......................................... 48
4.2 Simplified transducer beam pattern showing half-beam angle and footprint ..... 56 4.3 Schematic of multi-element transducer ripple measurement system ................... 60
4.4 Bottom return from new transducer ................................................................. 66
4.5 Bottom return from M esotech .......................................................................... 66




LIST OF SYMBOLS

a water semi-excursion
c speed of sound
D grain diameter
d. wave orbital diameter
f frequency
fp acoustic foot print
f2.5 wave friction factor
g acceleration of gravity
r range to seabed
S sediment specific gravity
um maximum near bottom orbital velocity
%, ripple length
02.5 grain roughness Shield's parameter
p density of water
11 ripple height
, specific gravity of sediment
Shield's relative stress
angle of repose
Mobility number skin friction Shield's parameter
(0 angular frequency
CwM maximum wave friction shear stress
A relative error




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
BEDFORM RIPPLE MODEL EVALUATION AND THE DESIGN OF AN ACOUSTIC RIPPLE PROFILER
By
Christopher D. Jett6
August 1994
Chairman: Daniel M. Hanes
Major Department: Coastal and Oceanographic Engineering
Under most wave environments the seabed is covered with bedformn ripples. The modeling of these ripples is important to the modeling of sediment transport. The ripples provide a bed roughness which influences the shear stress at the bed, thus affecting the concentration profile and the rate of sediment transport. Presently there are empirical models which can be used to predict bedform ripples, given sediment and flow parameters.
Ripple profiles were recorded during a large scale wave tank experiment called SUPERTANK. Near prototype wave conditions were generated during this experiment. Wave heights ranged from 0.27 to 1.4 meters with peak periods of 2.9 to 10.7 seconds. Broad banded and narrow banded spectrum as well as monochromatic wave conditions were generated. Under these conditions vortex ripples were generally present. The ripple profiles were measured and then analyzed to determine representative ripple heights and lengths for each run. These measured values were then compared to previous field data sets to better understand how the Supertank ripple data measurements compared in relation to previous field studies.




The large scale laboratory ripple measurements were then used to evaluate four predictive models for ripple dimensions. Comparisons were performed by determining the relative error between measured values and predicted values, as well as by plotting measured values with predictive model curves. Comparisons were also made between measured and predicted values for different types of wave spectra (narrow banded, broad banded, and monochromatic) as well as for different ripple types (orbital, anorbital, and suborbital).
It was found that models based on the type of wave spectrum' (regular or irregular) did not work as well as models designed to operate over all spectral types. It was also found that previous models designed to be used for field conditions agreed well with anorbital ripple measurements, and that most suborbital ripple measurements fell between field and laboratory predicted values. This was as expected since in the past most laboratory facilities were incapable of reaching conditions to form anorbital ripples, and inherently most field conditions on the continental shelf are in the anorbital ripple regime.
A review of previous ripple measurement techniques was also performed. Some of the techniques discussed include scuba diver measurements, under-water video, stereo photography, and ultra-sonics. The design of a stationary multi-element transducer to measure ripple profiles was also discussed. Such an instrument would be capable of measuring instantaneous bedform profiles over a range of 0.5 meters with millimeter vertical resolution and centimeter horizontal resolution. Such an instrument would allow for accurate field ripple measurements. From these measurements existing ripple models could be evaluated and modified, thus improving present sediment transport models.




CHAPTER 1
INTRODUCTION
In the coastal environment the seabed is rarely flat. In contrast, it is usually covered with bedforms such as bars, dunes, sand ripples, and biological matter. In modeling sediment transport it is very important to be able to predict the geometry of the bedforms. The geometry of these bedforms provide a bed roughness which influences the shear stress at the bed and the profile of the eddy viscosity or diffusion coefficient. Thus the bedform geometry is required to determine the concentration profile or the rate of sediment transport (Vongvisessomjai, 1984).
The modeling capability of bathymetric change is also very dependent on the modeling of bedform geometry. Vincent and Osbourne (1992) found that under similar wave conditions the suspended sediment over a flat bed was restricted to the lowest 5 to 10 centimeters above the bed, whereas when bedforms were present suspensions to 30 and 40 centimeters were common. They also found bedform migration to be a significant part of the total cross-shore transport when the bedforms present had low steepness. Thus the ability to model sediment transport and bathymetric change is dependent on the ability to model bedform geometry and bedform migration rates.
Most models currently in use are empirically based. Nielsen (1981) developed separate models for bedform geometry based on the type of waves present, i.e. one model for laboratory (regular wave) and a different model for field (irregular wave) conditions. These models are functions of the mobility number and the grain roughness Shield's parameter and can be applied to sediments of different densities. Wiberg and Harris (1994) developed a set of empirical models which are meant to work in both laboratory and field wave conditions. These models use the wave orbital diameter and sediment size to predict




the geometry of bedforms under oscillatory flows for a quartz sand bed. Another ripple model currently used is Wikramanayake (1993), which is a revised version of the Grant and Madsen(1982) ripple model. This model is an empirical curve fit of ripple properties versus a non-dimensional quantity (Z) representing wave and sediment conditions.
One of the major problems in modeling bedform geometries under waves is the lack of reliable field data. Nielsen's (1981) field ripple models were based on 126 data points, of which 54 were measured by scuba divers and 72 were measured using instrumentation. When Wiberg and Harris (1994) developed their models they took all of the data used by Nielsen plus 59 points taken since 1981. All reliable existing field data sets were used to construct this model, thus there are no data with which to check this model. A large field ripple data set covering many wave and flow conditions would be a substantial contribution to sediment transport research.
In the past, the most common method of measuring bedforms was for scuba divers to use some sort of manual measurement device. With the use of a meter stick divers can accurately determine ripple lengths; however, ripple heights tend to be more difficult to measure. When measuring heights the weight of the meter stick tends to flatten the crests of the ripples. In addition, the water motion due to the waves tends to complicate matters (Dingler and Inman, 1976). In the past divers have also used a piece of clear plastic and a grease pencil to try to measure sand ripples in the field (Inman, 1957). Also divers have tried to use a large "comb" covered with grease so that once it is pushed down into the bed the sand sticks to the grease and thus the bed profile is recorded.
More recently underwater video has been used to measure ripples. When water visibility allows, videography can be used to accurately measure ripple length. However, even using available image processing techniques, ripple height is still very difficult to determine in the field using underwater video.
The latest trend in measuring bedform dimensions is with the use of ultra-sonics. Dingler and Inman (1974) were among the first to measure bedforms with ultrasound.




They had a movable frame with a manually translated transducer which the divers moved back and forth over the rippled seabed recording the ripple profile. Today there are similar automated systems such as the HRRTS (High Resolution Remote Tracking Sonar). With the use of a stepper motor, the HRRTS tracks an ultrasonic transducer back and forth across a stationary frame recording the bottom profile (Greenwood, Richards, Brander, 1993). Also, transducers have been used in side-scan mode to measure ripple lengths in conjunction with downward aimed transducers to measure ripple heights as ripples migrate underneath (Vincent and Osbourne, 1992). There have been inherent problems involved in all of these methods. A new approach to measuring bedform geometries would be very helpful in collecting a reliable field ripple data set.




CHAPTER 2
PREVIOUS WORK
Mechanics of Ripple Formation

Once the wave shear stress acting on a movable sand bed reaches a strength strong enough for incipient sediment motion, the sediment begins to be carried as bed load. As the bed shear stress increases, the amount of suspended sediment increases and the flow becomes more vigorous. Then once another critical value of shear stress is surpassed the sediment begins to be carried as sheet flow. Bedforms may be active anytime the bed shear stress is above that required for incipient motion.
One nondimensional parameter used to classify these different regimes is the grain roughness Shield's parameter (02.5),

0 2.5 0.5f2.5 I

equation 2.1

where "f' is the wave friction factor, given by Swart (1974) as

f = exp(5.21 3(2.5 dla))0.194 5.977

equation 2.2

and TP is the mobility number, defined as

(a co )2 (s- 1)gd

equation 2.3




Where "d"' is the mean grain diameter, "a!' is the water semi-excursion, and Co is the angular frequency of the waves. The mobility number is a non-dimensional term representing essentially the ratio between the water velocity amplitude and the settling velocity of the sediment (Nielsen, 1981).
Values of the grain roughness Shield's parameter are given to classify the different regimes of flow. For 02.5 less than or equal to 0.05, the flow is considered to be too weak for sediment motion. For a 02.5 greater than 0.05 and less than or equal to 1.0 the bed will be active and covered with bedfonns which will be approximately in equilibrium with the flow conditions. When 02.5 is greater than 1.0, the ripples are flattened and sheet flow occurs. (Dingler, 1974).
Rolling Grain Ripples
Bedforms produced by the action of progressive waves on a horizontal bed were first classified into two groups by Bagnold (1946). Bedforms with a large enough height to length ratio to allow vortex formation in the lee of the crest he called "vortex ripples," and bedforms with too small of a height to length ratio to allow vortex formation he called "rolling-grain" ripples. On an initially flat bed without obstructions capable of forming vortices, rolling-grain ripples are the first bedforms to appear.
Sleath (1984) investigated rolling-grain ripple formation on a flat bed with a small disturbance present; the required disturbance could even be as small as a single grain of sediment projecting from the bed. He modeled the streamlines around this disturbance and found that the steady drifts which formed in the vicinity of the bed tend to be directed toward the disturbance. This would carry sediment from the trough of the ripple to the crest, thus the ripples would tend to grow. Gravity acts as an opposing force to ripple formation, therefore limiting the maximum height attainable of the ripples under given wave conditions.




Vortex Ripples
If the flow is strong enough, once the height to length ratio of the rolling grain ripples reaches a critical value, vortex formation will occur in the lee of the ripple crests twice every wave period. Vortex ripples are commonly found at low to moderate transport rates (Sleath, 1984). Once separation occurs in the lee of the ripple crest, both the mainstream flow on the upstream face and the reverse flow on the lee side face of the crest tend to carry sediment from the trough to the crest of the ripple. The forces acting in opposition to vortex ripple formation are gravity and the erosional effects on the ripple crest by the main stream flow. Thus for given sediment and wave conditions, an equilibrium bedform geometry will exist where there is no net transport across any cross-section of the bedform profile.
Classification Schemes
Bagnold (1946)
As mentioned in the above section, Bagnold (1946) was the first to develop a classification scheme for bedform ripples. He called ripples with a height to length ratio large enough for vortex formation in the lee of the ripple crest "vortex ripples", and ripples without this separation "rolling grain ripples". Bagnold's classification system is still widely used today. Rolling grain ripples appear to be stable at velocities smaller than twice that required for incipient motion (Bagnold, 1946). Because of this, rolling grain ripples are present when sediment transport is low; thus most of the bedform research has been done in the vortex ripple regime where sediment transport rates are greater. The vortices formed by the flow over vortex ripples are strong; Tunsdall and Inman (1975) found that the velocities within the vortices are of the same magnitude as that of the main stream flow.




Dingier and Inman (1976)
Dingler and Inman (1976) found that three distinct ripple types occur on fine sand beds in coastal areas. These are relict ripples, vortex ripples, and transition ripples. Relict ripples are found when wave parameters are not sufficient to initiate sediment motion on the bed. Relict ripples are the remains of ripples that were formed under a previous event when flow conditions were strong enough for sediment motion. Vortex ripples are defined as ripples which have a relatively constant steepness; even though the ripple heights and lengths change as the wave intensity becomes larger. Once the steepness of the ripples begins to decrease due to increased flow intensity, the ripples are called transition ripples. Transition ripples are found when the flow intensity is too large to maintain the relatively constant vortex ripple steepness of 0.15, but not large enough for sheet flow. Dingler and Inman (1976) used Shield's relative stress ((p) to classify flow intensity; defined as:
2
(P equation 2.4
,yD
where "u,," is the maximum near bottom orbital velocity, y, is the specific gravity of the sediment, and "D" is the grain diameter.
Values of the Shield's relative stress ((p) were determined for each of the ripple classes. When (p was less than 40 but great enough for sediment motion, the bedforms were found to be in the vortex ripple class. When the flow intensity increased and (p was greater than 40 but less than 240 the bedforms were found to be in the transition ripple class. When the flow intensity was greater yet ((p greater than 240) no bedforms were present and sheet flow was observed (Inman and Dingler, 1976). Clifton (1976)
Clifton (1976) found that when vortex ripple lengths were compared to the ratio of orbital diameter to mean grain diameter (d/D), the ripples could be classified into three




categories. First, when d/D is relatively small the ripple length (X) is proportional to orbital diameter, Clifton (1976) classified these ripples as orbital ripples. For large values of do/D the ripple length appears to be a function of grain diameter and nearly independent of orbital diameter. Clifton (1976) refers to these ripples as anorbital ripples. There exists a transition range for intermediate values of d/D where both orbital and anorbital ripple formation appears possible, as well as ripples with intermediate lengths. Clifton (1976) called ripples in this transition range suborbital ripples.
Wiberg and Harris (1994) used the above ripple classification system; however, they quantified values of flow parameters and bedform geometry for each of the different classes. Wiberg and Harris (1994) found orbital ripples to dominate in laboratory environments because of the limits on the maximum wave orbital diameter that can be generated in the laboratory under most wave flumes. Wiberg and Harris (1994) defined orbital ripples as ripples with heights twice as large as the thickness of the wave boundary layer, or 8/rT < 0.5 Since for this flow the thickness of the wave boundary layer (8.) is roughly proportional to the wave orbital diameter (d.), and do is more readily attainable in most instances, Wiberg and Harris (1994) defined orbital ripples as ripples with the ratio d/rA<10. The Wiberg and Harris (1994) ripple model classifies the ripple regimes according to the ratio of dA/rao, where io is the predicted anorbital ripple height. When predicted anorbital ripple height is used the definition of the orbital ripple regime becomes do/1.o<20, which was determined empirically. Wiberg and Harris (1994) classify anorbital ripples as ripples with heights several times smaller than the wave boundary layer. By definition anorbital ripples have heights less than one quarter of the wave boundary layer thickness, or 8/rTli > 4.0. For ease of calculation, this value was also put in terms of orbital diameter; giving d/rio > 100.
Wiberg and Harris (1994) then classify the transitional suborbital regime for conditions where the ratio 8/TIi. is greater than 0.5 and less than 4.0, or in terms of the wave orbital diameter; 20 < dj/rio < 100. When laboratory and field data are compared




for a given value of d/D in the suborbital regime, the ripple wavelengths can differ by more than a factor of three. Anorbital ripples dominate on the continental shelf, and on medium to coarse sand beds suborbital ripples can also be present. Under limited conditions on coarse sand beds orbital ripples can also be present on the continental shelf; however, it is not common (Wiberg and Harris, 1994). Nielsen (1981)
Nielsen (1981) studied vortex ripples and classified them by the type of waves present as either laboratory (regular wave) or field (irregular wave) ripples. He found that under field conditions, where the waves are often irregular and far from being sinusoidal, the steepness of the ripples tend to be less than those formed under laboratory conditions. In the past, laboratory studies could not generate prototype field wave conditions. However, with new large wave flumes operating under spectral conditions, prototype field wave conditions can be generated in the laboratory. This makes using the field/ laboratory classification system obsolete since it is difficult to draw a fine line between the two conditions. Wiberg and Harris (1994) suggest that the differences Nielsen (1981) found between lab and field data is probably due to most of the data falling into the orbital ripple regime for the laboratory data, and into the suborbital and anorbital regime for the field data.
Osbourne and Vincent (1993)
Based on a bedform field study, Osbourne and Vincent (1993) classified observed bedforms into two major categories; small-scale bedforms (11<4 cm., X<20 cm.) and large scale bedforms (11>4 cm., X>20 cm.). These bed types were then divided into subtypes depending on number of crest dimensions, type of vortex shedding/ suspension, and symmetry. The number of crest dimensions were defined as two dimensional if the bifurcation density was low (> 10 cm. between bifurcations) and as three dimensional if the bifurcation density was high (<10 cm. between bifurcations). The vortex shedding/




suspension classification named pre-vortex ripples as ripples with no vortex shedding and no suspension (rolling grain ripples). Vortex ripples were the same as defined previously; with sediment suspension and vortex shedding from crests at regular intervals under large waves. Post-vortex ripples were classified as ripples where sediment suspension and vortex shedding occurs at irregular bursts. The ripples were then characterized as being either symmetric or asymmetric in profile.
Osbourne and Vincent (1993) found that under non-breaking wave conditions smallscale bedforms dominated, while under breaking wave conditions large-scale bedforms dominated over the sea-bed. These large-scale bedforms were generally crescentic in planform and migrated on-shore, they have been called lunate-shaped mega-ripples by Clifton (1976). In their field study Osboume and Vincent (1993) found that two dimensional small-scale bedforms ('rq=.5 to 3 cm., X=8 to 20 cm.) had migration rates of up to 5 cm./min., and for well defined lunate mega-ripples (rj=3 8 cm., X=20 80 cm.) migration rates of up to 3 cm./min. were documented.
Predictive Models
Nielsen (1981)
As mentioned earlier, Nielsen (1981) classified vortex ripples by the type of waves present as either laboratory (regular) or field (irregular) ripples. Separate models were developed for each condition to predict ripple height, length, and steepness. Comparisons of ripple dimensions to mobility number (T) and Shield's parameter (0) were performed and it was found that ripple heights and lengths could be expressed reasonably well in terms of the mobility number. However, ripple steepness was best described by the Shield's parameter.
In a wave environment there is a well defined horizontal scale; the wave induced water particle semi-excursion (a). Under many flows the bedforms present tend to scale on




the water particle semi-excursion (a) or the wave orbital diameter (do = 2a). It was found that for flows with P < 20, the ripple wavelength is approximately equal to 1.33a (Nielsen, 1981).
Under more vigorous flow (' > 20), the relative ripple length (/a) tends to be smaller than 1.33; however, the actual mechanics of this are not well understood. Nielsen (1981) derived empirical models for ripple wavelengths that cover a large range of wave periods, sediment densities, and grain sizes. He found that for regular waves:
a= 2.2 0.345N' for 2 and for irregular waves:
Y=ex {693 0.37tn8N equation 2.6
/a= 1000 + 0.75tnTNt
where "a" is based on Hi, or Hr.. Nielsen's (1981) irregular (lower) and regular wave (upper) ripple model curves are plotted in figure 2.1 along with all available field ripple length data sets. These data sets include Inman (1957), Dingler (1974), Miller and Komar (1980), Nielsen (1984), Boyd et al. (1988) and the supertank ripple data set. The data sets prior to 1981 were used in the construction of the irregular model curve shown, except for Dingler's (1974) single wave data which is found on the extreme right of the plot.
Nielsen (1981) also investigated vortex ripple steepness and found that if the flow is not too vigorous (0.05<0<0.2) the maximum ripple steepness is limited by the angle of repose ((p) of the sediment. Thus the maximum steepness attainable along the ripple profile is equal to the tangent of (p. He then investigated the two geometrically extreme cases; one where the ripples were equilateral triangles, and another parabolic in profile with a maximum steepness of tan(cp). He found that for the equilateral triangle case

T'/X=0.5 tan((p)

equation 2.7




and for the parabolic case

rl/X=0.25 tan(q).

equation 2.8

For vortex ripples the maximum steepness falls within this range given by these two idealized geometries. He found that at vanishing flow speed

(TlX)mx = 0.32 tan(p).

equation 2.9

101
100 CO
-1
10-1

1 0 -21 ,, . i I .
10 10 10 10
Mobility Number
Figure 2.1 Relative field ripple length vs. Mobility Number with Nielsen (1981) curves

X
'x x +x x
+xx+x
+ YA . )K + )K ++ X
* =prior to 1981, x= after 1981 ,
o =anorbital supertank, + = suborbital supertank




When the intensity increases (62.5 >0.2) the ripple steepness begins to decrease due to the flattening effect of the contracted flow over the ripple crest, which tends to overpower the constructive effect of the lee vortices scooping sand up towards the crest. He found that when 02.5 approaches unity, sheet-flow occurs and the bed becomes flat. Nielsen (1981) derived expressions empirically from plots of ripple steepness (rj/%) vs. grain roughness Shield's parameter (62.5) which gives for regular waves
rl/X=0. 182-0.24(62.5)15 equation 2.10
and for irregular waves:
l1/=0.342-0.34(62.5).25 equation 2.11
0X
100
x
102 xx x x x IE xK
* = prior to 1981, x= after 1981
o= anorbital supertank, += suborbital supertank
1 0 '* . . . . ',
10 10" 10 10
Grain Roughness Shield Parameter
Figure 2.2 Ripple Steepness vs. Shield's Parameter with Nielsen (1981) curves 102 ~'=prior to 1981, x= after 1981 )< XXWII
o= anorbital supertank, += suborbital supertan
102 o 1010 10~
Grain Roughness Shield Parameter
Figure 2.2 Ripple Steepness vs. Shield's Parameter with Nielsen (1981) curves




where 02.5 is based on significant wave height. These curves are shown in figure(2.2) along with all available field data. The upper curve is Nielsen's (1981) laboratory ripple steepness curve, and the lower curve is his field ripple steepness curve.
It would have been more convenient to express steepness in terms of TP instead of 02.5, due to the friction factor corresponding to 02.5; however, Nielsen (1981) determined that an expression using P which could be used for sediment of different densities could not be found. Dingler (1974) successfully used P to describe quartz sand ripples, but when sediment with different densities were used different trends for steepness were observed when compared with T.
A function of ripple height vs. T was found by Nielsen (1981). Since the nondimensional ripple length (X/a) is expressed as a function of T, and ripple steepness for
1 0 . . . . . . . .. .
101
0
U 10
A 1
+) + K+ +~ X
.02
-2
-010- KXX)
COW
(= prior to 1981, x= after 1981 X
10-3
o= anorbital supertank, += suborbital supertank
104
10-0 3
100 101 102 10
Mobility Number
Figure 2.3 Relative ripple height (il/a) vs. Mobility Number with Nielsen (1981) curves




sediment of constant density is a function of T, Nielsen (1981) investigated nondimensional ripple height (l/a) vs. T to try and find a relation. He found for regular waves
r/a=0.275 0.022'o5 for T<156 equation 2.12
l/a=0 for T> 156 equation 2.13
and for irregular waves
1il/a=21-1''..85 for T'>10 equation 2.14
where P and "a" are based on significant wave height. Figure 2.3 shows both the field (lower) and the laboratory (upper) model curves along with all available field ripple data and the supertank ripple data.
Wiberg and Harris (1994)
Wiberg and Harris (1994) reexamined existing ripple data from both oscillatory flows in flume and field studies to construct a model to predict ripple geometry for all types of oscillatory flow environments. As described in the previous section, Wiberg and Harris (1994) classified bedforms according to the ratio of the wave boundary layer thickness and ripple height (8Jqi). From this ratio the ripples were classified as orbital, anorbital, or suborbital by the following criteria:
Table 2.1 Wiberg and Harris (1994) ripple classification
flow conditions ripple classification
ddrAno< 20 orbital ripples
20 100 anorbital ripples




From comparisons of non-dimensional orbital ripple length (?,/D) and nondimensional orbital diameter (d/D), Wiberg and Harris (1994) found that orbital ripple length can be represented as
Xo= 0.62d0 equation 2.15
From comparisons of ripple steepness (r1/A) and non-dimensional orbital diameter (d. /D) orbital ripple steepness was found to be nearly constant at
(il/,)oe, = 0.17 equation 2.16
which is the average value of ripple steepness for all orbital ripple data studied. From these two equations orbital ripple height can be found directly as the product of orbital ripple length and steepness.
When non-dimensional anorbital ripple length (X/D) was compared to nondimensional orbital diameter (d, /D) Wiberg and Harris (1994) found anorbital ripple length to be a function of only grain size (D). A best fit line through the anorbital ripple data yields equation 2.17.
X,o= 535 D equation 2.17
Quite a bit of scatter around this line exists. Previous studies, Nielsen (1981), and Grant and Madsen (1982), have found anorbital ripple steepness to be a function of nondimensional bed shear stress, however Wiberg and Harris (1994) found that anorbital ripple steepness is well defined in terms of (do/4l). This allows the calculation of anorbital ripple height without the calculation of bed shear stress, which eliminates some of the complications and uncertainties involved in the computation of bed shear stress. Wiberg




and Harris (1994) found by comparing ripple steepness (7/%) to non-dimensional orbital diameter (do Ij) the relationship:
S= exp -0.095 in- + 0.442 1n d- 2.28 equation 2.18
for do /i>10; if do / 100
oW
100 0.. .0...... .....
Co) C')
()
_.L ++
(D
*= field data sets
o= anorbital supertank, += suborbital supertank
10 101 102 ;''104
10 . . + ).. .% "'"" -- ... .
Orbital Diameter/ Ripple Height
Figure 2.4 Ripple Steepness vs. (do/ I) with Wiberg-Harris (1994) model curves




It was found that orbital ripples are a function of orbital diameter and anorbital ripples are a function of grain diameter, and by definition suborbital ripples have ripple lengths that fall between these two limits. Thus a weighted geometric average of the bounding values of 4. and ,orb was used to determine suborbital ripple length (,4). The result is equation 2.19.
ln~ inl1001
1x= jl ln20 -1nlO00 o(n Xrb orn b)+ iorb equation 2.19
Wiberg and Harris's (1994) ripple model works well over a large range of conditions since it was constructed using all available oscillatory flume and field data. The model is easy to use because it is based on grain diameter, estimated ripple height, and orbital diameter; rather than bed shear stress which is more difficult to calculate than orbital diameter. One problem is that all available data were used to construct this model, thus comparisons using an independent ripple data set were not possible. However when predicted vs. measured values were plotted using the data that the model was constructed with, much of the variation in the data was accounted for in the model. There was better agreement for ripple length than for ripple height using this model. Wiberg and Harris (1994) suggests that the scatter in the ripple height plot is largely due to the scatter about the regression between steepness and d /11 which was used for anorbital calculations. Over all, this model appears to work better than any other bedform model available at the present time.
Wikramanayake (1993)
Wikramanayake (1993) found that the environment ripples are formed under, which include laboratory or field conditions and wave spectral type, changes the ripple geometry even when similar rms. wave heights and peak periods are used. He found that the break-




off point for ripple steepness, which is defined as the point at which ripple steepness begins to deviate from the nearly constant value of 0.16 (Grant and Madsen, 1982), changes for irregular and regular wave conditions. The critical value of T' ( the skin friction Shield's parameter) for the break-off point is much lower for irregular waves than it is for regular wave conditions. This is due to larger individual waves which exceed the break-off value of T' present in irregular wave ripple data sets. Similar trends were found for ripple height and length measurements when regular wave conditions were compared to irregular wave conditions.
Wikramanayake (1993) decided that only field data should be used to construct a field ripple model because of the discrepancies he observed between lab and field data. Wikramanayake (1993) found less scatter when non-dimensional field ripple height (rl/Abr) and ripple steepness were plotted versus Z, where Z is defined as:
Z=' '/S* equation 2.20
S* =(d/4v)((S-l)gd)Al/2 equation 2.21
P'= %tj/(p(S-l)gd) equation 2.22
where ctwin is the maximum wave skin friction shear stress. He found better agreement when using Z than when using T', which was used for the Grant and Madsen (1982) ripple model. Wikramanayake (1993) found that for the field ripple measurements collected by Inman (1957), Dingler (1974), Miller and Komar (1980), Nielsen (1984), and Boyd (1988) that the relation of (rj/Abr) to Z is

for 0.0016 < Z < 0.012

,n/Abr= 0.0 18 ZO'5

equation 2.23




for 0.012 < Z < 0.18

and for ripple steepness (il/),):

il/%= 0.15 Z0-009 I,/,%= 0.010 Z-065

for 0.0016 < Z < 0.016 for 0.016 < Z < 0.18

equation 2.25 equation 2.26

One draw-back with this model is that the maximum wave skin friction shear stress
(t,) is not as easy to calculate as the quantities that the other ripple models are based on. Thus quick calculations for ripple dimensions are not as easily obtained using this model as with the other models.

'9/Ab,= 0.007 Z-1.21

equation 2.24




CHAPTER 3
SUPERTANK EXPERIMENT
Site Description
Supertank Project
The Supertank experiment was a large scale laboratory experiment studying sediment transport in the near-shore environment. The experiment ran from July to September of 1991, at the 0. H. Hinsdale Wave Research Laboratory, Oregon State University. The laboratory channel used during the experiment was 104 meters long, 3.7 meters wide, and 4.6 meters deep, into which a 76 meter long beach was constructed. The beach was composed of approximately 600 cubic meters of sand taken from the Oregon coast. The sand had a median diameter of 0.22 mm.
The waves generated consisted of broad banded spectrum, narrow banded spectrum, and monochromatic with a variety of different wave heights and wave periods. The wave generator used was capable of generating wave heights of 0.2 to 1.0 meters with peak spectral periods ranging from 3 to 10 seconds. The duration of the runs ranged form 10 to 70 minutes. The wave generator was equipped to absorb reflected energy at the peak spectral frequency so as to keep reflections from the beach and structures to a minimum.
The ripple measurement system used to collect the data set was located in 2.0 meters of water along-side the rest of the University of Florida's instruments. Other instruments deployed besides the ripple measurement system include a pressure sensor, an electromagnetic current meter, an acoustic concentration profiler, and an optical backscatter measurement device (OBS).




Equipment and Measuring Techniques

Camera Setup
The supertank ripple measurement system used an under-water video camera to measure ripple geometries. The under water camera setup consisted of a Sony CCDV101 8mm video camera set inside of an amphibian underwater housing. The camera was set up such that focusing, zoom, and all recording operations could be done through a personal computer set near the tank cabled to the camera. The video signal was sent through a coaxial cable to a monitor outside of the tank such that the video signal could be monitored during the runs. The camera was supported by an external mounting system so that throughout the runs the ripples could be documented on video. On the side of the
Camera Control & Signal
Cable
N
'Reference Grid

Figure 3.1 Supertank underwater video setup




tank a grid was placed with one inch squares such that the ripple dimensions could be measured with minimal video calibration problems. The field of view of the camera was on the order of twenty five inches (63 cm.).
After the runs the ripple video tape was then replayed on a Sony Trinitron color video monitor and the ripple dimensions were digitized visually. For every intersection of the vertical grid lines with the bottom profile a measurement was made to the nearest tenth of an inch in the vertical direction for the entire field of view of the camera. This gave 25 measurements over 63 centimeters of bed. These measurements were then entered into Matlab and analyzed
Determining Measured Ripple Heights and Lengths
The first step in analyzing the ripple profiles was to smooth the profiles. To do this the Matlab routine "spline" was used. "Spline" interpolates between data points using cubic spline fits, see figure 3.2. The smoothed profile, which when compared to the original video profile looks very similar, was then detrended using the Matlab routine "detrend ". This routine finds any linear trend in the profile, which is then subtracted out so that the remaining profile is horizontal, see figure 3.3.
The smoothed and detrended ripple profiles were then entered into Matlab routines to determine representative ripple lengths and heights from each profile. The Matlab program "reval.m" was used to find all maximums and minimums in a profile. Ripple heights were found by taking the average vertical distance between each adjacent maximum and minimum over the entire profile. Ripple lengths were found by taking the average horizontal distance between adjacent maximums and adjacent minimums. Ripple steepnesses were then found by dividing the average measured ripple height by the average measured ripple length for each profile.
The second method used incorporated a threshold on ripple height. First the average ripple height was determined as described above, then a threshold of one half of this




average ripple height was set. A Matlab routine "revalt.m" was then used to determine if the distance between each adjacent maximum and minimum was greater than this threshold value. If it was, then this distance was recorded as a ripple height. If it was not, then if the last point to exceed the threshold was a maximum, the routine continued to search for a minimum that did meet the threshold requirement. If during this search a larger maximum was found than the last one recorded, this larger maximum replaced the previously recorded maximum. This process was continued until a minimum was found that met the threshold requirement. If the last recorded value was a minimum, then a similar process was executed to look for a maximum that met the threshold requirement. Average ripple height, length, and steepness were then determined by this new set, of threshold maximum and minimum values. The threshold value of one-half the average ripple height seemed to work well to find a best fit ripple height and length through most of the ripple profiles in this data set.
The threshold method was used because for many of the runs the recorded ripple profiles were quite irregular. For many of the runs there seemed to be two or more different ripple height and length scales present within the recorded profile. This made determining a representative ripple height and length for the profile difficult. Because of this comparisons were made between predictive models and measured values for both the threshold measurements and the non-threshold measurements.
Figure 3.3 is an example of a recorded bed profile with possibly two different ripple height and length scales present. There seems to be small ripples present with heights on the order of 0.2 inches and lengths of approximately 2.0 inches as well as larger ripples with heights over 0.5 inches and lengths of approximately 5.0 inches. In figure 3.3 the threshold method maximums and minimums used are denoted by an "*" where as the nonthreshold maximums and minimums are denoted by a "o". The values given for ripple height and length are in inches.




(D
C
510 1 5 20
Horizontal reference -inches Figure 3.2 Supertank ripple pattern with mean subtracted for run # 63

2
Avg. Ripple Height= 0.3235 Thresh. Pipple Height= 6.4725
5 ........... ...... ... .. ... ...
Avg. Ripple Length= 3.6: Thresh. Ripple Length= 4.417
1...........
0 5 10 15 20
Horizontal Reference- inches

Figure 3.3 Supertank detrended ripple pattern for run # 63




Supertank Data Analysis
Comparison to Previous Data Sets
Comparisons were made between previously collected field ripple data sets and the supertank ripple data set in order to determine agreement between the two. Almost every plot comparing ripple dimensions to any sediment or flow parameter is plotted on a loglog scale. This shows the amount of variation present in measured values, even within the same data set. The supertank measured values of 1l/a and X/a were plotted versus V, along with previously collected data sets (figure 2.1 and 2.2). The measured values from the supertank experiment seemed to fit with previously measured data well. The same holds true for ripple steepness versus the grain roughness Shield's parameter (02.5) (figure 2.3).
The supertank ripple steepness data along with previously collected field data were also compared to the non-dimensional parameter, djr, used by Wiberg and Harris (1994). Both the orbital diameter (do) and the ripple height (11) are measured quantities (figure 2.4). The scatter of this data compared to the scatter of previous plots is much less. Here again the supertank data seems to follow the same trends and agree well with previously collected field data measurements. Over all the supertank measured ripple length, height, and steepness data agree well with previously collected field data sets. Nielsen (1981) Model Comparison
The supertank ripple length data were compared to Nielsen (1981) laboratory and field ripple models. For every run the wave conditions were entered into both the laboratory and the field ripple length models, these results were then plotted against the measured ripple lengths (figure 3.4). It was found that as a rule for this data set the laboratory model over-predicted ripple length whereas the field ripple model under predicted ripple length. The field ripple model had better agreement with measured values than did the lab model.




E 2 102
0
9
,c
-0

-o
(D 10
(CO
0

10 10c

0

101 102
Measured Ripple Length (centimeters)

Figure 3.4 Measured versus Nielsen (1981) predicted ripple lengths (lab and field)
The relative error (A) between measured and predicted values defined as;

A = exp {[I( n(y) ln)) 2 }

equation 3.1

where "y" is the measured value and y primed is the predicted value. This quantity is a multiplicative factor that indicates the possible variation about the predicted value (Wikramanayake, 1993). For example if A equals 1.34, the average error is equal to 34 percent. The relative error found for Nielsen's (1981) ripple length models was 1.35 and
6.84 for the irregular wave model and the regular wave model respectively.

* = irregular o = regular
0 0 0
0
00
0
0
0
0
)KI

.1 .1




During the Supertank experiment several different wave types were generated (monochromatic, narrow-banded spectral, and broad-banded spectral) covering a range of wave heights (0.2 to 0.9 meters) and wave periods (3.0 to 10.0 seconds). Because of this comparisons were made between wave types on plots of non-dimensional measured ripple length vs. mobility number (figure 3.5). No trend was found between measured ripple

100

10 210 0 . . . .II. . .. I ... .
10 101 102
Mobility Number

Figure 3.5 Measured (,/a) vs. Vl for supertank data with spectral types
length and the type of wave spectrum for the Super tank data. The majority of the measurements fell in between Nielsen's (1981) laboratory (solid) and field (dashed) ripple models.

0
o = monochromatic
* = narrow banded spectrum + = broad banded spectrum




Similar plots were generated to investigate the effects of ripple type, i.e. orbital, anorbital, and suborbital. Wiberg and Harris (1994) definitions were used which define anorbital ripples when d/iJ >100, orbital ripples when dj/rl <10, and suborbital ripples when 10< doj <100, where i1 is the measured ripple height. This resulted in classifying 8 runs as anorbital ripples and the remaining 19 runs as suborbital ripples. The results showed for the anorbital ripple runs the measured ripple lengths were scattered around the field ripple length model curve (dashed), and for the majority of the suborbital runs the measured values fell between the laboratory (solid) and field model curves for the two models (figure 3.6).
Measured values of ripple heights were compared to Nielsen's (1981) ripple height models. It was found that the lab ripple height model over-predicted most of the measured
10 ..... . ..
10
o'+'. + o+
00

0.0
10
+ = suborbital ripples
o = anorbital ripples
10-1 ,. I
10 101 102 103
Mobility Number

Figure 3.6 Measured (X/a) vs. V for supertank data with ripple types




values where as the field ripple height model agreed much better (figure 3.7). The relative error calculated for Nielsen's (1981) ripple height models was 1.97 and 4.11 for the irregular wave and regular wave models respectively. The irregular wave (field) ripple height model had much better agreement with this data set than did the regular wave (lab) model.

101
0), E 0
10
a)
a
.
Cc
01
0

10 2 10

-2

10 1 100
Measured Ripple Height (centimeters)

Figure 3.7 Measured versus Nielsen (1981) predicted ripple heights (lab and field)
Comparisons were made of non-dimensional measured ripple height (11 /a) vs. mobility number (') for the different types of spectrum wave conditions. Similar results were found. There was no apparent trend between measured ripple heights and the type of wave spectrum conditions. The data were generally scattered between Nielsen's lab and

* ~~~. u U...........,
0 a 000
0 0 0 /
*=irregular 0 0
o = reg u la r K K K Ao o0
0 0
)'K
A~ )K )K )K7
-K )K ) 'K XK
XK 0




field ripple height model curves (figure 3.8). However when comparisons were made between (ij /a) and T for different types of generated ripples, similar to the plots described above, definite trends were observed. The measured anorbital ripple heights were scattered around Nielsen's (1981) field ripple height curve, and the suborbital ripple heights were generally scattered between the two model curves (figure 3.9).
As a rule Nielsen's lab steepness model over-predicted ripple steepness for most of the Supertank runs. The relative error computed for these ripple steepness models was 1.16 and 5.230 for the irregular wave and regular wave ripple steepness models respectively. Again, much better agreement was found using the irregular wave model for this data set. His field steepness model had better agreement with measured values.
101
100 i(U
S10
0) 0
-3
. -2
~10
* = narrow banded spectrum
10 o = monochromatic
+ = broad banded spectrum
1-4023
10 .. .. .. .. .. ....I. .. . .. I. .
10 101 102 10
Mobility Number

Figure 3.8 Measured (Tl/a) vs. V for supertank data with spectral types




10
100
10-1 ++
.0+ ++
I
. ++ + +
CL 0 0 +
-2
.10
o = anorbital ripples
10- + = suborbital ripples
10-4 0 2 3
100 101 102 10
Mobility Number
Figure 3.9 Measured (rl/a) vs. i for supertank data with ripple types
Ripple steepness measurements were plotted versus the grain roughness Shield's parameter comparing the wave spectrum conditions for each of the runs (figure 3.11). No definite trend was found between ripple steepness and the type of wave spectrum conditions. Comparisons were also made of ripple steepness to ripple type (figure 3.12). It was found that the majority of the measured steepness values for anorbital ripples fell on or below the field model curve. For the suborbital ripple runs, the majority of the measurements fell between the laboratory and field model curves, however some of the suborbital runs even fell below the field model curve. This is probably due to the similarity of the two curves, and the fact that some of the runs classified as suborbital were very close to being classified as anorbital runs.




CL CD
a
CL
.10
cc

t10-2'

10.2 101 1
Measured Ripple Steepness
Figure 3.10 Measured versus Nielsen (1981) predicted ripple steepness (lat
100L

10-31 ,
102 0-1
Grain Roughness Shield Parameter
Figure 3.11 Measured (n/) vs. 02.5 for supertank data with spectral types

100
b and field)

=irregular ,
o= regular
oJ
o
W., K X
AK 3
, J l
-

0 ) +

o = monochromatic
* = narrow banded spectrum + = broad banded spectrum




O0
10.
10"1 + 10+
2) +
0)0
0) 0)
0)5
C C 1 0 2
+ = suborbital
o = anorbital
10,3'
10~ 1 0 100
Grain Roughness Shield Parameter
Figure 3.12 Measured (i'rVX) vs. 02.5 for supertank data with ripple types
After comparing measured ripple geometry to Nielsen's (1981) lab and field models it appears that classifying bedforms by the wave environment present, spectral (field) or monochromatic (laboratory), is not the best classification scheme for the supertank ripple data set. In comparisons between measured values and Nielsen's models for ripple length, height, and steepness for different types of wave spectrum conditions no real trends were found; agreement did not significantly improve when the field model was used for irregular wave conditions and the lab model for regular wave conditions.
When comparing Nielsen's (1981) models for ripple length, height, and steepness to measured values for different ripple types, definite trends were present. For each of the models better agreement was found when anorbital ripple measurements were compared to field models. For each of the models suborbital ripple measurements generally fell




between the lab and field model values. The majority of the laboratory data collected prior to 1981 was in the orbital ripple regime due to the inability to create prototype orbital diameter conditions in most of the wave flumes. In contrast, most of the field ripple data is inherently in the anorbital and suborbital ripple regimes. It appears, at least by comparisons with this data set, that better results can be found by using the ripple type classification scheme than by using the wave environment method when using the Nielsen (1981) ripple models.
Wiberg and Harris (1994) Model Comparison
Comparisons were made between measured ripple dimensions and calculated ripple dimensions using the Wiberg and Harris (1994) method for each of the supertank ripple runs. As stated earlier the Wiberg and Harris (1994) model uses a ripple type classification scheme classifying anorbital ripples when dirl >100, orbital ripples when dJ7r<10, and suborbital ripples when 10 < d/ < 100. With this method using measured ripple height
(1l), 19 of the runs were classified as suborbital ripples and the remaining 8 were classified as anorbital ripples. However when using the Wiberg and Harris (1994) predictive model calculated ripple height is used to classify the ripple regime. Anorbital ripples are classified when do/rico >100, orbital ripples when djril, <10, and suborbital ripples when 10 Comparisons between measured ripple length and calculated ripple length using the Wiberg and Harris (1994) method were made. Measured versus predicted values were plotted (figure 3.13). For the majority of the runs the model over predicted ripple length,




however in comparison to other models the scatter about measured values was the lowest. The relative error (A) between measured and predicted ripple lengths was 1.27, which was the lowest of all of the ripple length models for this data set.

W Cl)
E
a,
10, CL 0.
.D
CO
0

10

10'
Measured Ripple Length (centimeters)

Figure 3.13 Measured versus Wiberg and Harris (1994) predicted ripple lengths
Similar comparisons were performed for the Wiberg and Harris (1994) ripple height
model. As shown in figure 3.14 this model over predicted ripple height for most of the runs, however it still did better than any of the other ripple height models. The relative error (A) for these ripple height predictions was found to be 1.25, which is much better
than any of the other models for this data set.

+= orb, o= ano,*=sub .. "
+ W K
I.

0




10
+= orb, o=ano,*=sub + .
)K
10-,E
"- I ,
100 1
O ,"
oJ
1
1 0101 Measured Ripple Height (centimeters)
Figure 3.14 Measured versus Wiberg and Harris (1994) predicted ripple heights
For ripple steepness the Wiberg and Harris (1994) model again did better than any of the other models. As seen in figure 3.15 this model tends to over-predict ripple steepness for most of the runs, however the spread around measured values was low with a relative error of just 1.08. When measured values for ripple steepness are plotted versus orbital diameter over ripple height (dJAr), along with the Wiberg and Harris (1994) steepness model curve (figure 3.16) it can be shown that even though the model curve falls above most of the measured values, the trend of the data follows the curve.




100
+= orb, o= ano, *= sub
10
0.
10 --o o')
Ca
W/
+10 2 +0u ,
3 10 10r 102 10 104
..
u
o
1CD +
C
CL +
2 + C10 + 100 0
0 .
10 I
0.0
+ = suborbital ripples 0
o = anorbital ripples
10.
1
100 0 1010 1

Figure 3.16 Steepness (r1A) versus (dJ) for supertank data




Over all the Wiberg and Harris (1994) ripple prediction models agreed relatively well with the supertank data set. They did better than any other models presently available at predicting ripple length, height, and steepness. The ripple misclassification problem between measured dd/r and calculated do/ra was probably due to the large amount of runs where d/rt was close to the transition point between the suborbital and anorbital ripple regimes of d/rt=100. However since the suborbital ripple length model is simply a weighted geometric average between the orbital and anorbital ripple regimes, the misclassification of these runs near the transition point probably did not effect the calculated values greatly.
Wikramanayake (1993) Model Comparison
For each of the supertank runs the flow and sediment data were entered into the Wikramanayake (1993) ripple model. The ripple dimensions calculated with this model were then compared to measured values in a similar manner as that used for the previous model comparisons. Calculated ripple lengths using the Wikramanayake (1993) ripple model were compared to measured ripple lengths. From figure 3.17 it can be seen that the predicted values for most of the runs were larger than the measured values. The relative error (A) for this ripple length model was 1.33 for the supertank data set.
Predicted ripple heights using Wikramanayake's (1993) model were also plotted versus measured ripple heights (figure 3.18). The predicted values were scattered around the measured values with a calculated relative error (A) of 1.73.
A plot of li/a versus Wikramanayake's (1993) "Z" parameter, from equation 2.20, for the supertank data set along with his model curve shows that the ripple height model bisects the cloud of measured values (figure 3.19). For this ripple height data set the nondimensional parameter Z does approximately just as well as the mobility number (W) at organizing the data points, however there seems to be no apparent trend in the data when ilia is compared to Z for this ripple height data set.




Q
E
r
3101
..
Co .0
U

100 10' 102
Measured Ripple Length (centimeters)
Figure 3.17 Measured versus Wikramanayake (1993) predicted ripple lengths
101 01.

0
E
U
.0
*10' 01o
Ca
z CO

1 0 . I
101 100 101
Measured Ripple Height (centimeters)
Figure 3.18 Measured versus Wikramanayake (1993) predicted ripple heights

00 /0
S000 0
0 0 o0 0
0 0
0, 0 0%
O OO 7
,
O O0

0,
0 00 0 00
0 0
O /
0 0 0 0
0., 0
0
0 0
0
/o/
0
0
0
//

100

I

IV




C 0
10 X
0X
EE
1 10.2 10"1 10o
Z from Nalin (1993)
Figure 3.19 (iq/a) vs. Z for supertank data with Wikramanayake (1993) model curve
Ripple steepness predictions using Wikramanayake's (1993) model agreed relatively well with measured values of ripple steepness (figure 3.20). The relative error (A) for this ripple steepness model using the supertank data set was 1.11.
The measured ripple steepness values were also compared to the Wikramanayake (1993) Z parameter, along with his model curve (figure 3.21). Again the curve bisects the data cloud well for this data set. There seems to be a trend in the data that follows the model curve; however there still is a fair amount of scatter about this curve.
The non-dimensional parameter djrj seemed to group the data in this data set the best, doing slightly better than Wikramanayake's (1993) non-dimensional parameter Z for ripple steepness. Both do/rl and Z grouped the measured values better than 25, for this data set. However there still was quite a bit of spread present in all plots, which is typical for ripple dimension data.




100
O
/O/
10- .
10-20 0010
(,n
10
0~ 0
0
Figur 3.0Maue essWkaaaae(19)peitdrpl tens
c I.
(U
- 0
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-2I" mo
10"
102 io' 10
Meaurd ipleStepes
Fiur .2 Maurd esu Wkamnaae 193 pedcedripe tepese
0/
lOF ]

(D
(
W
0.
CD
E
1010
10-

10.2 101

Z from Nalin (1993)
Figure 3.21 Steepness versus Z with Wikramanayake (1993) model curve




Table 3.1 Values of relative error (A) between measured and predicted values Wiberg and Harris Wikramanayake Nielsen field Nielsen lab
(1994)............. (1993) (............... 198 1) (1981)
................................................... .(....9...9................................... .. .19 .... ..................... ...........(. ......... ........................... ... .....................
ripple height 1.25 1.73 1.97 4.11
ripple length 1.27 1.33 1.35 6.84
ripple steepness 1.08 1.11 1.16 2.69
ripple height 1.08 1.36 2.15 2.25
with threshold
ripple length 1.11 1.19 1.58 3.35
with threshold
ripple steepness 1.05 1.06 1.12 2.56
with threshold
Values for the relative error were also calculated with measured threshold values, see table 3.1. The results were similar, however the Wiberg and Harris (1994), Wikramanayake (1993), and the Nielsen lab (1981) models had better agreement when measured threshold values were used. The Nielsen field (1981) model agreed better for ripple steepness, but agreed less for ripple height and length, when threshold values were used.
The Wiberg and Harris (1994) ripple prediction models worked better than the other models for the supertank data (both threshold and non-threshold) in predicting ripple length, height, and steepness. The Wikramanayake (1993) models worked second best in all three categories, working slightly better than Nielsen's (1981) field ripple models. As expected for this data set Nielsen's (1981) laboratory ripple models worked the poorest, probably because none of the runs fell in the orbital ripple regime ( which is most likely what his laboratory models are based on.)




CHAPTER 4
RIPPLE MEASUREMENT TECHNIQUES AND DESIGN OF RIPPLE PROFILER
Ripple Measurement Techniques
SCUBA Diver Observations
Until 1972 all field ripple data sets were obtained through visual observation and measurement by divers. SCUBA equipped divers have the advantage of being very mobile. This allows coveting a large area of the seabed and observing in detail the bedform patterns over a relatively large area. Divers can relatively easily measure ripple lengths and record plan view observations of the seabed showing it's three dimensionality as well as large bedforms which are difficult to measure by other methods.
Problems divers encounter when measuring bedforms generally occur when attempting to record ripple heights. With a meter stick ripple lengths can be recorded relatively easily. However when attempting to measure ripple heights, the weight of the meter stick tends to flatten the crests of the ripples. There have been other methods used by divers; such as Inman (1957) who used a clear piece of plastic and a grease pencil to record ripple profiles. Also divers have used a large comb covered in grease or petroleum jelly such that when pressed into the bed, perpendicular to ripple crests, the ripple profile is recorded by the sand remaining on the comb after extraction. This profile can then be traced onto a slate or paper and measured relatively easily. There are problems of distorting the profile when an instrument is pressed into the sediment, however over all these techniques work relatively well.




The two main problems with measuring ripple dimensions when diving is that some water visibility is required and currents (both oscillatory and unidirectional) are generally present. When in the surf zone, or just outside of the surf zone, generally the visibility is not very good and the water currents are fairly strong. It is not uncommon to have the water motion due to the waves moving back and forth with a semi-excursion of over one meter and a period of around ten seconds in the surf zone. This makes trying to remain off of the seabed, so as not to disturb it, and remaining in a single spot to make a measurement very challenging. Thus under active anorbital ripple conditions it is very difficult to accurately measure ripple dimensions.
Other problems include measuring wave and current conditions while making ripple measurements. Unless instruments are deployed, accurate measurements of waves and currents are almost impossible. In the past fathometers placed on a surface craft have recorded time series of bottom returns as waves passed underneath, thus crudely recording wave heights and periods while divers make measurements of the ripples below. This method was used by Inman (1957) when he collected his field ripple data set.
It is becoming apparent that the time varying ripple profile is important in the development of sediment transport models. It is almost impossible to record how the rippled bed changes under individual waves, wave groups, and even under changing wave conditions over periods of hours by using SCUBA equipped divers. Thus alternative measurement techniques have been and continue to be developed. Video
Underwater video has been used to measure bedformn ripples in the in the field. Video has the advantage of recording bedforms as they migrate and change with time, as well as visually recording the general mechanics of ripple formation visually. Video cameras today can be set up to sample at any number of different schemes, giving the capability of remote operations for extended periods of time. Small, low-light, high resolution underwater




cameras are manufactured that do not obstruct the flow greatly and allow video imaging in extremely low light conditions (approximately I lux). However water clarity is still required for video ripple measurements.
The main problem with making video measurements of bedform ripples is determining the heights of the ripples. Ripple lengths can be measured relatively easily once the video field of view has been calibrated, however ripple heights are difficult to measure. One possible technique is to use an array of calibrated vertical rods set into the sand bed within the field of view of the camera. When ripples form they can be measured roughly by recording where on each of the rods the sand level is, and since the exact dimensions of the rod array are known, the ripple profile can be measured. Stereo Video/ Photography
Since unobtrusively determining ripple height using video or still photography is difficult, another method that may be used to measure bedforms is stereo photography. This would allow for three-dimensional measurements of a relatively large area of sea-bed. Stereo photography uses parallax, which is the apparent displacement in the position of an object with respect to a frame of reference caused by a shift in the position of observation (Wolf, 1993). This is the same principal that makes the motion of objects nearer ones eyes seem greater than the motion of objects further away. In stereo photography parallax is used to determine elevations.
One method in determining elevations of a recorded stereo image is with a stereoscopic plotter. This instrument has two projectors which are situated such that their positions agree with the positions of the cameras used to record the initial image. These projectors project an image down to a tracing table. Above the tracing table there is a white disk, called a platen, which can be moved in both horizontal and vertical directions. Below the platen is a tracing pencil. The platen is moved until reference points from both projected images coincide on the platen. At a certain elevation of the platen a contour line




can be plotted as long as the projected images on the platen from both projectors coincide. 'ne platen can be raised and lowered to plot other contour lines in a similar manner.
Automated stereo plotting systems are also available, however they are very expensive (over $ 100,000) and still can not achieve the accuracy attainable by human eyes and a manual stereo plotter. The problem with stereo photography and measuring ripples is that distinct objects are not generally present along the sea-bed, and suspended sediment and other matter can interfere with the quality of recorded images. Stereo photography works well for aerial survey work where many objects are present which can be used for references, however bedform ripples tend to look very similar to each other and not have distinct objects that can be used as references. Stereo photography possibly could be used to measure bedform ripples, however constructing contour plots of the seabed would be a very slow and labor intensive process.
Video with Image Processor
Another video apparatus that can be used to measure ripple lengths fairly accurately is a video image processor. Video images can be digitized and then brought into an image processor such as Global Lab Image. If the exact location of a few points located on the same horizontal plane are known, these points can be entered into the program and the whole video image can be calibrated for that horizontal plane. Positions can be measured along this horizontal plane by moving the cursor to the location of the point of which the position is wanted and the program will output the desired calibrated coordinates. This method works well for measuring ripple lengths, however it is unable to measure ripple heights.
Holl5omood Deployment Example
An underwater package was deployed between December I and 3, 1992 off of Hollywood, Florida in thirty feet of water. The package contained a pressure sensor, an electromagnetic current meter, two optical back-scattering measurement devices, and an




under- water video camera. The underwater video camera setup consisted of a Sony CCD VIOI 8 mm video camera enclosed inside of an amphibian underwater housing. All of the instruments were controlled by a Tattle-tale model 6 data logger. The camera was set up to record for two seconds every five minutes. The camera was controlled by the Tattletale via a communication cable which was wired to the camera's remote control inside of the camera's housing.
Within the field of view of the camera an array of stainless steel rods was set up. This rod array consisted of two rows of four, 1/8 inch diameter, 6 inch long stainless steel rods welded to a 1/4 inch thick steel plate. The rods were calibrated vertically in alternating yellow and black one centimeter wide bands. The rods were 4 inches apart from each other, thus the array covered a 12 inch by 4 inch area. When deployed the rods were buried and the sand smoothed out between the rods protruding through the sand. See figure 4. 1.

Camera Control Cable

Stainless Steel
Rod Array

I I

Figure 4.1 Hollywood underwater video set-up with rod array




The underwater package was then turned on and left for three days. During this time there was no significant swell and the water visibility remained excellent; greater than 50 feet. After three days the package was retrieved. Measurements were made of the bed elevation along each of the rods by divers. There were no bedform ripples present within the study area which was smoothed out at the beginning of the deployment. Because no ripples were present, sand ripples were fabricated in order to test the video measuring technique. Ripples with lengths of 8 inches and heights of 1 inch were constructed through the array, and elevation measurements were made at each of the rods by hand.
Upon return, the time lapse video was watched and the video monitoring system was found to work as planned. The fabricated ripple video images were digitized and loaded into Global Lab Image, where the field of view was calibrated and measurements of ripple lengths were made. For this example calibrated measurements made using Global Lab Image for known distances, such as the horizontal distance between rods, were generally within five percent of the known measured values. For measurements of ripple length, underwater video and an image processor can deliver relatively accurate measurements as long as a few points are known such that the image can be calibrated correctly. Acoustic
In recent years hydro-acoustics has proven to be an effective method in measuring bedform geometries. Distance measurements are made with an acoustic range-finder by first sending a pulse from the ultrasonic transducer and simultaneously starting a timer. This pulse then is reflected, from the bottom, back to the transducer and the time taken for the sound pulse to travel this path is recorded. The total distance that the pulse traveled can then be calculated by multiplying the time for the sound to travel this distance by the speed of sound in water. Thus the distance from the transducer head to the seabed is half of this product.




Acoustic range-finders have been used since W.W. II to accurately measure depths and detect objects (Urick, 1983). However most underwater range-finders operate in the Kilo-hertz (KHz) frequency range because the distances being recorded are generally large. The attenuation of higher frequency signals is much greater than that of lower frequency signals, subsequently the signal level drops off more rapidly at higher frequencies thus the range over which the signal can travel is less for higher frequencies. However since the wavelength at lower frequencies is proportionally larger than the wavelength at higher frequencies, the resolution at lower frequencies is less. Thus for measuring bedforms, where millimeter vertical resolution is required, the transmitted pulse should be in or near the Mega-hertz (MHz) frequency range.
Dingler and Inman (1976) were the first to use acoustics in the field to measure bedform ripples. They used a single, 1 MHz, transducer which was slid along a horizontal track by SCUBA divers while the returns of the transducer were being recorded along with its horizontal position. This allowed the profile of the bed to be recorded with greater accuracy than previous methods would allow.
'Most acoustic range-finders used today, especially those working in MHz frequencies, rely on piezoelectric crystals for both the transmission and the reception of the ultra-sonic signal. Piezoelectric materials are materials which when mechanical pressure is applied the crystalline structure produces a voltage proportional to the pressure. Conversely, when a voltage is applied, the crystalline structure changes shape producing dimensional changes in the material. The piece of piezoelectric material used to make a transducer is generally called a piezoelectric crystal, or just crystal. Every crystal has a natural frequency which is dependent on the chemical properties and geometry of the crystal. Generally crystals used in making transducers are either shaped as thin disks, rectangles, or occasionally, rings. The natural frequency of the crystal along the axis most important to transducer design is a function of the thickness of the disk, rectangle, or ring.




There are many different types of piezoelectric materials. The most common type used in high frequency, MHz range, transducer design are composed of polycrystalline ceramics. The physical, chemical, and piezoelectric properties of these ceramics can be tailored for specific applications. These properties include being chemically inert, immune to moisture, and having the electrical axis precisely oriented in relation to the shape of the finished ceramic piece. High sensitivity, permitivity, and time stability are also properties associated with these ceramic crystals. The crystals are silver plated on each side with leads so that the voltage may be applied evenly across the crystal, giving a uniform displacement.
In order to generate the desired pulse, the crystal must be exposed to an oscillating voltage so as to create the oscillating deformation of the crystal which produces the pressure waves of the signal. The oscillating driving voltage applied to the crystal should be at the same frequency as the natural frequency of the crystal being driven. As an example, if the required signal is 1 MHz, the crystal chosen should have a natural frequency of 1 MHz and the oscillating voltage applied to the crystal should have a' frequency of 1 MHz. The duration of the oscillating voltage applied to the crystal is generally very short, on the order of tens of micro-seconds ( Is), and the voltage applied is generally large, greater than 100 volts.
The reception of the pulse, like the transmission, is also through the crystal. Since when a pressure wave strikes the face of a piezoelectric material a voltage is generated, the piezoelectric crystal can be used as a receiver. The bottom return, or echo from the sea-bed, strikes the face of the transducer which in turn causes the crystal to create a voltage potential between its two silver-plated faces.
Two methods can be used for receiving and interpreting the bottom return from the return signal. First the entire time series of the return signal can be recorded. The time series contains the whole signal from transmission to bottom return with corresponding time delays. From the recorded time series, the time taken for the signal to travel to the




seabed and back to the transducer can be found. From this the distance to the bed can be determined. Another method that can be used to receive and record the bottom return is the threshold method. Since the bottom return generally corresponds to the largest return, a threshold can be set so that when the return signal exceeds this threshold a timer is stopped. The time from transmission to the bottom return is then recorded, which can then be used to calculate the range from the transducer to the sea-bed. Both the time series method and the threshold method can be used to accurately measure distances between the transducer and the sea-bed. If only distances to the sea-bed are needed, the threshold method has the advantage of only storing one time delay for each measurement, where as with the time series method there is a lot of data which must be stored and later analyzed in order to make a single measurement.
Transducer with Stepper Motor
There are a few different methods that can been used to remotely measure ripple geometries using acoustics. Each has its advantages and disadvantages. The first method is very similar to that used by Dingler and Inman (1976). It uses a single transducer mounted on a frame which tracks back and forth mapping the profile of the sea-bed below. However instead of manually tracking the transducer back and forth as Dingler and Inman (1976) did, a stepper motor can be used. The High Resolution Remote Tracking Sonar (HRRTS) used by Greenwood, Richards, and Brander (1993) used a stepper motor to track a single transducer across a frame. The main problem with this method is that there are a lot of moving parts, and in the high energy near-shore environment this can lead to problems. During the field deployment of the HRRTS 11, the ranging system had problems with vibration due to the strong currents present in the near-shore environment.
Another possible set-up is a multi-element transducer with a stepper motor. A multielement transducer is a transducer with more than one crystal. This allows for multiple measurements to be taken without physically moving the transducer. Each of the crystals




have separate leads and can be "fired" sequentially in order to map out a segment of the bottom profile. In this system the multi-element transducer would be on a tracking system similar to the one described above, however the range of motion would not have to be as large as that with a single element transducer. This would be an improvement over the single element transducer because it would not have to move as frequently nor as far. It does still contain moving parts and thus would be subject to problems with jamming and vibration due to the forces exerted on it in the field. Side-scan Transducer
There are two systems that can be designed without any moving parts. The first uses a transducer in side-scan mode in conjunction with a transducer orientated vertically. This method has been used by Osbourne and Vincent (1993) to measure bedform geometries and migration rates. The transducer in side-scan mode is generally mounted less than a meter above the bed and aimed slightly downward from horizontal. This transducer should be oriented such that it is aimed perpendicular to the ripple crests. When used in side-scan mode a transducer can record ripple wavelengths because the transmitted signal is reflected from the up-slope of the ripples. The side-scan transducer has proven to be able to measure ripple wavelengths. A vertically oriented transducer is then used to measure ripple heights. The theory is that as ripples migrate under the transducer their heights can be recorded by measuring the changes in bed elevation below the single transducer. This system has no moving parts, which is advantageous when working in the near-shore environment. However it relies on the migration of ripples under a transducer to measure ripple heights. This means that instantaneous ripple height measurements can not be made, which is an important measurement.
Stationary Multi-element Transducer Amay
The optimum design would be one with no moving parts and the capability of measuring instantaneous ripple profiles. A system which satisfies both of these criterion is




a ranging system using a stationary multi-element transducer. This system would incorporate a multi-element transducer array similar to the one described previously. However, this array would be of such a size that the desired length of bed could be mapped out without having to move the array. This would allow the transducer to be mounted securely so as to eliminate the vibrations found in moveable systems, and allow for near instantaneous profiles.
Design and Construction of an Acoustic Ripple Measurer
Determination of Frequency
There are many factors which must be considered when determining an operating frequency for a ranging system. Some of these include the design operating range between the transducer and the sea-bed, the required vertical resolution, and the required horizontal resolution. As mentioned earlier, higher frequency signals attenuate much faster in water than do lower frequency signals. This can be shown by the following expression for the absorption coefficient taking into account the two major sources of attenuation; ionic relaxation and viscosity (Urick, 1983).
(x f2 f2 + bf2 equation 4.1
Where 'f' is the operating frequency, "a7 and "b" are constants, and f, is equal to 166.2 for water at 75 degrees Fahrenheit. It was found that frequencies up to 5 MHz could be used for a ranging system with a 2 meter range without problem.
The second factor considered when determining the operating frequency was vertical resolution. The maximum vertical resolution attainable is a function of the wavelength of the transmitted signal, which is related to the frequency of the transmitted signal by:




C equation 4.2
f
where "c" is the speed of sound in water, which is approximately equal to 1500 meters per second, and 'T' is frequency. For a 5 MHz signal, the wavelength is 0.3 mmn. This would easily allow for measurements to be made to millimeter accuracy in the vertical direction.
Another factor governing the decision of operating frequency is horizontal resolution. The main concern here is the footprint of the transmitted signal. The footprint of the transmitted signal is defined as the cross-sectional area of the transmitted signal when it contacts the desired target. The acoustic footprint is a function of the diameter of the crystal, and the beam angle of the transmitted pulse. The beam angle is the angle at which the transmitted signal spreads tangent to the direction of wave propagation. This angle is generally measured as a half-beam angle. The half-beam angle is measured from a perpendicular extending downward, from the edge of the crystal, outward to a point where the signal is 50% of the value at the perpendicular See figure 5. 1. The half-beam angle to 50% intensity was described by Coates (1989) as:
half-beam angle = 30X/D equation 4.3
where X is the wavelength of the transmitted signal, defined by equation 5.2, and D is the diameter of the crystal face. The footprint of the signal is equal to the diameter of the crystal plus the spreading of the signal from the crystal to the sea-bed. The footprint (fp) can be expressed as
fr=D+ 2rta -3) equation 4.4




where r is the range from the transducer to the sea-bed.
This value varied greatly with frequency and crystal diameter. The desired horizontal resolution, or footprint, was on the order of one centimeter. It was found however that at a range of 50 centimeters above the sea-bed this resolution was not attainable. The most reasonable set up is a disk shaped crystal one centimeter in diameter working at a frequency of 5 MHz. This gives a footprint of 2.57 cm., by equation 4.4. Where as a one centimeter disk at 2 MHz and 1 MHz gives a footprint of 4.9 cm. and 8.9 cm., respectively. For a frequency of 5 MHz the optimum crystal diameter was found to be 1

I D ---

crystal

half-beam angle

- footprint on sea-bed

figure 4.2 Simplified transducer beam pattern showing half-beam angle and footprint
cm. by equation 4.4.
It is not feasible to operate at a frequency greater than 5 MHz for this application. This is due to attenuation of the transmitted signal and difficulties in the generation of a

fp




driving signal at higher frequencies. It was decided that a one centimeter piezoelectric crystal operating at 5 MHz was the best solution for a ripple profiler located 50 centimeters above the bed. This theoretically allows for measuring the distance to the bed to an accuracy of at least 1 millimeter with 2.5 centimeter horizontal resolution. Selection of Materials
Once the frequency and dimensions of the crystals to be used are known, the next step is to find a crystal that has the required specifications for the transducer application. Lead zirconate titanate (PZT) polycrystalline piezoelectric elements are the best suited for high frequency under-water transducers. PZT crystals have a high dielectric constant with high voltage sensitivity. There are many different varieties of PZT crystals. Properties that should be looked for in choosing a PZT crystal include rigidity, high sensitivity, and stability. The crystals chosen for this application are APC 840 crystals, manufactured by American Piezo Ceramics, Inc.. Their exact specifications can be found in Appendix B.
The next step is to choose a potting resin. The purpose of the potting resin is to create a rigid matrix around each crystal that will allow the transmitted signal to pass from the crystal through the resin and into the water without much energy loss. Once again there are many different kinds of potting resins. Properties important in choosing a potting resin include hardness, the thermal expansion coefficient, the pc constant, and electrical insulation.
Since there will be voltages in excess of 100 volts with electrodes separated by only 0.3 mm, it is important that the resin be a good electrical insulator. As long as the resin chosen is specially designed for electronic insulating applications, this is not a problem. Another factor is the pc constant. The pc constant is a way of determining the acoustical compatibility of two materials. It is the product of the material's density (p) and the speed of sound in the material (c). There are resins that have pc constants very similar to that of sea-water, which means that theoretically sound should be able to propagate from one




medium to the other with minimal losses. At lower frequencies, in the KHz range, this is a very important property, however at higher frequencies, in the MHz range, this property is not as important as some of the others.
One of the most important properties of a potting resin used in high frequency transducers is its hardness. When the design frequency of the transducer is in or near the MHz frequency range it is very important that a hard potting resin is used, If a resin that does not set-up hard is used, the transmitted signal will lose a lot of energy to viscosity while propagating through the resin.
Another extremely important physical property of the potting resin is its coefficient of thermal expansion. The coefficient of thermal expansion of the potting resin should be very close to that of the housing material, If the potting resin and the housing material have coefficients of thermal expansion that differ from each other, when the instrument is subjected to a change in temperature, differential expansion will result. Differential expansion can lead to cracking of the potting resin and failure of the instrument. If an aluminum housing is used, the potting resin should have a coefficient of thermal expansion around 23.0 in./inJ0OC x 10-6.
The epoxy potting resin chosen for this transducer is E341FR manufactured by Castall, Inc. with hardener RT-7, a product of the same manufacturer. It is a very hard electronic insulating resin that has a thermal expansion coefficient within eight percent of aluminum. See Appendix B for detailed potting resin specifications.
While choosing a resin, the material used for the housing must also be chosen. For this application aluminum was chosen. Aluminum has the advantages of being easy to machine, light-weight, and a coefficient of thermal expansion close to that of many potting resins, If long under-water deployments are expected, it is important that the entire aluminum housing be anodized. Anodizing should be performed after the machining of the housing is complete.




Geometry of Transducer
For the multi-element transducer array the configuration of the crystals as wen as the dimensions of the transducer had to be established. In order to get an accurate representation of the bedforms on the sea-bed it was decided that a profile at least 30 centimeters in length should be recorded. Since the optimum crystal diameter is 1.0 centimeter, as previously discussed, a transducer with approximately thirty individual crystals would be required.
The crystals should be configured such that they are as close together as possible without interfering with adjacent crystals. The design separation distance between crystals for this instrument is 2.0 millimeters. This will keep interference between crystals to a minimum. Thus the total length of profile that this instrument will be capable of measuring is 36 centimeters. This should allow the capability of accurately representing most types of bedforms found in the near-shore environment.
As mentioned before the chosen material for the transducer housing is aluminum. Aluminum "C" channel 3 inches wide with 2 inch flanges was chosen for this instrument. The "C" channel supplies the transducer with a rigid housing that can be easily machined or even welded to fit a mounting system. The flanges of the "C" channel act not only to stiffen the housing, but also as protectors of the transducer face. If something were to strike the front of the instrument, most likely the blow will be taken by the aluminum flanges rather than by the potting resin. The overall length of the transducer housing should be less than 50 centimeters, which allows for lay-up of the transducer in the Coastal Engineering facilities at the University of Florida. Figure 4.2 is a schematic of the stationary multi-element transducer ripple profiler.




multiplexer, transmitter and receiver circuitry

cross-section of multi-element transducer

cork-neoprene insulation backing

transmitted 5 MHz ultrasonic signal

bottom profile
Z

piezo electric I
crystals wire leads to
crystals
recorded points
along bottom profile

* ~ *

* * * *

* * * *

sand sea bed

scale 5cm. =
Figure 4.3 Schematic of multi-element transducer ripple measurement system
Potting of Transducer
Several smaller multi-element transducers ( containing two to five crystals) were
potted using different types of resins, crystals, housings, leads, and potting methods. Since minimal information is available on the actual building of MHz frequency ultrasonic transducers, there was a lot of trial and error involved before satisfactory results were
obtained.




The first sets of transducers were potted using 1 centimeter square crystals. The square crystals were used with the thought that they would be easier to lay-up than diskshaped crystals. Since 5 MHz PZT crystals are only 0.3 millimeters thick and are very brittle, they are easily broken. The corners of the square crystals tended to break off and there turned out to be no real advantage in potting rectangular crystals over disk-shaped crystals. The beam pattern of disk- shaped crystals is better understood than that of rectangular crystals. There is a possibility that in the future this instrument will be used to measure not only ripples but also concentration profiles. Since knowledge of the beam pattern is very important in calibrating concentration profiles, further lay-ups were performed using disk-shaped crystals.
The first transducers potted used a relatively soft potting resin that had a pc constant very similar to that of sea-water. It was thought at the time that the pc constant was the most important parameter of a potting resin. The resin used was a urethane resin used by the military to pot lower frequency transducers. It did not work well for this application.. Even after curing in an oven for over one week, the resinwas too soft to hold the crystals rigidly. The resin also had problems of out-gassing carbon-dioxide while curing which left entrained bubbles in front of the crystals. Even though the resin was supposed to be acoustically similar to water, there was significant signal loss due to the entrained bubbles and to the viscosity of the resin. It was later learned that the most important acoustic property of a potting resin when used for applications in the MHz frequency range is hardness. The epoxy potting resin mentioned previously was used with much greater success. No out-gassing problems were observed, and the resin after set-up at room temperature was very hard.
Different housing materials were also tried. The first transducer housings were made out of fiber-glass "C' channel. The "C" channel was 1.0 inches wide and had flanges of 0.5 inches. The fiber-glass created good bonds with the potting resin, however the structural integrity of the finished transducers was questionable. The fiber-glass channel




was not very stiff. Flexing of the channel could lead to cracking of the potting resin if too much stress is applied. There also was a problem with rigidly mounting the fiber-glass transducer. Because of these problems aluminum was chosen for the housing material. As mentioned earlier aluminum channel 3 inches wide with 2 inch flanges was used in the final design. Transducers potted in anodized aluminum channel are very rigid, have good bonds between the anodized aluminum and the resin, and are easy to machine for mounting.
Different potting methods were tried in constructing the smaller transducers. The first method used involved an "acoustic window" machined in the bottom of the channel through which the transducer was to be aimed out. The acoustic window was slightly wider than the diameter of the crystals and was as long as the line of crystals to be used. Lay-ups using the acoustic window method were made from the face of the transducer to the back of the transducer. A small piece of plexi-glass was first temporarily fastened to the exterior of the channel bottom, covering the acoustic window, and the ends of the channel were dammed. Then a thin layer of resin was poured into the bottom of the channel and allowed to cure. Later the crystals were placed face down on the thin layer, such that they were facing out of the acoustic window. The backing insulation material was then laid over the crystals and resin was poured into the channel until all components were completely submerged. Upon curing, the plexi-glass was then removed. Transducers potted in this manner worked, however there were some problems that could be avoided by changing the potting process. Such problems include; stressing the crystals while removing the plexi-glass, movement of the crystals while resin is curing, and entrapped air bubbles on the face of the crystals.
Best results were obtained when the crystals were potted from the back to the front. In this case the back of the crystals were facing the bottom of the channel, thus the front of the crystals were facing out the open side of the channel. Consequently no acoustic windows had to be machined. The first step in this potting process was to glue the insulating backing material to the bottom of the channel. The backing material used was a




cork-neoprene mixture 2 millimeters thick. Two plies of backing material were glued to the bottom of the channel, covering the whole bottom of the channel. Two more plies, slightly wider than the crystals, were then glued in the center of the channel on top of the existing backing material. The purpose of the bottom two layers was to provide a surface that could have grooves dremmeled out in order to run the main wires. The top two layers provided a surface that could be dremmeled out for the crystal leads so that the crystals could lie flat.
Leads were then soldered onto the crystals. Best results were found when solid light gauge wire leads approximately one inch in length were soldered onto both sides of the crystals, near the crystal's edge. From these leads coaxial cable was run for the remainder of the distance to the driver and receiver circuitry. The light gauge leads allowed for greater flexibility when placing the crystals before set up than when coaxial cable was run all the way to the crystal face. Since the transmitted signal is high frequency and must be transmitted over a distance of at least a couple of feet, coaxial cable was used because of its shielding ability.
Next grooves were dremmeled into the backing material for the leads and coaxial cable to run. The location of each crystal as well as the position of the leads and coaxial cable for each crystal were marked on the backing material. The top layer of the backing material had spaces dremmeled into it for the solder joint and lead on the back side of every crystal. This allows for the crystal to lay flat on the cork-neoprene backing. Grooves were also be dremmeled for all of the wires to run through.
A permanent rubber dam was built to serve as both a dam while pouring the resin as well as a water-proofing barrier for the transducer. The most successful damming material used was a 1/4 inch black rubber gasket cut to fit inside of the aluminum channel. Holes were drilled through the gasket so that the coaxial cable could be run through it. The holes drilled were as small as possible, so as to provide a tight seal. The gasket was glued in place with an epoxy resin forming a tight seal around the edges. This type of dam could




have been used on both ends of the channel, however a removable plastic dam at the other end worked just as well at retaining resin during pouring.
Next the crystals and the leads were glued into the grooves using an epoxy based adhesive. Great care was taken during this step. Each crystal was adjusted so that it was lying perfectly flat and its leads were run through the grooves previously dremmeled for it. The crystals were oriented with their grounded side facing up (pointing out of the channel). It was important that the crystals were oriented properly before gluing, because once they were glued they could not be removed. The main purpose of gluing everything in place was to keep the crystals fixed in their proper positions when pouring the potting resin. Gluing everything in place eliminated the shifting problem that was present when the "acoustic window" lay-up method was used.
The potting resin was then prepared. Both the resin and the catalyst were first thoroughly mixed in their containers. A sufficient amount of resin and the required amount of catalyst were then weighed out on an electronic scale. The resin was then placed in a 1100 F oven for ten minutes to decrease its viscosity. The resin and the catalyst were then mixed together. For a uniform cure, it was very important that the two parts were mixed thoroughly. Then the mixture was placed under a 29" hg. vacuum. The vacuum was held for about five minutes. This was long enough for the resin to degas, but not long enough to release the volatile components within the resin. Once the resin was degassed, it was ready to be used for potting the transducer.
The resin was slowly poured into the dammed transducer housing. Great care was taken not to allow for any air entrapment in the resin. The resin was poured very slowly so that the thickness of the resin within the channel remained even. The resin was poured until the top of the crystals were submerged. The coverage over the top of the crystals was approximately one millimeter.
The filled transducer was then placed inside of a dessiccator. This allowed the resin to cure in a moisture free environment, since in some resins moisture can have adverse




effects on the curing process. The transducer was allowed to set, undisturbed, for 24 hours at room temperature. After this time the resin was fully hardened and the transducer was removed.
Once the resin was fully hardened, the plexi-glass dam on the one end of the transducer was removed. The transducer was then finish-sanded where needed. At this time the transducer potting process was complete and the transducer was ready for testing.
Testing of Transducer
Since access to a complete 5 MHz ranging system was available, the easiest way to test the new transducer was to use electronics within the already operating ranging system. The ranging system used to test the transducer was a 5 MHz Mesotech model 810 system. This system had a driver which supplied the crystals with a 100 volt peak to peak signal for 10 micro-seconds. It also had a receiver with time varying gain. The output of the system was monitored on an oscilloscope. First the transducer built into the system was used and then each of the crystals within the new transducer were tested.
The Mesotech unit was opened up and the leads from one of the crystals of the new transducer were attached in parallel with the leads of the Mesotech crystal. This allowed for firing simultaneously both the Mesotech crystal and a crystal of the new transducer. Testing was done in a bucket of water. Only one transducer was placed in the water at a time. When the Mesotech transducer was first used, the magnitude of the return signal was observed as well as the sensitivity of the return to vertical movement of the transducer. Then each of the crystals of the new transducer were tested. Differences between bottom returns from the Mesotech transducer and the new transducer were negligible. The new transducer worked as well as the Mesotech transducer at recording bottom returns. See figures 4.4 and 4.5 for bottom returns from bucket tests.




, dT=180.75
I
t ar_ __bttome rllrnn
/ +
t 'ansmtre It
_ igned
2 voltstdciv
Figure 4.4 Bottom return from new transducer
A dT=180.75

2voltsdv
Figure 4.5 Bottom return from Mesotech




Design of Electronics
The main components of the electronics for a multi-element transducer include driver circuitry, receiver circuitry, and a multiplexer. As mentioned earlier, the driver and receiver circuitry of the Mesotech worked well with the new transducer. For the multielement transducer one driver and receiver board could be used if all of the leads from the crystals were run through a multiplexer. This would greatly cut down on the size and the cost of the electronics needed.
The transmitter circuitry should provide a pulsed 5 MHz signal for a specified duration and voltage. It was advised by the manufacturer of the piezo-electric crystals that an oscillating peak to peak voltage of approximately 10 volts per mil be applied to the crystals. This corresponds to a peak to peak voltage of approximately 120 volts for 5 MHz transducers. The driving signal does not have to be a sinusoidal wave; it can be a square wave. The pulse duration is not extremely important when just looking for bottom returns. The duration should be at least 10 micro-seconds, but not so long that the pulse is still being transmitted when the return echo reaches the transducer. The transmitter should be such that it either pulses the transducer automatically, or it pulses the transducer when a trigger is sent to it. The test with the Mesotech was run at a sampling frequency of 100 Hz.
The receiver circuitry for this transducer can be designed to either record complete time-histories of the return or just record the bottom location for each pulse. If only ranges to the bed are needed, the simplest method is the latter. When only bottom locations are to be recorded the threshold method mentioned earlier is probably the best method. Once the transmitted signal reaches the crystal a clock is begun. The return signal runs through a comparitor that controls the stopping of the clock counter. The voltage comparitor allows the counter to continue as long as the return signal's voltage is below a previously set threshold. Once the return voltage exceeds this threshold voltage, which corresponds to the bottom return, the voltage comparitor stops the counter. The counter




is then read by a data-logging system, such as one of the Tattle-Tale Data-loggers, and then the counter is reset. The only data recorded for each measurement would be the date, the time for the threshold return echo, and the identification number of the crystal. This would allow for considerable information with little storage space.
As mentioned earlier, the transducer would only have one transmitter and one receiver board. Thus the transducer would have to use a multiplexer. The main consideration of the multiplexer is the range of voltages that it would have to handle. The driving voltages sent through the multiplexer from the transmitter will be greater than 100 volts, whereas the return voltages sent to the receiver through the multiplexer will be on the order of milli-volts. The design of such a multiplexer is not a trivial task. It has been one of the major set-backs in the construction of the multi-element ranging system.
In conclusion, many different measurement techniques have been used to measure bedform ripples over the years. Today the measurement techniques are becoming more accurate and automated than past methods. One of the current trends in bedform measurement systems is hydro-acoustics. The acoustic systems currently being used either have moving parts or are not capable of recording instantaneous profiles. The construction of a stationary multi-element acoustic profiler would allow for accurate measurements of the bedform geometry without any moving parts. Such measurements are much needed for the testing of existing models and the building of improved models.




CHAPTER 5
CONCLUSIONS
The objective of this study was to evaluate existing ripple models with ripple observations during a large scale wave tank experiment. Also studied were possible field ripple measurement techniques as well as the design of an acoustic ripple profiler. It is emphasized that the ripple model evaluations are based on large scale laboratory tests which may not have replicated field conditions exactly.
Many of the observed ripple profiles were irregular. For some of the runs it appeared that there were more than one ripple regime present. This made the determination of representative ripple heights and lengths for many of the runs difficult. Both a threshold and a non-threshold method were used to determine ripple heights and lengths from the recorded profiles.
The final conclusions are listed below:
1. Four bedform ripple models have been evaluated using the Supertank experiment ripple data. These are: the Wiberg and Harris (1994), the Wikramanayake (1993), and both the Nielsen (1981) laboratory and field models. The relative errors of the models were compared. The Wiberg and Harris (1994) model agreed better with measured values for ripple height, length, and steepness than did the other models. The Wikramanayake (1993) model agreed second best, slightly better than the Nielsen (1981) field model, for all three ripple dimensions, see Table 5.1. Relative error in Table 5.1 is defined by equation 3.1. The Nielsen (1981) laboratory (regular wave) model had very poor agreement with measured values, even when compared to monochromatic wave conditions.




Table 5.1 Values of relative error (A) between measured predicted ripple values
Wiberg and Harris Wikramanayake Nielsen field Nielsen lab
__________ (1994) (1993) (1981) (1981)
height 1.25 1.73 1.97 4.11
length 1.27 1.33 1.35 6.84
steepness 1.08 1.11 1.16 2.69
height,
using threshold 1.08 1.36 2.15 2.25
length,
using threshold 1.11 1.19 1.58 3.36
steepness,1.61 12 57
using threshold 1.05 10 .225
2. No trends between ripples formed under irregular and regular wave conditions and Nielsen's (1981) irregular wave (field) and regular wave (laboratory) ripple models were found.
3. The Nielsen (1981) irregular wave (field) ripple model predicted anorbital ripple geometries well. Most suborbital ripple measurements fell between irregular wave model and regular wave (laboratory) model predictions.
4. The ripple type classification scheme (orbital, anorbital, and suborbital) worked better than the wave type (irregular [field], and regular [laboratory]) classification scheme.
5. Presently there is no ripple measurement system capable of accurately recording instantaneous bed profiles.
6. A stationary multi-element acoustic ripple profiler could accurately record instantaneous ripple profiles. The resolution of this instrument would be millimeters in the vertical direction, and centimeters in the horizontal direction along the ripple profile. The length of the measured profile would be on the order of 0.5 meters. Such measurements would be very helpful for improving the capabilities of ripple prediction, and subsequently improving sediment transport models.




APPENDIX A
SUPERTANK RIPPLE PROFILE DATA AND PLOTS
The following pages contain bedform profile plots for each of the Supertank runs, as well as their corresponding measured wave parameters. The first plot for each run is the smoothed ripple pattern with only the mean subtracted. The second plot for each run is smoothed and detrended. On the second plot the maximums and minimums used to determine representative ripple height and length are plotted along the profile as "*" for the non-threshold method, and as "o" for the threshold method. The average (nonthreshold method) and the threshold ripple height and length are also included on the plots; these measurements are in inches.

-1 . . . . . . . . . ... . . . . . . . . . . . . . . . .. :. . . .. . . . . .. . . . . . . . ...
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 54 Avg. Riople Height= 0.2019 Thresh. ipple Height= 0..3368
Av....... Ag.R. ipple ........ Thre .h., ippl .Length- 5.4.......
0 ........................
-1 ........ .......................... ...... ............... ..... ..... ........... ...................

10 15
Horizontal Reference- inches




8 . . . . . . . . .. ........... . . . . . . . . . . . .
f-2
0!
t
-2 i I I II
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 55
2 1
Avg. Ripple Height= 0.6237 Thresh. Ripple Height= 0.7693
1....... Ayg.. jpple.L.ngth- ..4 J ....... Thres.h, gppe.Le gth-. 5.333
--> ............... . . . . . . . . . . .
0 --2
0 10 15 20 2
Horizontal Reference- inches

0 CD
>

-Z'
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 56 Avg. Ripple Height= 0.5794 Thresh. Ripple Height= (d.656 1.......Av Rippl.e.1-ngth=. 5..111.........Thr b ..ipple.Le gt -.5..1. .
- 1............... ..... . ........
.-. . . ..1. . . .. . . . . . . . .. . . . . . . .

10 15
Horizontal Reference- inches

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




"T
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 57
2 1 1 1
Avg. Ripple Height= 0.6931 Thresh. nipple Height= 6.6164
1 ....... Avg, Fippl.Length-=. 5.2 ........Thresh, ipple.Length. .. ..............38
0T. ....
-21
0 5 10 15 20 2
Horizontal Reference- inches

-r
C)
0>

0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 58
2

L)
0

C)
.)

Avg. Ripple Height= 0.5237 Thresh. nipple Height= 0.6176
......... Ayg, RiPPle.lPngth-. 4.89... ..... Thresb,:Ripple.Length- .444 ..............
0 5 10 15 20 ,
Horizontal Reference- inches

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

I

9B

I




-2
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 59 Avg. Riople Height= 0.5124 Thresh..'ipple Height= 0.697
S ......... Ayg, RijPl qngth=. U.5. .......... Thre~fkb,;'R~ipPlq.l ngtbh-. A...M ..............
1 ...... ...........i.. ....8 3
-2
0 5 10 15 20 2E
Horizontal Reference- inches

0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 60

10 15
Horizontal Reference- inches

'0
a) >)


' 0 .)

II I j
Avg. Rip'ple Height= 1.04.1 Thresh. Ripple Height= 0.9396
.......... I .. pl...L. .n.gth.1.. .. ....Th .ipp .e.Le.ngt.h-. .I ...........

2

. . . . . . . . . . ........
. . . .. . . . . .. . . .
. ........ ... ........ .. .... ................... ..... .... .. ...... ............. ......... .......
. . . . . . .. .. . . . .. . . . . .. . . . . .. . . . . . . . ' .. . . . .. . . . . .. . ..




-1......................................... .................... .....................................
0 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 63

-2
0 5 10 15 20 25
Horizontal Reference- inches

-2I
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 64

0
_21
0

5 10 15 20
Horizontal Reference- inches

Avg. Ripple Height= 0.3235 Thresh. !ipple Height= G.4725
........ Avg, RippleL gt=.M...6........ Three s.h 1ppQ.Length=. 4.41.7 .............
.. .. .I

0 a)

Avg. Ripiple Height= 0.3667 Thresh. Apple Height= 1:07
......... .vg .ipp.l. ... ........... ..... ...... ..........6.. . ...

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

9

r]




-2
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 65 Avg. Rip'ple Height= 0.4727 Thresh. !Ripple Height= 6143
....... As jijPI[Q.Ugthi=. 4...... TNPO, ffippW l,.ength= Pq. .........
0 .... .... ,y .... ...... t ...4...... ....... hr...., .i ... ~ th .93.............
-1. ....... ..........."................... .............. ..... :.................... .. ,.......... .
-2
0 5 10 15 20 25
Horizontal Reference- inches
-1 .".. . . . . . . . . . . . . . . . . . .
-21i
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 66 Avg. Riople Height= 0.3636 Thresh. nipple Height= d..4255
1 ...... Avg.. j pl..Le.ngth=. A ........ Three b, .ipp.e.Length- 5 ..............
0 10 15 20 2E
Horizontal Reference- inches




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

0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 67

5 10 15 20 2E
Horizontal Reference- inches
I

-2
0 510 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 68
2'

-2
0 5 10 15 20
Horizontal Reference- inches

II I I
Avg. Ripple Height= 0.8661 Thresh. Ripple Height= 6.9644
........ Ayg, Bjpple.Length-=. 33. ....... Thresh, .ipple.Length- ,0,89 ............
I

A
al
0
C
'0

I I
Avg. Ripple Height= 0.3~07 Thresh. Ripple Height= 06.5742
........A. Avg RBip.ple.Le gth= 7.33 ....... Thres.h, lipple.Length-. 67 ... ...........
- .

A,

.

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

0

13

*




0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 69

10 15
Horizontal Reference- inches

0 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 70

0 10 15 20
Horizontal Reference- inches

I . .. .

CO
0 0)

0
t
a)
-2
0

Avg. Ripple Height= 0.3694 Thresh. .'ipple Height= 6.7224
......... Ayg.. Bipple.Le.ngth=. 4.33 ........ Threb .. pp.e.Length- A ...................
....... ........ ..........

Avg. Riple Height= 0.4345 Thresh..Ripple Height= 6.6261
-. Avg... Tres Ripple Legh611...........
... ..... A ...... . gth ,g 8 .9 . .... ...., ... ..e . .. ............... .
.............................. .......... .....

. ........ ..... ............. ... .. .........
......... ......
. ........ .. ........ ... ..... .. ..... ... .. .............. ...... .. ..
. ....... ...... ..... ... ...... *'*** ......




-0
0510 15 20
Horizontal reference inches Detrended Ripple Pattern run# 71 Avg. Rippie Height= 0.31 97 Thresh. Ripple Height= 0.4587
.............. ... ... Thres. R. ippe.Length- ..... .............
--0
0,
A2
0 10 15 20
Horizontal Reference- inches
--0
010 15 20
Horizontal reference -inches Detrended Ripple Pattern run# 72

0G
"T
_'Q

_0 5

10 15
Horizontal Reference- inches

Avg. Riople Height= 0.50;63 Thresh.:Ripple Height= 6.8705
......... Ayg, J31PptQ. gmgth=. 5.-M ........ ThreAhRipp1Q. Pngth= 9.07 ..............
..... ... .. .... .. ..
.... . . . . . . . . . . . . .. . .. . . . . . . . . . . . . . ..
. ........ ..... ...... ....... .. ..... ............ .... ... ..... ..... ..... .. .. .... ..............




1
0
-1
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 73

-2
0 5 10 15 20 2
Horizontal Reference- inches

I !
-2
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 74

Avg. Ripple Height= 0.21:19 Thresh. Ripple Height= (.7041
. .
......... A Ripple.Length- 6..833........Thresh, R.ipple Length- .... ..........
0 5 10 15 20
Horizontal Reference- inches

CD
0

(D)

Avg. Ri.ple Height= 0.369 Thresh. Ripple Height= (.7865
.... Rppie.Lp. gth -M .. 333........Threh.. ,Ripple.L. e gth .7... .....
. .- . . . . . . . . . . .. . . . . . . . . .
. . ..-. . . .. . . ..-. .. . . ..-. . . . .

0 1
C
0
> -

-




-1 ..... ... ........... ........... ........ ..... ........ ....... ..................... :................
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 75
Avg. Rilple Height= 0.6396 Thresh. Ripple Height= d.9098
......Avg. Rjppl.Length= % ~....ThrPbJiPp~.Le ngth= 11..........
.1 ......... ...y... .. .' .. ....ng ............. T h eshi .ple en ..... ...................
. .. ... ......... i... ....... .. ......... .
0 10 15 20 2
Horizontal Reference- inches

-2
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 76

0 5 10 15 20
Horizontal Reference- inches

0
'0
ci

Avg. Ripple Height= 0.29122 Thresh. Ripple Height= d.5701
......... Ayg, ipp. l.ength= 3.75 ...... Three ..sh. lQ.pp.eL length = 5........ ....

. ........ ........... ....... ................... .......... ... .. ... .. ............... ... .......
. ..... . . .
. ..... .. .................. ...... ... .................
:7\
.................... ...... I ............ 7 -: ............




-2
0
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 77
Avg. Rip'ple Height= 0.73M0 Thresh.:'Ripple Height= 6:'746
1......... Rjp. B plQ.Length=. 6 ....... Thr~e*.b,:iKppl~.Length=. A .................
0
-I .... .... ...... ..................................... .......................................
-21
0 5 10 15 20 25
Horizontal Reference- inches
a) ........ ..... ........ .. ........ .. ....................... ...... ...... .. .............
'0)
(D 1 ...... .. ........... ..................... ..... ......... ...... .................... ...............
-2I
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 78
2
Avg. Riople Height= 0.51-12 Thresh.:Ripple Height= 6.5668
1 A...... .g, ppl..L.n.gth=. 7 ........ ipp .Lngth .................
0"
.. . . . . . . .
.. . . . . . . . . .* . . . . .
. . . . . .. .. . .. .

10 15
Horizontal Reference- inches




-1 ........................................ ..... ................... ............... .. ...............
-2
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 79 Avg. Riple Height= 0.7461 Thresh. !Ripple Height= 1!.047
1........ A. j ppj. .l gth=. 5 7 ........ Threh, .ippe..Length ..5 ..............
-21
0 10 15 20 2E
Horizontal Reference- inches
2
-2 L
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 80 Avg. Ripple Height= 0.92 22 Thresh. Ripple Height= 1:531
1......Avg. RjpplLn .. ..... Tr' j IpW .Wgt h= ... .....
0 .............. .. .. .. .. .. ................ .... .. . .. .. ...... ........ .
_t ... ..... ...... .... "-. ................. -.. ..... .. ... ..: ................... ... ........ .......

10 15
Horizontal Reference- inches




. . . . . . . . . . . . . . . .. . .. . .... . . . . . .
"1 .... ...... ........... .................... .................... ....... ............ ...............
0 5 10 15 20
Horizontal reference inches
Detrended Ripple Pattern run# 82

-2,
0 10 15 20 2
Horizontal Reference- inches
- 1 . . . . . . . . . .. i. . . . . . . . . . ... . . . . . ... . . . . . . . .. . . . . . . . ..
0 5 10 15 20
Horizontal reference inches Detrended Ripple Pattern run# 83 15

0 5

10 15
Horizontal Reference- inches

C
CO
*0
t .o_

Avg. Riople Height= 0.574 Thresh. ripple Height= 0-8449
......... Ay ppl. .Lp gth=. 5..5. .......... Th 1 re hipp1 .Length-..A? ..................

*0
C_.
0-

Avg. Ripple Height= 0.3509 Thresh. Ripple Height= 0.6386
......... Avg. RiPple.e mgth.-4 7 ........ Th r esb. ;Ripple L e n gth- = .6 .................
.. . . . . . . . . . . .




Table Al: Supertank wave parameters and measured ripple dimensions
Run Wave Spectra Wave Wave Water Measured Measured Measured
Number shape Period Height Depth Ripple Ripple RIpple
Height Length Steepness
NBR,BBR,MON seconds meters meters cm. cm.
54 MON 2.9 0.27 1.97 0.48 5.69 0.09
55 BB 2.9 0.36 1.96 1.54 10.34 0.15
56 MON 2.9 0.58 1.98 1.39 12.98 0.11
57 BB 2.9 0.55 1.95 1.57 13.30 0.12
58 MON 2.9 0.81 1.91 1.26 12.42 0.10
59 BB 2.9 0.67 1.92 1.23 13.97 0.09
60 MON 2.9 1.04 1.91 2.50 33.02 0.08
63 BB 8.0 0.40 1.84 1.02 8.74 0.12
64 BB 8.0 0.40 1.82 1.77 14.68 0.12
65 BB 8.0 0.33 1.91 1.14 11.86 0.10
67 BB 8.0 0.41 1.89 2.08 23.70 0.09
68 BB 8.0 0.49 1.86 0.94 18.62 0.05
69 NB 8.0 0.37 1.87 0.93 11.00 0.08
70 NB 8.0 0.30 1.92 1.04 12.42 0.08
71 NB 8.0 0.29 1.93 0.77 9.53 0.08
72 NB 8.0 0.30 1.93 1.21 13.54 0.09
73 NB 8.0 0.45 1.87 0.81 8.46 0.10
74 NB 8.0 0.34 1.76 0.51 17.35 0.03
75 NB 8.0 0.36 1.75 1.53 8.46 0.18
76 BB 5.3 0.41 1.99 0.70 9.53 0.07
77 BB 6.4 0.48 1.98 1.75 16.94 0.10
78 BB 6.4 0.41 1.99 1.37 19.48 0.07
79 BB 10.7 0.40 1.98 1.79 14.40 0.12
80 MON 6.4 0.51 1.96 2.21 16.94 0.13
82 MON 6.4 0.57 1.94 1.29 13.97 0.09
83 MON 10.7 0.40 1.96 0.84 8.81 0.10




APPENDIX B
MANUFACTURER SPECIFICATIONS FOR CRYSTALS AND POTTING RESIN
The piezo-electric crystals and potting resin used in the construction of the small
multi-element transducers is recommended for use in the construction of the large
transducer. The manufacturer specifications for the crystals and the potting resin follow.
Table B 1: PZT Piezo-electric ceramic crystal specifications.
Manufacturer American Piezo Ceramics, Inc.
Model number APC 840
frequency 5 MHz
composition Lead Zirconate Titanate Polycrystalline
geometry 1 cm. diameter disk
thickness 0.38 mm
density 7.6 (g/cc)
Young's Modulus 6.8 N/m2 x 1010
Curie Temperature 340 0C
Mechanical Q 400
Dielectric Constant 1250 @ 1Hz
Dissipation Factor 0.4 %
d33 (ratio of strain to field) 300 x 10-12 m/v




Table B2: Potting resin specifications

Manufacturer Castall, Inc.
Product number (resin) E341FR
Product number (hardener) RT-7
specific gravity 1.61 @ 25 C
viscosity 15000 c.p.s.
shore hardness D91
temp. range -65 155 C
water absorption 0.20 % (10 days @ 25 'C)
coefficient of thermal expansion 25.0 in/in/C X 10-6 dielectric constant 5.6 100 KC (@ 25 0C)
dissipation factor 0.020 100KC ( @ 25 -C)
dielectric strength 500 Volts/Mil.




APPENDIX C MATLAB PROGRAMS USED FOR DATA ANALYSIS
The following programs were used for the analysis of the Supertank ripple data set,
and the calculation of predicted values using the Wiberg and Harris (1994) and the Nielsen
(1981) ripple models.
"riplott.m"
% plots measured ripple data (smoothed and detrended) % computes ripple height and length using local min. and max. values
clg
clear
z=0; p=l; while z==0, filename=input('Filename: ','s'); disp(['Loading filename]) eval(['load filename])
subplot(211) s=bedlev; m=detrend(s,0); bedlev=m; smrip
plot(xi,yi) axis([0 24 -2 2])
hold on grid
%title(['Ripple pattern with mean subtracted run# filename(4:5)]) xlabel('Horizontal reference inches') ylabel('Vertical inches') hold off
d=detrend(s); bedlev=d; smrip
subplot(212) revalt
hold off
%z =input('enter 0 to continue ');
z=l;
if z==0; clear, clg, z=0; end
end




"smrip.m"
% smoothes the measured profile values (bedlev) % uses "splile.m to perform a cubic spline fit" nrs=length(bedlev); x=linspace(O,nrs-l,nrs); xi=linspace(0,nrs-1,3*nrs-2); yi=spline(x,bedlev,xi);
"revalt.m"
%% follows ripple profile recording each local maximum and local min. %% averages elevation differences between local max. and local min. %% averages horizontal differences between local max. and min. %% input values are yi and xi (smoothed detrended ripple output for riplot.m %% recalculates ripple dimensions with a threshold of .5*aht
if length(yi) <70, %%only use first 23 inches of data set due to scour
j=length(yi); % past inch 24
else
j=70;
end
k=l; min=0; t=3; max=0;
%% t=type of slope l=upslope 2=downslope, 0=no slope
while k+l s=yi(l,k);
e=yi(1,k+l);
el=xi(k);
% if up slope
if s if t == 2,
min=min+l;
hmin(min)=s; imin(min)=el;
t= 1;
elseif t == 0,
min=min+l
hmin(min)=s; imin(min)=el;
t=l;
else t=l; end

% if down slope