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Use of multi-transducer array in determining bed profiles and transport rates under various wave conditions

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Use of multi-transducer array in determining bed profiles and transport rates under various wave conditions
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Use of multi-transducer array in determining bed profiles and transport rates under various wave conditions
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Cranston, Elizabeth A.
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Gainesville, Fla.
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Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
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English

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UFL/COEL-2000/009

THE USE OF A MULTI-TRANSDUCER ARRAY IN DETERMINING BED PROFILES AND TRANSPORT RATES UNDER VARIOUS WAVE CONDITIONS
by
Elizabeth A. Cranston Thesis

2000




THE USE OF A MULTI-TRANSDUCER ARRAY
IN DETERMINING BED PROFILES AND TRANSPORT RATES
UNDER VARIOUS WAVE CONDITIONS
By
ELIZABETH A. CRANSTON

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA

2000




ACKNOWLEDGMENTS

I would like to thank my committee, Dr. Hanes, Dr. Dean, and Dr. Mehta, for helping me throughout my graduate studies and for lending their expertise. To the participants of the SISTEX99 experiments, I would like to say "thank you" for making the six weeks in Hanover, Germany, a fun-filled experience. I would also like to thank those who helped me through the non-thesis struggles my parents, Stewart and Peggy, my roommate, Carrie, and all of the people in room 530. 1 would also like to thank my friends for still being my friends after not hearing from me for the last three months.




TABLE OF CONTENTS
pag~e
ACKNOWLEDGMENTS ......................................................... 11
ABSTRACT ......................................................................iv
CHAPTERS
1 INTRODUCTION............................................................. 1
2 BACKGROUND INFORMATION ...........................................2
Sediment Transport ............................................................ 2
Bedforms ...................................................................... 8
3 SISTEX99 EXPERIMENTS................................................... 16
Set-up ........................................................................16
Data Processing...............................................................26
4 RESULTS AND DISCUSSION................................................ 36
Bedforms......................................................................36
Transport Rate................................................................. 54
Sources of Error ............................................................... 64
5 CONCLUSIONS.............................................................. 67
APPENDICES
A BED PROFILES AND BEDFORM DATA..................................... 71
B SEDIMENT TRANSPORT RATE CALCULATIONS ........................ 155
C MATLAB PROGRAMS AND DATA PROCESSING VALUES ..............166
REFERENCES.................................................................. 208
BIOGRAPHICAL SKETCH ..................................................... 211




Abstract of Thesis Presented to the Graduate School
Of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science THE USE OF A MULTI-TRANSDUCER ARRAY
IN DETERMINING BED PROFILES AND TRANSPORT RATES UNDER VARIOUS WAVE CONDITIONS By
Elizabeth A. Cranston
August 2000
Chair: Dr. Daniel M. Hanes
Major Department: Civil and Coastal Engineering
To gain a better understanding of near-bed processes under varying wave conditions, Small-Scale International Sediment Transport Experiments 1999 (SISTEX99), an international experiment in Hanover, Germany, was organized. The bed profile data collected using a Seatek multi-transducer array and the transport rates calculated following various wave conditions are presented here. The wave conditions consisted of
6.5-second or 9.1-second period waves of the following type: monochromatic, Jonswap random, natural group, or bi-modal, and wave height ranging between 0.4 and 1.6 m. The resulting bedforms are determined from seabed profiles using a peak-trough method, and sediment transport rates are calculated based on the continuity equation. The bedforms and sediment transport rates are compared to determine the effects of the preceding wave conditions on the bed.




The effect of a change in period on the ripple height and length is most apparent. The ripple length increased with increasing wave period, while the ripple height decreased. The effect of wave height is more variable. For most wave conditions, an increase in the ripple length corresponded to a wave height increase. For natural group waves, a similar trend was observed for the ripple height, increasing wave height resulted in an increasing ripple height. Under sheet flow conditions, the opposite trend was noticed. The ripple height decreased with an augmentation in wave height. The water depth also had an observable effect on the ripple length and height. In shallower water, the ripple lengths tended to be greater while the ripple heights tended to be smaller. Although it is difficult to quantify, the relic bedforms are believed to have an impact on the resulting bedforms. The effect of wave type on bedform dimensions is not clear.
Comparing wave conditions to the resulting sediment transport rates indicate that
sediment transport rates increase with increasing wave period and height, and decreasing water depth. The highest sediment transport rates occur under sheet flow conditions during which the bed was relatively flat. Again, the effect of wave type on sediment transport is not clear.




CHAPTER 1
INTRODUCTION
Ripples influence the flow parameters near the bed which can greatly affect sediment suspension and transport. Because the seabed is most commonly composed of ripples or larger bedforms, an understanding of how these bedforms influence sediment transport is important in determining littoral transport rates. This knowledge is beneficial to many areas of science and coastal engineering. Applying this understanding could result in better approximations of the life of beach nourishment projects and maintenance of navigation channels.
To gain a better understanding of the relationship between wave conditions, sediment transport, and ripple formation, an international experiment in Hanover, Germany, was organized SISTEX99 (Small-scale International Sediment Transport Experiments 1999). The bedforms generated and the sediment transport rates experienced by different wave conditions during the SISTEX99 experiment are presented here.




CHAPTER 2
BACKGROUND INFORMATION
Sediment Transport
Sediment Entrainment
Sediment motion occurs when the disturbing forces on a particle exceed the
stabilizing forces. For a steady flow over a cohesionless bed, the disturbing forces, composed primarily of fluid forces, include a lift force and a drag force. The lift force is generated in part by the lower pressure region that exists above a sediment particle due to the curvature of the fluid streamline over the grain. Flow separation from the grain also contributes to the lift. The drag force consists of two parts: the skin friction acting on the surface of the grain and the form drag caused by the pressure difference upstream and downstream of the body due to flow separation. The drag force is given by the following equation, in which u is the characteristic velocity near the bed, p is the density of the fluid, d is the grain diameter and C, is the drag coefficient that depends on the local Reynolds number.
FD !pCD /Td2U2 (2.1)
2 4
Combining the driving forces gives the equation
F-' PD- (2.2)
D 2 4




The friction velocity is represented by u., and a is a non-dimensional coefficient. The product of the two is the flow velocity at a distance of the order of magnitude d from the bed.
The stabilizing force consists of an intergranular or frictional force and the submerged weight of the grain. The combined stabilizing force is therefore given as F, = og(s -1) -d#, (2.3)
The coefficient of static friction between the grain and surrounding grains, can be equated to the tangent of the angle of repose (0) of the sediment.
,a = tan(o,) (2.4)
The Shields parameter is the ratio of the disturbing to stabilizing forces for which there is a critical value at which sediment motion occurs, denoted as 0,. By equating these opposing forces, Shields found the critical value for sediment motion to be 0.05 for sand in water.
U. 4 2 (2.5)
(s -1)gd 3 CDa
In describing the balance of forces between stabilizing and disturbing forces, many forms of the Shields parameter are used depending on the existing bed and flow conditions. Often the skin friction Shields parameter (0') is applied, because the form drag contribution to the shear stress is believed to be irrelevant to the stability of an individual grain on the bed. This form of the Shields parameter is used to predict incipient motion and the magnitude of moving sediment concentrations (Nielsen, 1992). The skin friction Shields parameter is given by




of= T(2.6)
p(s 1)gd
where v' is the skin friction component of the total stress and considered the effective stress in terms of sediment transport. The grain roughness Shields parameter is another form of the Shields parameter that is used under wave conditions. This equation is given as
1 f25,p(Aco)2 1
2.5= = .5 (2.7)
p(s 1)gd 2
for which the grain roughness friction factor (f2.5) is given by Swart's equation f25 =exp 5.213( 2.d50 0194 5.977 (2.8)
For these equations d,, is the median grain size, A is the semi-excursion of water particle, wv is the angular frequency, and V/is the mobility number, an additional dimensionless measure of the fluid forces on a sediment particle under waves. It is defined as (ACO)2
(s-1)gd
The semi-excursion of a water particle is given as the following for which H is the wave height, k is the wave number, h is the water depth, and z, is the depth of the water particle.
A = H cosh k(h + z1) (2.10)
2 sinh kh
The angular frequency is defined as co= 2/r(2.11)
T




Dingier and Inman (1977) suggested an empirical formula for the initiation of sand motion based on his laboratory experiments and those of Bagnold. He defined this relation as the following for material of quartz density in sea water.
T = 0.17 (2A) J (2.12)
Sediment Transport
Sediment transport is commonly categorized as one of three modes, with the
distinction between modes being physically difficult to discern. These modes are bed load, suspended load, and wash load. Wash load is the transport of extremely fine particles that tend to stay in suspension and are not representative of the bed. For this reason, it is typically not considered in sediment transport models. (See Partheniades, 1977 for a further discussion on wash load.)
Suspended load is characterized as transport that occurs when the sand particles are supported by the fluid turbulence. To maintain sand particles in suspension an opposing force to gravity must be present. This opposing force is due to upward eddy velocities of the fluid flow. Suspension of a particle will occur when the fall velocity of the particle is of the same order of magnitude as the root-mean-square value of the vertical component of the eddy velocity, which can be represented by the shear velocity. Writing this in terms of the Shields parameter gives a criterion for sediment suspension, in which w, represents the settling velocity.
0S- ( .) (2.13)
(s 1)gd




During bed load transport the grains are more or less in continuous contact with the bed. Grain to grain interaction is important in maintaining transport as well as the effective bed shear stress in determining the transport. Sand grains usually jump, roll or slide along the bed in this type of transport.
Sheet flow is sometimes considered a fourth mode of transport or it is included as a subset of bed load transport. During sheet flow, transport occurs as a thin layer of sand grains close to the bed. Conditions for sheet flow transport occur under storm conditions where the shear stress at the bed is very large. TranEport Rate Calculations
Understanding the mechanics of sediment entrainment and transport is fundamental in predicting transport rates. Many models have been introduced without complete success in accurately describing sediment entrainment and transport for various flow conditions and sediment properties. The SISTEX99 data set can be used to verify existing models and as input in the derivation of new models.
One of the most fundamental, but most limited, means of calculating transport rates is the application of the continuity equation. This method of calculating sediment transport can be used if the bed elevation is known prior to the initiation of sediment motion and the bed elevation can be determined after sediment motion has ceased. The continuity equation approach maintains that the difference between sediment flowing into a given region (q,,,,,) and the sediment flowing out of the region (q,.,) must be accounted for by a change in the bed elevation of that region per unit time (dVIdt). The grain packing is also considered by including a packing factor, p.




qsn q~u pdV (.4
dt
The continuity equation is also important in deriving equations for bed geometry as will be illustrated later. Because the above requirements for application of the continuity equation are consistent with the conditions of the SISTEX99 experiment, this method was used to calculate the transport rate for the SISTEX99 data set.
Transport models can typically be classified as either a concentration-velocity integral model or a particle trajectory model. In the concentration-velocity (or cu) integral model, transport at a given location and time is simply a product of the velocity and the concentration of the sediment at that location and time. The following equation illustrates this concept integrating over the depth, D.
The velocity of the sediment can be assumed to be equal to the fluid velocity at a given location. Although this appears to be a simple equation for determining the transport rate, the difficulty arises from the variation with time and space of the sediment concentration and fluid velocity and the limitations in obtaining accurate measurements of the sediment concentration and velocity without disturbing the flow characteristics.
Experimental data suggest bed load transport rate formulas of the form
9OB CC('-9,)iI (2.16)
with
9B q (2.17)
d (s -1-)gd




H. A. Einstein derived the above non-dimensional formula for sediment flux (eq. 2.17) by basing sediment transport on the theory of probability to account for the variation in forces on the bed particles (Fredsoe, 1992). The variable qB represents the rate of bed load transport in a volume of material per unit time and width.
The most common semi-empirical formula of this form is the Meyer-Peter and Mfiller equation given as
OB =8(0'-0O)Y (2.18)
This formula overestimates bed load at high shear stresses and therefore, should be used for stress values for which 02.5<1 (Nielsen, 1992).
The particle trajectory theory is concerned with the distance a particle will travel after being set into motion. The time averaged transport rate, i, can be expressed in terms of the time-averaged pick-up rate of the sediment, P, and the average distance the particle travels, I, giving the equation
q = plx (2.19)
Van Rijn suggested the following pick-up function for steady flow (Nielsen, 1992) P =.00033(0'-O,)N Y2( (-1)gd3 (2.20)
V(s -1)gd V 2
Bedforms
The study of bedforms is of great importance to understanding and modeling near-bed flow and sediment transport. Larger bedforms can greatly influence the flow properties, such as sandbars resulting in rip current formation. Smaller scale bedforms affect the




boundary layer and turbulence near the bed and therefore, have a large impact on sediment suspension. Osborne and Vincent (1993) stated that bedforms modify near-bed flows, enhance entrainment and resuspension of sediment, and influence the timing and spatial distribution of sand resuspension.
Bedforms will be present if the flow strength is large enough to cause sediment
transport. Flows with a small grain roughness Shields parameter (02.<.05) will not cause bedforms to develop. In this condition, if bedforms exist they are the result of past flow conditions. Under flow conditions with a grain roughness Shields parameter between
0.05 and 1 (.05<0.5<1), bedforms are thought to exist in equilibrium with the flow conditions. The flow can consist of a unidirectional flow such as a current, an oscillatory flow resulting from waves, or a combination of the two. Bedforms as a result of current are typically classified as current ripples, dunes, or antidunes. The most common wavegenerated bedforms are rolling-grain ripples, vortex ripples, and megaripples. As the driving mechanisms behind current-generated and wave-generated bedforms are very different, they are often described separately. Current-generated Bedforms
Current-generated bedforms are often found in rivers and tidal channels. They are characterized as having longer more regular crests in relatively deep, slow flows and shorter crests in shallower, faster flows. Current ripples are described as being asymmetrical with long convex up-stream surfaces and short, steep leeward sides with wavelengths between 10 and 60 cm and heights up to 4 cm. Ripple formation is restricted to finer grain sands (d<0.6 mm) or to grains that do not penetrate the viscous




sublayer (hydraulically smooth bed). As coarser sediment will often result in a hydraulically rough bed, coarser sediment tend to form dunes. Dunes typically are described as having wavelengths greater than 60 cm with some reaching up to more than 100 m. As they are larger than ripples, dunes tend to affect the near-bed flow causing flow separation at the crest. The term "antidune" implies an up-stream migration of the bed and surface profiles. Under this configuration, the bed profile is sinusoidal and inphase with the water surface. These occur under a higher energy system than dunes or ripples.
The height of current bedforms can be calculated by combining the geometry of the dune with the continuity equation. Noting that the sediment transport is a function of the Shields parameter, 0, Fredsoe (1992) derived the following equation for the dune height.
HD =____ 1+ O D(.1
D 20 dO dO (2.21)
dO / dO
Here, HD represents the dune height, D the depth of the flow, 0- the Shields parameter calculated at the top of the dune, OT- the total sediment transport rate in dimensionless form, and OD is the deposited load on the dune face. At Shields numbers for which the transport cam be considered to consist only of bed load transport, the Meyer-Peter formula can be applied resulting in a dune height of HD _2(O- 9c)
D- (2.22)
D 70-0,
Again, Ois calculated at the top of the dune.
If bed load transport is the dominate transport mechanism, the maximum bed shear stress is located approximately 16 times the dune height from the previous crest. As the




maximum bed shear stress occurs at a dune crest, the dune length can be determined by the equation
LD =16HD (2.23)
For higher Shields number, the suspended sediment must also be considered as a contributor to bedform geometry. The trend for fine sediments is that as the shear stress increases, more sediment is suspended, causing a decrease in dune height and an increase in wavelength. At a high enough Shields parameter, the bedforms will be reduced to a plane bed.
The addition of waves to the current-generated bedform models has a great effect on the bedform dimensions. Again, by manipulation of the continuity equation, the dune height can be expressed by (Fredsoe, 1992) HD qD (2.24)
aq, V (aqT ,
aD D aV)
Wave-current models follow a similar trend to current only models. In higher velocity flows (higher Shields number), the suspended load dominates bed formation, causing a decrease in the dune height and an increase in the dune wavelength. In combined wavecurrent flows, however, the suspended load dominates even at low fluid velocities.
Wave-generated Bedforms
Wave-generated bedforms, due to the oscillatory flow, have different characteristics than bedforms of a unidirectional flow. They consist of rolling-grain ripples, vortex ripples, and megaripples. Rolling-grain ripples occur under lower energy waves and tend to have wavelengths much shorter than the wave orbital diameter. Megaripples tend to be




more irregular and have wavelengths on the order of one to two meters. They are found in higher energy areas such as the breaker zone.
Vortex ripples are of great interest because of their influence on sediment suspension and transport. They have wavelengths similar to the wave orbital diameter and are characterized by the vortex formed twice each wave period at the crests. These vortices scale on the ripple height and therefore, have a profound effect on sediment suspension. Based on the timing of the suspension related to the wave motion, net transport may occur in the opposite direction of the mean flow due to vortex ripples (Inman and Bowen, 1963).
Vortex ripples are commonly described by their length and height, which are closely related to the wave environment. Many formulas for calculating ripple height and length have been derived based on empirical data. Most commonly these formulas are a function of the mobility number (0) or the grain roughness Shields parameter (925). For regular waves Nielsen (1992) defined the ripple steepness as O .182 -O.242.,Y2 (2.25)
He calculated the ripple length by the following equation where A is the water particle semi-excursion.
A= 2.2 .345V0.34 (2.26)
A
This equation is valid for a mobility number between 2 and 230. The ripple height is defined as
-0.275 0.022~VIY (2.27)
A

for a mobility number less than 156.




For irregular waves, the ripple steepness, length, and height are smaller than the values predicted by the above equations. Nielsen (198 1) therefore suggests for irregular waves, the wave steepness be given by
2 = .342 -0.3402,4(.8
and the ripple length by
2 (693 -0.37In 8 V
A exp(0OO+0.75 In 7 V (2.29)
The ripple height can also be described in terms of the mobility number if the sediment densities are close to that of quartz (s=2.65) which is true for most field conditions. Nielsen (198 1) suggested the ripple height be calculated by the following formula for irregular wave conditions with a mobility number greater than 10.
)7 = 21V/-1.8 (2.30)
A
Here, V/and A are based on the significant wave height.
Dingler and Inman (1977) plotted ripple steepness of a field data set collected in La Jolla, California, against the mobility number (V4' in order to investigate the relationship between wave and ripple data. They found vortex ripples, defined as having a steepness
()712) equal to 0. 15, to occur at a mobility number less than 40. During V/values between 40 and 240 (the onset of sheet flow), they observed the transition ripples to decrease in steepness due to a reduction in the ripple height. At V/values greater than 240 the bed becomes flat as sheet flow conditions are met.
Clifton (1976) introduced another means of classifying ripples. He categorized ripples as orbital, suborbital, and anorbital ripples based on the ratio of orbital diameter to grain




size (d/d). Orbital ripples, equated to vortex ripples by Allen, are found in the lower part of the ripple regime, under lower energy wave conditions (Dingler and Inman, 1977). The ripple length, or spacing between ripples, for orbital ripples is proportional to the orbital diameter (do) where d. is twice the semi-excursion of a water particle (A). Miller and Komar (1980) describe the relationship between ripple length and orbital diameter as 2 = 0.65d, (2.31)
for conditions in which the ratio of the orbital diameter to the grain size (dod) is between 100 and 3000. Anorbital ripples, on the other hand, are found in the upper ripple regime under high intensity wave conditions (dod>5000). Their ripple spacing appears to be a function of grain diameter and stabilizes at a value independent of the orbital diameter
(do). Suborbital ripples are the transition between orbital and anorbital ripples and show a dependence of ripple length on both the orbital diameter and grain size (Dingler and Clifton, 1984).
Differing observations have been made as to the effects of certain wave parameters on the bedform geometry. Bagnold observed no dependence of the ripple length on the wave period for his data set (Dingler and Inman, 1977). Similarly Miller and Komar (1980) concluded that the ripple length for anorbital ripples does not change with a wave period range between 8 and 16 sec. Nielsen (1981), Willis et al. (1992), and Mogridge et al. (1994), however, suggested the ripple length does depend on the wave period. Mogridge et al. (1994) compared the bedform dimensions to the water particle semiexcursion for various period parameters (defined as pd/s7) and found an increase in the wave period resulted in an increase in ripple length.




The relationship between the orbital diameter and ripple length is also not clear. Bagnold observed an increase in the ripple length due to an increase in the orbital diameter until a limiting value was reached as determined by the grain size. Contrarily, Inman noted that the ripple length decreased as the orbital diameter increased. Combining these observations with results of their own experiments, Mogridge et al. suggested that ripple length increases with increasing orbital diameter until it reaches a maximum. It then decreases and stabilizes at a value equal to 500~d. The effects of the different wave parameters on bedform geometry are investigated for the SISTEX99 data set.




CHAPTER 3
SISTEX99 EXPERIMENTS
The SISTEX99 experiments were an international endeavor that consisted of
participants from the University of Twente, the University of East-Anglia, the University of California at Santa Barbara, Delft University of Technology, Albatros Flow Research, and the University of Florida. These experiments were conducted in the Groger WellenKanal (GWK) of ForshungsZentrum Kfiste in Hanover, Germany over a threemonth period in the summer of 1999. The purpose of this experiment was to obtain a better understanding of sediment transport processes in the near-bed region under propagating wave conditions. Data collected on bedform morphology, near-bed sediment concentrations, near-bed flow velocities, and net transport rates can be used as a comparison for existing models and perhaps as a basis for the development of new models.
Set-up
Tank
The Groger Wellenkanal is a 300x5x7.5 m wave tank. The test section consisted of a 45x5x0.75 m sand bed located at position 85 m to 130 m from the wave paddle. The sand bed was composed of a median diameter grain size of 0.24 mm (d50=0.24 mm) and a




standard deviation of 1.14 (a=1.14). On either side on the sand bed, an asphalt bed (15x5x0.75 m) with a tapered end of slopel:20 was constructed to minimize the impact of the test section on the waves and to maintain sand bed integrity. A sand trap was installed within each asphalt bed (3m from the sand bed) as a means to measure sediment transport. A cement block (0.3x0.3x0.1 m) was secured to the asphalt Im from the outside edge of each sand trap (fig. 3-1) in order to give a vertical reference for the sand bed elevation. The z-coordinate at the top of the block is 0.85 m while the x-coordinates of the inside edge of the blocks (closest to the sand bed) are 79.5 m and 135.5 m. These coordinates provide fixed reference datum for the interpretation of the moving MTA data. Opposite the paddle, a beach of slope 1:6 with coarser sand (d,,=0.3 mm) was used to absorb wave energy and decrease wave reflection. The wave paddle was also equipped with reflection compensation (see fig.3-1 for test section setup).
paddle beach
test section
I I I I
50 100 150 200 250
block sand bed sand trap
/i i ii l i l ll i 1- 1" "T-]-L -- ,,.......... ......... ........ ..... C
50 60 70 80 90 100 110 120 130 140 150 160 170 Figure 3-1. Schematic of the set-up for the SISTEX99 experiments in Hanover, Germany.
a) Overview of Grol3er Wellenkanal. b) Design scheme of the test section.




Waves
A variety of wave conditions were generated including monochromatic, bi-modal,
natural group, Jonswap random waves, and duplicated field waves (Duck). Although the wave paddle is capable of producing regular or irregular waves with wave heights up to 2 m and wave periods +/-2-15 sec, the waves generated for this experiment consisted of a period of either 6.5 sec or 9.1 sec and design, significant wave heights ranging from 0.4 to 1.6 m. The natural group waves consisted of a narrow-banded Jonswap spectrum (y=l 0) with a repetition time of 90 sec or 100 sec for the peak wave period of 9.1 sec and
6.5 sec respectively. The monochromatic waves were "Corrected Shallow Trochoidal (CSWT) waves which are very asymmetic, as is apparent from figure 3-2. This figure shows the wave shape for the monochromatic and the natural group waves.
Monochromatic wave, T=6.5 s Natural group waves, Tp=6.5 s, rt=100s
Monochromatic waves, T=9.1 s Natural group waves, T =9.1 s, rt=90 s

mean water level

Figure 3-2. Wave shape of monochromatic and natural group waves.




The Jonswap random waves were narrow-banded (=3.5). This wave type was somewhat random with many groups. The bi-modal waves consisted of combined 6.5 sec and 9.1 sec monochromatic waves of various wave heights.
The water depth was varied between 3 and 4 m above the sand bed. For the Duck
waves, the water depth was increased to 4.25 m above the sand bed, and the design wave period was 7.1 sec. A given wave condition was run for thirty minutes during which time the instruments from each university collected data. The wave conditions were then stopped and a profile of the entire sand bed using a Seatek multi-transducer array (MTA4) was collected. The wave conditions were repeated for an additional thirty minutes at the end of which another profile was measured. The wave parameters, water depth, and duration of the waves prior to each MTA profile are given in Table 3-1. Instruments
A wide variety of instruments were used to measure concentration, bed morphology, and flow characteristics. The instruments were deployed between x-coordinates 106 m and 110 m. (Figure 3-3. Instrument deployment.) The numbers on the figure correspond to the instrument descriptions below.
1. The University of Florida frame (Figure 3-4. Detailed schematic of UF frame)
- 2 Acoustic Doppler Velocimeters (ADV) measure flow velocities at two
different heights above the bed.
- Optical Backscatter (OBS) measure sediment concentration.
- Acoustic Backscatter (ABS) with a 1, 2, and 5 MHz transducer measure
sediment concentration.
- Pressure sensor measure wave height.
- Multi-Transducer Array (MTA) measure bed profiles.
- Acoustic Backscatter (ABS) with a 2, 4, and 5 MHz transducer measure
sediment concentration. University of East Anglia instrument.
2. University of East Anglia frame:
- Electromagnetic flow meter measure the flow velocity at a single point.




3. Carriage Pole
- Transverse Suction System (TSS) measure time averaged suspended sediment
concentration profiles.
- Acoustic Doppler Velocimeter (ADV) measure near-bed velocities and record
distance from the sand bed.
4. Conductivity Concentration Meter (CCM) measure concentrations and grain
velocities in sheet flow layer.
5. Rotating Side-Scan Sonar record bedform development within 5 to 10 m radius of
instrument.
6. Electromagnetic (EMF) and Acoustic velocity meters (ADV) meausre wave
velocity.
7. Multi-Transducer Array (MTA) measure bed profile over total length of test section.
1. UF Frame
2. UEA Frame
3. TSS and ADV
4. CCM
5. RSS
6. EMFs and ADVs
7. MTA
106 109 111.5 113 114
carriag
centerline 3 crig
35 cm 4
100 m 105 n 110m 115m 120 m
Figure 3-3. View from above of instrument locations.




Table 3-1. Summary of wave parameters, water depth, and duration of waves for each run prior to profiling with the MTA4. Mono-=monochromatic, Gr=natural group, JR=Jonswap random, Bi=bi-modal, and Duck=field waves. g indicates spectral width of waves.
Table 3-1. Summary of Conditions for each Profile
Phase I
File After Runs Wave Wave Wave Water Duration of
Period (s) Height (m) Type Depth (m) Waves (min)
m0629 la Tec 6.5 1.62 Mono 4 5
m0629 2a Ted-01/Ted-20/Tee 6.5 1 Mono 4 90
m0630 la Maa 6.5 1 Mono 4 30
m0630 2a Mba/Mbb 6.5 1.3 Mono 4 60
m0630 3b Mca/Mcb 6.5 1.6 Mono 4 40
m0701 la Mac/Mad 6.5 1 Mono 4 60
m0701 2a Gaa 6.5 1 Grg=10 4 30
m0701 3a Gab 6.5 1 Gr g=10 4 30
m0701 4a Raa/Rba 6.5 0.9 JR g=3.5 4 32
m0702 la Rbb 6.5 0.92 JR g=3.5 4 30
m0702 2a RbclRbd 6.5 0.92 JR g=3.5 4 50
m0706 la Rca 9.1 0.4 JR g=3.5 4 30
m0706 2a Rcb 9.1 0.4 JR g=3.5 4 30
m0706 3a Gba 9.1 0.4 Grg=10 4 30
m0707 la Rda/Rdb 9.1 0.6 JR g=3.5 4 60
m0707 2a Rea/Reb 9.1 0.7 JR g=3.5 4 60
m0707 3a Rfa/Rfb 9.1 0.8 JR g=3.5 4 60
m0707 4a Rga 6.5 0.8 JR g=3.5 4 30
m0708 lax Rgb 6.5 0.8 JR g=3.5 4 30
m0708 2ax Baa/Bab 9.1/6.5 .4/.7 Bi 4 60
m0708 3ax Bba/Bbb 9.1/6.5 .6/.6 Bi 4 60
m0708 4ax Bca/Bcb 9.1/6.5 .7/.4 Bi 4 60
m0709 lax RfclRfd 9.1 0.8 JR g=3.5 4 60
m0709 2a Gca/Gda/Gdb 9.1 1 Grg=10 4 72
m0712 la Gea/Gea 9.1 0.8 Gr g=10 3 34
m0712 2a Gfa 9.1 0.7 Gr g=10 3 30
m0712 3a Gga 6.5 0.7 Gr g=10 3 30
m0712 4a Gha 6.5 0.8 Gr g=10 3 30
m0712 5a Gia 6.5 1 Gr g=10 3 30
m0712 6a Rha/Ria 9.1 0.6 JR g=3.5 3 60
m0713 la Gja/Gjb 9.1 0.6 Grg=10 4 60
m0713 2a Gka/Gkb 9.1 0.7 Gr g=1l0 4 60
m0713 3a Gla/GIb 9.1 0.8 Gr g=10 4 60
m0714 l1a Rja/Rjb 6.5 0.4 JR g=3.5 4 60
m0714 2a Rka/Rkb 6.5 0.6 JR g=3.5 4 60
m0714 3a Rla/RIb 6.5 0.7 JR g=3.5 4 60
m0714 4a Daa/Dab 7.11 1.1172 Duck 4.25 72
m0715 la Gma/Gmb 6.5 0.6 Gr g=10 4 60
m0715 2a Gna/Gnb 6.5 0.7 Gr g=10 4 60
m0715 3a Goa/Gob 6.5 0.8 Grg=10 4 60




Table 3-1. continued
Phase 2
File After Runs Wave Wave Wave Water Duration of
Period (s) Height (m) Type Depth (m) Waves (min)
m0823 la ** ** ** 3.5
m0823 2a ** ** ** 3.5
m0823 3a Mda/Mea 9.1 1.5 Mono 3.5 32
m0823 4a Mfa 9.1 1.3 Mono 3.5 30
m0824 la Mga 9.1 1.1 Mono 3.5 30
m0824 2a Mha 6.5 1.6 Mono 3.5 30
m0824 3a Mia 6.5 1.35 Mono 3.5 30
m0824 4a Mja 6.5 1.1 Mono 3.5 30
m0824 5a Meb 9.1 1.5 Mono 3.5 30
m0825 la Mec 9.1 1.5 Mono 3.5 30
m0825 2ax Med 9.1 1.5 Mono 3.5 30
m0825 3a Mee 9.1 1.5 Mono 3.5 30
m0825 4a Mef 9.1 1.5 Mono 3.5 30
m0826 1a Meg 9.1 1.5 Mono 3.5 30
m0826 2a Mfb 9.1 1.3 Mono 3.5 30
m0826 3a Mfc 9.1 1.3 Mono 3.5 30
m0826 4a Mfd 9.1 1.3 Mono 3.5 30
m0826 5a Mfe 9.1 1.3 Mono 3.5 30
m0827 la Mff 9.1 1.3 Mono 3.5 30
m0827 2ax Mfg 9.1 1.3 Mono 3.5 30
m0827 3ax Mhb 6.5 1.6 Mono 3.5 30
m0830 la Mhc 6.5 1.6 Mono 3.5 30
m0830 2a Mhd 6.5 1.6 Mono 3.5 30
m0830 3a Mhe 6.5 1.6 Mono 3.5 30
m0830 4a Mib 6.5 1.35 Mono 3.5 30
m0830 5a Mic 6.5 1.35 Mono 3.5 30
m0830 6a Mid 6.5 1.35 Mono 3.5 30
m0831 la Mie 6.5 1.35 Mono 3.5 30
m0831 2a Mka/Mia/Mma/Mna 9.1 1.2 Mono 3.5 120
m0831 3a Dac/Dad 7.1 1.25 Duck 4.25 60
m0831 4a Rma/Rmb 7.7 1.5 JRg=3.5 4.25 70
m0901 la Gpa/Gpb 9.1 0.9 Gr g=10 3 60
m0901 2a Gpc/Gpd 9.1 0.9 Gr g=10 3 60
m0901 3a Gpe/Gpf 9.1 0.9 Gr g=10 3 60
m0901 4a Gpg/Gph 9.1 0.9 Gr g=10 3 60
m0902 l_1a Gpi/Gpj 9.1 0.9 Grg=10 3 60
m0902 2a Gib/Gic 6.5 1 Grg=10 3 60
m0902 3a Gid/Gie 9.1 1 Grg=101 3 60
m0902 4a Gif/Gig/Gih 9.1 1 Gr g=10 3 90




3 frequency

70.7 cm &-25.6 cm
98.1 cm 50.0 1 98.1 cm.
105.75 m (b ed on building 1.217 m to tank bottom specifications)
Figure 3-4. Detailed schematic of University of Florida frame. Seatek Multi-Transducer Array (MTA4)
MTA4 consists of 32 transducers spaced 2 cm apart giving dimensions of 64x10xl.5 cm (fig. 3-5). The maximum sampling rate is 1.67 Hz, and the maximum range for a threshold value of 40 mV is approximately 1 m. During the SISTEX99 experiments, MTA4 was deployed by securing the instrument to a crane arm attached to a moveable carriage (fig. 3-6). The crane arm was in the raised position during wave generation and lowered for profiling such that MTA4 was approximately 40 cm above the initial bed or 1.15 m above the tank floor. Steel cables were attached to the crane arm and carriage to ensure positioning of the MTA. The crane arm was lowered until the cables were taught supporting the full load. This was repeatable to +/- 0.3'. MTA4 was initially aligned parallel to the sidewall with transducer number 32 closest to the paddle. On July 6, four

Beach

Paddle

T 1.0
- cm6




days after the experiments began, the alignment of MTA4 was shifted to a 450 angle (transducer 32 closest to paddle).

1.5 cmi

64 cm

Figure 3-5. Seatek Multi-Transducer Array (MTA4).
Bed profiles were obtained by initiating data collection on the beach side of the 135.5 m block (denoted 'first block') and continuing data collection until MTA4 was located on the paddle side of the 79.5 m block (denoted 'end block'). The carriage moved at a fixed speed of 6.5 m/min, although minor variations in the speed may have occurred as the carriage passed over inconsistencies in its track. The parameters may have varied from run to run in order to optimize data collection, but typical values consisted of a sampling rate of 1.67 Hz, a threshold of 40 mV, a blanking of 200, water temperature of 20'C, and a duration of 1200 profiles.




Carriage

XCarriage
Direction

Paddle

transducer 32

MTA4

Beach

Figure 3-6. Schematic of MTA4 deployed on crane arm.

transducer 1

guide wires




Data Processing
The data is collected from MTA4 as an ASCII file and is converted to a Matlab file using the program Mta4readB.m. This program creates the variable mtar4 in which the raw distances collected from MTA4 are stored. All programs used in the data processing are included in Appendix C.
The converted data set consists of a matrix of the number of transducers by the number of measurement points. The number of transducers is always 32, while the number of measurement points varies run to run, but is typically between 800 and 1000. A given transducer and point number corresponds to the distance measured by the given transducer from MTA4 to the bed at that point in time. In time sequence point number 1 is collected before point number 2, and for a given point number, transducer I is initiated before transducer 32. A time delay of 0.017 sec exists between the activation of adjacent transducers. Given the speed of the carriage and the sampling frequency, the distance between adjacent measurement points for a given transducer is approximately 6.5 cm. Despiking
"Despiking" is the replacing of erroneous data points with a reasonable value, usually the average value of the adjacent points. The raw Matlab data is despiked using one of two programs ref.m for profiles collected with MTA4 at a 450 angle or refstr.m for profiles collected with MTA4 positioned parallel to the wall. By using several averaging routines, ref.m and refstr.m remove the inaccurate data points those outside a given threshold value or above a given value. The first routine is concerned with single point discrepancies. If the difference between a point and the previous point is greater than a




given threshold, an average of the proceeding and succeeding points is substituted for the incongruous one. The second routine checks for consecutive points greater than a given value and replaces those points with the average of +/- 3 data points on either side. The next routine locates and removes consecutive points outside a given threshold. The last averaging routine is a repeat of the first using a smaller threshold value. The thresholds and values used to convert each file are given in Table C-i, Appendix C.
Referencing
The ref~m and ref str.m programs assign the data points coordinate axes values and
reference them to the block height before inverting and storing the data points as variable rdesp. The "right handed" coordinate system origin is located at the paddle (x=O, positive x toward the beach), the tank bottom (z=O, positive z upward), and the sidewall of the tank (y=-O, positive y across the tank).
The z coordinate for each data point of a run is referenced to the tank floor in order to analyze and compare data sets. This is achieved by first adjusting the data to be a set value above the blocks and then referencing the corrected data to the tank floor. The data is referenced to the blocks by subtracting the height of the MTA above the blocks, initially measured to be 30 cm, from the mean of the end block values of a given transducer number, as specified in Table C-i, Appendix C. The difference between the MTA height (30 cm) and the average end block value is then subtracted from the entire data set. (This corrected data is denoted "offset data".) Because the raw MTA output is referenced to the location of the MTA and not the selected z-axis of the tank floor, the profile of the bed appears inverted (fig. 3-7 b). To account for this and to obtain the z-




coordinates of the data set referenced to the tank floor, the offset data is subtracted from 115 cm the referenced height of the MTA above the tank, and stored as variable rdesp.
The x-coordinate for each data point is determined by referencing the data to the first block. The profile number of the first block location for a given transducer number is found and assigned a x-coordinate value of 13550 cm, the known coordinate location of the first block. The x-coordinate values for the remainder of the data points of that transducer are determined by subtracting a calculated, offset distance for each profile number from 13550 cm. The offset distance is determined by taking the difference of a given point number and the first block point number, dividing the difference by the sampling frequency (profiles/sec) and multiplying by the velocity (cm/s) of the MTA. The x-axis locations for the remaining transducers are determined by adjusting for spacing and the delay in pinging of the transducers. This is done by multiplying the delay (.01 7s) by the velocity of the MTA, adding the distance between the transducers, and multiplying this value by the difference of the given transducer and the reference transducer. The distance between the transducers along the x-axis is 2 cm for the MTA parallel to the wall (ref str.m) and the square root of 2 cm (sine of 45' multiplied by 2 cm
- the distance between transducers) for the MTA at a 45'angle (ref.m). The corresponding x-coordinate values for a given transducer and data point number are stored in the matrix variable xax.
The center of MTA4 was positioned 35 cm off of the tank centerline, y-coordinate
value of 250 cm. Therefore, the y-position for the MTA parallel to the wall is set at 215 cm. The y-axis locations for each transducer of the angled MTA are calculated based on




E 100
S80
E 60 a) 40 C:
20
i5 0
E 100
80
a)
E 60
() 40 A 20
0

0.95

0.95

1 1.05 1.1 1.15
Location Along the Tank (cm)

1 1.05 1.1 1.15
Location Along the Tank (cm)

1.3 x 104

1.2 1.25 1.3
x 104

1.2 1.25 1.3
x 104

8 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 104
Figure 3-7. Bed profile of run m0708-4ax during different stages of data processing. a) Raw MTA data of transducer 32. b) MTA data after despiking of transducer 32. c) MTA data after referencing transducer 32. d) Averaged profile of all transducers.

1.05 1.1 1.15
Location Along the Tank (cm)

.9

9

90
E
0
o 80
m
C
70
E
0
50
90
0
o80
i- 70
E
' 60
il 50




the assumption that transducer number 4 lies on the centerline of the tank and knowing the distance between transducers in the y-direction to be the square root of 2 cm. Multiplying this value by the difference of a given transducer and four and subtracting the value from 250 cm gives the y position for a given transducer.
Averaged Profile
After the data has been despiked, inverted, and referenced using ref.m or refstr.m,
the profiles for each of the 32 transducers are averaged using the m-file makeave.m. This file finds all of the data points for a 2 cm span in the x-direction over the length of the profile. The mean of the points is assigned as the average value for the x-location. Therefore the averaged profile consists of a data point every 2 cm for the entire distance over which data was collected. The averaged profile is used for all of the data analysis. Averaging of the profiles of the individual transducers assumes that the bedforms were two-dimensional for a width of 45.25 cm for the SISTEX99 experiments. Examples of the data at different stages during the data processing are shown in figure 3-7. Figure 3-8 is a three-dimensional plot of the bed after the data have been despiked and referenced to the tank bottom. All thirty-two transducers are represented. Special Cases
A few of the runs had unusual features that required slightly different processing.
During two runs (m0702-1a and m0702-2a) MTA4 slipped causing the MTA to be at a 26.10 angle from horizontal. The data is corrected for this offset using correct.m and then processed with refstr.m. Run m0823-la was stopped before the MTA reached the end




block. In this case, vertical referencing is made to the first block. Several runs experienced a collection error that resulted in the omission of a small amount of data. The missing data in these files were assigned a value of 20 as placeholders so that Mta4readB.m could read the file. The files are processed as normal. These runs are denoted with the suffix x in the processed data file name. They are believed to be of equal quality to the normal runs.
90,
- 8 0" .'" .. ..........
,.....Q. 8"
E
0 60
50 i. ....
240 40..
.. ... ........
1 0 ... .... .... ....
50
260 4
23 10: .....
2 10 X 104
21 0 0. 9
Distance Across Tank (cm) Location Along Tank (cm)
Figure 3-8. Three-dimensional plot of bed profile collected from MTA4.




Bedforms
Two different approaches of locating bedforms were considered. The first consisted of filtering the averaged profile. The methods of subtracting out a running mean average (low-pass) and using a Butterworth filter (band-pass) were both investigated. Filter bandpass and low-pass averaging lengths of 3, 5, 10 and 20 m were applied with 5 m giving the best results. The zero-crossings of the filtered profile were then found as a means of determining bedform location. This method was unsuccessful at discerning bedforms that after filtering did not cross the zero line. For this reason, the peak-trough method was used to determine ripple locations. Figure 3-9 compares the zero-crossing and peaktrough method for file m0715-2a.
The peak-trough method locates the minimum and maximum points throughout the averaged profile. Height and width thresholds are applied so that only the larger bedforms are indicated. A minimum height threshold of 3 mm is used due to the accuracy of the MTA, and a width threshold of typically 50 cm is used. A width threshold of 50 cm proved to be the optimum width for locating the peak and trough values of the larger bedforms that existed. The program, pavelg.m, finds one maximum and one minimum height for each 50 cm section of the test area. Smaller ripples were also investigated using pavesm.m. This program still maintained the height threshold of
3 mm due to MTA accuracy, but it removed the width threshold. After closely comparing the small ripples found for the averaged profile to the unaveraged profiles of the individual transducers, the small ripples found seemed to be a product of the averaging of the 32 different profiles for each run (fig. 3-10). Therefore small ripples cannot be determined using this process. Only the bed between 90 and 130 m is examined




for most of the runs. An erosion pit developed during the experiments immediately following the asphalt section nearest the paddle. For runs during which the erosion pit

Location Along the Tank (cm)X10

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm)X 0
Figure 3-9. A comparison of the bedforms located using the zero-crossing method versus the peak-trough method for file m07 15-2a. a) Zero-crossing method. b) Peak-trough method.
was present and encompassed the 90 m location, the starting location was adjusted to 95mrnor 100 m.
The height and length of the bedforms are calculated through the subroutine 'ripple'. This routine uses the x-location of every other point found (trough location minus trough location or peak location minus peak location) to determine the ripple length. The ripple height is found by taking the greatest difference of the middle defining point of the ripple and the two adjacent points. For example, if the length of the ripple was found by




subtracting a trough value from a trough value, the peak is the middle defining point. The difference of the peak value and a trough value immediately preceding the peak location is compared to the difference of the same peak value and the trough value immediately succeeding the peak location. The maximum difference is taken as the ripple height.
Once the ripple height and lengths are determined, statistical analysis is performed on the data in an attempt to describe ripple height and length formation as a function of various wave parameters. The mean, standard deviation, maximum and minimum values, skewness, median, and mode for both the ripple length and height were found. This information can be found in Appendix A.
8078
,a76
0
=74M 72
70
681II
1.03 1.035 1.04 1.045 1.05 1.055 1.06 1.065 1.07 Location Aiong the Tank (cm) X 10,
80
78
5S76
C
1.03 1.035 1.04 1.045 1.05 1.055 1.06 1.065 1.07 Location Along the Tank (cm) X 10,
Figure 3-10. Profile of run m0708-2ax. a) Averaged profile with peaks and troughs indicated using a height threshold of 3 mmn and no width threshold. b) Unaveraged profile of transducer 20. Small ripples appear to be a result of averaging.




Sediment Transport
In order to calculate the sediment transport rates, rn-file volume.m is used to determine the change in bed elevation for adjacent averaged profiles. Volume.m, for example, takes file m06291la and file m0629_2a, subtracts the values at every 2 cm location, and multiplies this difference by 2 cm (the distance between points) to give an area. Volume.m stores these values in an array, area. The transport rate is determined for each location along the bed by summing the area calculations up to a given location, dividing by the time of wave generation between profiles, and then multiplying by a packing factor of 0.65 to give a transport rate in centimeters squared per minute. The packing factor of 0.65 was chosen based on data collected by Allen (1970). Before the transport rates are calculated, the averaged profiles are aligned using the program adjust.m so that the inside edge of the paddle side sand trap was set to 81.82 mn for phase 1 runs and 82.1 m for phase 2 runs. The difference is due to the removal of the sand traps during phase 2. Because the erosion pit was often out of range of the MTA, the data points for this location give a noisy, misrepresentation of the bed. For the bed profiles in which this occurs, the data points encompassed by the erosion pit are replaced by finding the slope of the bed of the erosion pit for which the MTA was still in range and continuing this line to the tank bottom. The profile of the tank is adopted once the line intercepts the bottom of the tank until the 'in range' profile resumes at the edge of the asphalt located at 86.9 m.




CHAPTER 4
RESULTS AND DISCUSSION
This chapter highlights similarities and trends in the data that might be of merit for
further investigation. Most of the observations are qualitative or rudimentary quantitative studies. The complete data sets can be found in Appendices A and B. Appendix A contains the figures of the bed profiles with the peaks and troughs of the bedforms indicated for each run, as well as histograms of the ripple heights and lengths found. A table indicating the statistics of the bedforms is also included in Appendix A for easy reference. Appendix B contains plots of the sediment transport rate for each run along the test section. Many factors, such as wave parameters, water depth, and bed shape, were investigated in an attempt to relate bedform formation and sediment transport rates to existing wave conditions.
Bedforms
Bedforms can only develop if sediment motion is present. As was discussed in chapter 2, the Shields parameter is often used as an indicator as to whether or not sediment motion will occur. Past research has shown bed ripple dimensions to increase with increasing Shields parameter, but as the sheet flow regime is entered (Shields parameter value of 0.8 to 1) the ripples disappear (Janssen, 1995).
The driving force behind destabilization of the sand grains is due to the shear stress at the bed (as can be seen from the equation for the Shields parameter, eq. 2.6). Therefore a




change in wave conditions that would increase the shear stress at the bed would increase ripple formation until the sheet flow regime is reached. The shear stress is given as r= twf.su (4.1)
with p,, being the density of water, f2 the friction factor, and ii the orbital velocity. A decrease in the water depth and an increase in wave period and height would result in a greater orbital velocity. It is therefore expected that the longer period waves, shallower water depth, and higher waves will promote ripple formation.
Qualitative Observations
Qualitatively, the bed profile appears to be greatly influenced by the previous bed. The change in bed profiles will be explored in sequential order, noting differences in bedform shape and number as the water depth and the wave period, height and type are changed. The files corresponding to the observations are given so that the bed profiles may be referred to in Appendix A. Table 3-1 lists the wave parameters, water depth, and duration of wave generation for each run.
Phase 1
m0629-la to m0701-la. As the wave height increased for monochromatic waves of period 6.5 sec, the number of ripples decreased, but the pattern remained fairly consistent
- regularly spaced ripples with peaks and troughs occurring at the same locations. As the wave height is decreased from 1.6 m to 1 m, the number of ripples more than doubles.
m0701-2a. Changing wave type from monochromatic to natural group waves of the same wave height (1 m), the number of ripples decreases slightly as the smaller, unstable relict ripples are wiped out. The bedforms appear more regular.




m0701-3a. Under the same wave conditions (natural group, wave height of 1 m), the smaller ripples become absorbed into the larger ones resulting in a reduction of the number of ripples.
m0701-4a. As the wave conditions change to Jonswap random waves of 0.9 m wave height, the bed profile experiences little variation.
m0702-la to m0702-2a. The pattern is relatively the same as the wave height is
increased to 0.92 m. A little more noise is apparent in the profiles. This may be due to data collection and processing. During the two runs in which the wave height was 0.92 m the MTA had slipped so that it was 26.1 0 off the horizontal. The tank was drained between runs m0702-2a and m0706-1 a.
m0706-la to m0706-3a. The wave conditions after the bed had been somewhat
smoothed out were lower energy waves Jonswap random waves of 0.4 m wave height and natural group waves of 0.4 m both of period 9.1 sec. These conditions had little effect on the overall bed profile. The profile did appear to be noisier as the type of wave switched form Jonswap to natural group.
m0707-la to m0707-3a. A progression in height from 0.6 to 0.8 m of Jonswap
random waves followed the 0.4 m natural group. During this progression, the bedforms became more symmetric. The profile shape remained fairly constant with the augmentation in wave height. The greatest changes occurred at the maximum peak and trough locations (107 m and 125 m, respectively).
m0707-4a to m0708 lax. The period was next changed to 6.5 sec with the other conditions remaining constant. The bed profile is noisier following the period change with no other noticeable effects.




m0708-2ax to m0708-4a. A series of bimodal waves was generated. The series
consisted first of a 9.1-sec wave of 0.4 m combined with a 6.5-sec wave of 0.7 m, then a
9.1-sec wave and a 6.5-sec wave both of 0.6 m wave height, and finally a 9.1-sec wave of
0.7 m and a 6.5-sec wave of 0.4 m. The pattern of the profile underwent little change between the first two conditions, but as the 9.1 period wave became dominant, the number of ripples decreased and appeared to be of longer wavelength. The height of the ripples steadily increased during the series.
m0709-lax. A Jonswap random wave of 0.8 m, 9.1-sec period flattened some of the smaller ripples resulting in larger ripple heights for the remaining ripples.
m0709-2a. A natural group wave of the same period and 1 m wave height followed the Jonswap wave. This had a profound effect on the bed profile substantially reducing the number of ripples and altering the overall appearance of the bed. Some similarities between profiles remain such as a double trough between 100 m and 105 m, a gradual incline from 95 m to 100 m, and a trough around 125 m. The water level was lowered from 4 m to 3 m above the bed.
m0712-1a to m0712-2a. A natural group of period 9.1 sec and wave height 0.8 m was generated resulting in little change to the overall pattern of the bed. A ripple height decrease was apparent as the waves were reduced from 1 m to 0.8 m. The height appeared to increase slightly from 0.8 to 0.7 m.
m0712-3a to m0712-5a. A series of 6.5 second waves of the same type with increasing wave height (0.7, 0.8, and 1 m) was generated. The number of ripples increases as the larger bedforms develop double-peaks. At the 1 m wave condition the bed becomes smoother and more regular.




m0712-6a. This 6.5-sec series was followed by a 9.1-sec Jonswap random wave
group of 0.6 m. A slight change in the bed is observable as the ripples increase in height. The water level was increased to 4 m above the bed.
m0713-la to m0713-3a. Another natural group series of period 9.1 sec was generated with wave heights increasing from 0.6 to 0.8 m. The noticeable effect of this progression is an increase in the number of smaller ripples that grow in height over time with increasing wave height. The number of ripples nearly doubles from the Jonswap to the natural group waves of 0.6 m wave height.
m0714-la to m0714-3a. A 6.5-sec Jonswap random wave progression of 0.4, 0.6 and
0.7 m is created resulting in a noisier profile as the bedform attempts to readjust to the shorter wavelength. The bed profile is highly irregular and continuously changing during the series. Although the number of ripples only increases slightly from the natural group series, an accurate measure of small-scale ripples would most probably reveal a large number of small ripples.
m0714-4a. Waves similar to those experienced during a field experiment in Duck, North Carolina were generated in order to compare field data to large scale laboratory data. The conditions consisted of a slight increase in wave period to 7.1 sec, an increase in the water depth to 4.25 m above the bed, and an increase in wave height tol.1 m. This resulted in a profile similar to the proceeding one with more defined ripples. The water level was drained to 4 m above the bed.
m0715-la to m0715-3a. The final series of phase 1 consisted of 6.5-sec natural group waves of increasing wave height. The first profile of the series is noisy and




irregular as the bed profile adjusts. The ripples become more regular and defined as time and wave height increases.
Phase 2
The waves generated during phase 2 were intended to achieve sheet flow conditions. The bedforms from the initial sand placement (m0823-1a and m0823-2a) are quickly flattened, resulting in a few, very large bedforms that migrate and evolve during phase 2.
m0823-3a to m0824-1a. The first wave conditions of phase 2 consisted of 9.1-sec
monochromatic waves with the wave height decreasing from 1.5 to 1.3 to 1.1 m. The few smaller ripples that existed after the initial run were soon eliminated. The number of ripples decreased from 69 before the series began to 7 after the 1.1 m waves. Some irregular, very mild sloping bedforms resulted from the 9.1-sec waves.
m0824-2a to m0824-4a. Monochromatic waves of 6.5 sec with decreasing wave height from 1.6 to 1.35 to 1.1 m follow the 9.1-sec waves. In response to the change in wave period, the steepness of the bedforms increased with time. The bed is still irregular consisting of only a few, large wavelength bedforms.
m0824-5a to m0826-1a. The wave conditions return to a 9.1-sec monochromatic
wave of 1.5 m in wave height for six consecutive runs. During these runs, the erosion pit grows into the observed region (90 m to 130 m) and an accreting mound develops at the opposite end around 130 m. The scour hole in the vicinity of the CCM and suction pole (109 m) is increasingly more apparent. As the peak-trough method locates only three bedforms for the last four runs in the series of six, the bed can be considered to be for the most part flat.




m0826-2a to m0827-2ax. The wave height is decreased to 1.3 m and six runs are conducted under these conditions. The bedforms evolve very slowly into a more pronounced peak-trough-peak configuration with the trough located between 105 and 110 m. (fig. 4-1). Smaller ripples can be seen on the second peak area. The erosion pit continues to grow during these runs.

45 1 I I I
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 104
Figure 4-1. Bed profile of run MFG, file m0827-2ax indicating the peak-trough-peak configuration.
m0827-3ax to m0830-3a. Four consecutive runs of 6.5-sec monochromatic wave set of height 1.6 m follows the 9.1-sec waves. The peak-trough-peak configuration is flattened somewhat and replaced with several smaller bedforms (on the order of 5 m in length).




m0830-4a to m083 1-1 a. The height is then decreased to 1.35 m for four more runs. During this time the overall bed pattern changes very little.
m0831-2a. A monochromatic wave set of 9.1-sec period with a wave height of 1.2 m follows. The bed is substantially flattened resulting in smaller bedforms. The mean ripple steepness is reduced by approximately 27%. The water is increased to 4.25 m above the bed for another Duck wave series.
m0831-3a. The bed experiences little change during the Duck wave set. An increase in the depth of the scour hole is apparent.
m0831-4a. A Jonswap random wave of period 7.7 sec and wave height of 1.5 m at the same water depth (4.25 m above the bed) resulted in a slight smoothing of the bed profile.
The water depth was decreased to 3 m above the bed.
m0901-la to m0902-la. A series of natural group waves of 9.1-sec period and wave height of 0.9 m was generated. During these runs, the bed appears to be smoothed even more, although the scour hole is still apparent.
m0902-2a. A 6.5-sec natural group wave set of 1 m wave height followed the series of four 9.1-sec waves. This had little effect on the bed except to create a ripple in the vicinity of the scour hole.
m0902-3a to m0902-4a. Following the 6.5-sec wave set two profiles of 9.1-sec
natural group waves of wave height 1 m were collected. These two profiles indicated a propagation and growth of the ripple initiated around the scour area by the previous wave condition.




Effects of Wave Parameters
According to wave theory, the bed will mimic the wave conditions with the ripple
length being related to the wave orbital diameter at the bed. Therefore, waves of longer periods will result in longer wavelength bedforms. For the runs in which only the wave period varied holding wave type, wave height, and water depth constant, twelve out of thirteen times the ripple length corresponding to the 9.1 second wave was greater than that corresponding to the 6.5 second wave. The ripple length prior to the run did not appear to alter the effect of the longer period wave. Regardless of the initial ripple length prior to the 9. 1-sec wave generation being larger or smaller than the ripple lengths prior to the 6.5 -sec wave generation, the resulting ripple length of the 9. 1-sec wave was greater than that of the 6.5-sec wave. The trend is not as clear observing the change in bedforms in sequence. Exactly 50% of the time, a* decrease in wave period corresponds to a decrease in ripple length. The ripple height, on the other hand, experienced the opposite effect. An increase in ripple height with a decrease in the wave period was observed.
An increase in the wave height for a given water depth, wave period, and type
indicates an increase in the wave energy, as wave energy is proportional to the wave height squared. A larger energy at the bed will increase sediment suspension and have more potential for ripple formation and growth up to a certain point. Once sheet flow conditions are met, sediment transport occurs as a thin layer of sand close to the bed. In this mode of transport the bed is relatively flat. Two different trends can be seen in the data due to a variation in wave height. For most cases of the 6.5-sec waves, as the wave height increased, the ripple length decreased resulting in steeper, more defined ripples.




Contrarily, the 6.5-sec monochromatic wave resulted in an increase in the ripple length as the wave height increased. For the 1 and 1.3 mn wave heights, an increase in ripple steepness accompanied the ripple length increase. For the maximum wave height (1.6 mn) of the 6.5-sec monochromatic wave series a decrease in ripple steepness of 28% was observed. A decrease in the ripple steepness following the maximum wave height in a series is apparent for one of the natural group wave sets also. Prior to the maximum wave height, an increase in ripple steepness was observed. This decrease in ripple steepness after the maximum wave height run could be due to the energy of the wave reaching the critical level in which flattening of the bed occurs. If this were true, one would expect to see a higher transport rate at the maximum wave height. The transport rates for the monochromatic 6.5-sec wave at a wave height of 1.6 mn was 27.1 cm 2/min, a factor of four greater than for the previous wave height of 1.3 mn. The transport rate of the 6.5-sec natural group wave likewise experienced an increase in the transport rate at the maximum wave height of 1 mn. This would support the hypothesis that the wave energy is such that the bed begins flattening.
For wave periods of 9.1 sec, the trend relating bedform dimensions and wave height varies between types of waves. As the wave height is increased for Jonswap random waves, the general trend is an increase in ripple length causing a decrease in the ripple steepness. Similarly for the monochromatic waves, as the wave height was decreased the ripple steepness increased. The statistics depicting mean ripple length, height, and steepness indicate that there is much variation in the profile under repeated conditions. During the six consecutive runs in which the wave conditions were held constant at a wave height of 1.5 mn (monochromatic wave, period 9.1 sec), the ripple steepness first




increased with time and then began to decrease in time approaching the initial steepness. This was true for the six consecutive runs at constant wave conditions of 1.3 m in wave height as well. However, in looking at the profile of the bed during these runs (Appendix A), the profiles indicate a gradual adjustment to the change in wave conditions resulting in a relatively steady-state profile.

0.1600 0.1400 0.1200

0.1000 S.iooo 0.0800
CL
R 0.0600

0.0400 0 0200 0.0000

0 02 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Wave Height (m)
Figure 4-2. Plot of the ripple steepness vs. wave height for the various wave conditions and depths.
The natural group waves tended to have the opposite results. As the wave height was increased, the ripple steepness increased due to a growing ripple height. The ripple length did not vary much. As there were only one or two examples in which the wave height increased holding all other factors constant for the 9.1-sec waves, not enough evidence

* MonoT=6.5, h=4m
* Mono T=6.5, h=3.5m + Mono T=9.1, h=3.5m a Group T=6.5, h=4m 4 Group T=6.5, h=3m o Group T=9.1, h=4m I* Group T=9.1, h=3m
- Random T=6.5, h=4m A
A
o Random T=9.1, h=4m a Random T=9.1, h=3m
0
A
A
0
0
A
A + +

I




exists to draw definite conclusions on the general trend of the data relating wave height to ripple formations. Figures 4-2 to 4-4 show the variation in ripple steepness, ripple length, and ripple height as a function of the wave height. Although the above mentioned trends can be seen, a great deal of scatter exists in the data. The small ripple steepness in Figure 4-2 at the higher wave heights occurred for most cases during phase 2 of the experiments for which sheet flow conditions were met. This would explain the relatively flat bed observed under those conditions.

1200.0 1000.0

800.0 600.0
400.0 200.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Wave Height (m)
Figure 4-3. Plot of ripple length vs. wave height for the various wave conditions and depths.

* Mono T=6.5, h=4m
* Mono T=6.5, h=3.5m + Mono T=9.1, h=3.5m A Group T=6.5, h=4m A Group T=6.5, h=3m + +
O Group T=9.1, h=4m +
* Group T=9.1, h=3m
- Random T=6.5, h=4m 0 Random T=9.1, h=4m o Random T=9.1, h=3m I *
* + *
* +
+
++
0 +
A A
** *




48
25.0
* Mono T=6.5, h=4m
Mono T=6.5, h=3.5m +Mono T=9.1 h=3.5m AGroup T=6.5, h=4m
20.0 & Group T=6.5, h=3m
* Group T=9.1, h=4m
*GroupT=91, h=3m A
-Random T=6.5, h=4m oRandom T=9.1, h=4m
15.0 Random T=9.1, h=3m
U
v A
0 0
CL A
A +
+. +
5.0
0+ +
5.0 .. .
8 0050.0
0 02 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Wave Height (m)
Figure 4-4. Plot of the ripple height vs. wave height for various wave conditions and depths.
As another approach to determining trends in the bedform data as related to the wave
conditions, the ripple steepness was plotted against the wave steepness in Figure 4-5. The
data points with a ripple steepness less than 0.02 correspond to the runs under sheet flow
conditions and the first run of phase 1 with wave generation of only 5 minutes. Ignoring
the runs under sheet flow conditions (phase 2), the phase 1 data show the ripple steepness
increasing with wave steepness. The phase 2 data remain fairly constant with perhaps a
slight decrease in the ripple steepness as wave steepness increases. Looking at the
individual bed profiles for phase 2, this trend is also observed. The bed initially has a few
bedforms that are diminished over time.




0.16
0.14
0.12
0.1
C9
CL
0.08 9 9
0.06
0.06
0.04
0
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
Wave Steepness
Figure 4-5. Plot indicating the effect of wave steepness on ripple steepness.
The experimental ripple steepness was compared to the predicted values based on the equations expressed in chapter 2, eq. 2.25 and 2.28. The equation for regular waves (eq.
2.25) was used to predict the ripple steepness for monochromatic waves, while the equation for irregular waves was used to calculate the ripple steepness for Jonswap random, natural group and Duck waves. The natural group waves show both regular and irregular wave characteristics. The irregular wave equation, however, was a better predictor of ripple steepness. Often the experimental value for natural group waves fell between the predicted value for regular and irregular waves. Figure 4-6 shows the relationship between experimental and calculated ripple steepness. The equations are valid for mobility number less than 230 for the regular wave case. Runs in which the mobility number was greater than 230 were not plotted.




The experimental ripple length and height were also plotted against the calculated values. These equations greatly underestimated both the length and height found experimentally. These equations are based on vortex ripple dimensions that are characterized as having ripple lengths less than 60 cm. The average ripple length found experimentally was approximately five times this value. The model of Miller and Komar (eq. 2.3 1) also greatly underestimates the ripple length. The ratio of did is much greater than the accepted limit of 3000 for this model. However, even for the lower energy waves, in which the ratio of d0/d was approximately 3500, the model underestimated the ripple length by almost a factor of three.
0.16
0.144
* Calculated
*~ mExperimental
0. 12 0.1
,0.08WE U)U
0'0.064-~- u
.02
0
10 20 30 40 50 60 701 80 9 i0
-0.02
-0.04
Profile Number
Figure 4-6. Plot of experimental ripple steepness and calculated ripple steepness.




The ripple steepness was also plotted against the Shields roughness parameter to
determine a relationship between increasing Shields parameter and ripple steepness. From figure 4-7, an increase in ripple steepness with increasing Shields roughness parameter is observed until a roughness parameter of approximately 0.8 is reached. This is generally classified as sheet flow conditions, under which ripples become washed out.

0.1600
0.1400
0.1200
0.1000
(n
CL
0.0800 CL
.2
0.0600
0.0400
0.0200

0.0000

0 0.2 0.4 0.6 0.8 1 1.2 1.4
Shields Roughness Parameter
Figure 4-7. Shields roughness parameter versus ripple steepness. An increasing trend is observed until sheet flow conditions are reached at approximately 02.1=.8. Effect of Water Dgpt
The water depth also had an observable effect on the ripple dimensions. In shallower water given the same wave type, height, and period, the ripple lengths were generally larger and ripple heights were generally smaller than in deep water. For a given wave height and period, the wave in shallower water will cause a greater shear stress at the bed.




This is fundamental in sediment suspension and ripple formation. Examining the effect of a change in water depth from linear wave theory, one would expect the orbital diameter of the wave to decrease as the water depth increases. Relating the wave orbital diameter to the bed, the ripple length should also decrease.
Effects of Bed Profile
The bedforms were highly variable and seemed to be very dependent on the relict bedforms. Two profiles following the same wave conditions but separated by runs of different wave conditions resulted in very different bed formations. The profiles of run m0712-5a and m0902-2a both follow natural group wave of a period of 6.5 sec and a wave height of 1 m. The mean wavelength, however, is 185 and 495 cm respectively. The bed topography of these two cases is most probably the result of the initial bed. Run m0712-5a is the last run of a progression of wave heights (0.7, 0.8, and 1 m) of natural group waves of period 6.5 sec. The bedforms appear to be more regular and rounder as the wave height increases. The mean wavelength of the bedform is decreasing with increasing wave height suggesting that perhaps the bed is adjusting to the shorter wave period. Run m0902-2a follows a series of natural group waves of a period of 9.1 sec. The bed can be considered to be a flat bed prior to and after the run. A more defined bedform was apparent around 109 m, the location of the CCM and suction pole. The ripple statistics did show a similar trend as with run m0712-5a, a decrease in the ripple wavelength and height. However, as only four ripples were found, these statistics are somewhat unreliable.




Statistics
The statistics calculated for the bedform dimensions can be found in Table A-i of Appendix A. They include the mean, standard deviation, skewness, maximum and minimum values, median, and mode for both the ripple length and height, as well as the mean of the ripple steepness and the total number of ripples located. These statistical values are helpful in determining trends in the data, although they should be regarded with caution. There is a great deal of scatter in the data and not a large enough sample space to adequately reduce the uncertainty of the data. Profiles of phase 2 often located only three bedforms. This is hardly enough data to confidently calculate the statistics for these runs. The standard deviation, a measure of the variability of the data, ranged from 24 to as much as 817 for the ripple length and from 2.5 to 10.6 for the ripple height. This indicates the large extent of the scatter and variability in the data. Depending on which was located first, a peak or a trough, a ripple that consisted of a larger bedform adjacent to a small ripple followed by a larger bedform, could be interpreted as one of the following: two medium bedforms of approximate wavelength and height or two halves of larger bedforms and one small ripple. Therefore, the statistics could vary substantially for nearly identical bed profiles. As is apparent from the histograms, an outlier often exists that affects the mean calculations, especially for the ripple length. It is therefore important to examine all characteristics of the ripple data the profile, the previous bed conditions, the wave parameters, the histograms, and the statistics.




Transport Rate
in determining trends for sediment transport, the sediment transport rate is compared to varying wave parameters, as well as water depth and bed configuration. Based on earlier works, sediment suspension and transport is closely related to the Shields parameter. From the equations for Shields roughness parameter (02.5), the Swart's friction factor (f,.5), and the velocity amplitude (Ao) given in Chapter 2, a greater wave height, wave period, and shallower water depth result in a greater shear stress at the bed. A rippled bed increases the friction at the bed also generating a greater shear stress. One therefore expects a greater contribution to sediment transport from a rippled bed opposed to a flatter bed. The comparisons made concerning the transport rate use an averaged value of the transport rate between 103.5 mn and 114.5 mn excluding the meter from 108.5 to 109.5 mn where a scour hole was often present due to the carriage pole. Plots of the transport rate calculations along the length of the bed for each run are given in Appendix B.
Effects of Wave Parameters
Although the transport rates were greater under the high-energy waves of phase 2, they appeared to increase with wave height during both phases of the experiments. The most illustrative example of this is of the 9. 1-sec monochromatic waves as can be seen in Figure 4-8. Figure 4-9 presents the effect of wave height on the sediment transport rate for all of the runs associated by similar type, period and water depth. An increase in the transport rate with a wave height increase is observed for the 6.5-sec Jonswap random waves, 6.5 -sec monochromatic waves, and the 9. 1-sec natural group waves all at a depth




of 4 m. The increase in the transport rate, as well as the transport rate itself, is relatively low for these runs. An increase in the transport rate with increasing wave height was also observed for the 9.1-sec monochromatic waves. For the remaining wave conditions, the trend of increasing transport rate with wave height is observed until the maximum wave height for a given condition is reached. One example of this is the 9.1-sec Jonswap random waves. The transport rate increases from a wave height of 0.4 m to a wave height of 0.7 m. At 0.8 m however the transport rate decreases. The decrease in transport rate may be a consequence of the bed stabilizing and approaching equilibrium. Another example of this trend is for the case of the monochromatic type waves. The waves are decreased from 1.6 m to 1.35 m with a calculated increase in transport rate. Perhaps the
M EA
MFA
MGA
150
100
E
.: 50
o/
0.
0
-50
0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35
Location Aiong the Tank (cm) X 104
Figure 4-8. The transport rates for 9.1-sec monochromatic waves of decreasing wave height. The wave heights are 1.5, 1.3 and 1.1 m for runs MEA, MFA, and MGA respectively.




1.6 m wave height transformed the bed to one more conducive to transport for a 6.5-sec
wave period. The bed shape does change considerably during the series of 1.6 m waves,
while the shape is fairly constant during the 1.35 m waves that experienced greater
transport.
120
# Mono T=6.5, h=4m
100 Mono T=6.5, h=3.5m
X Mono T=9.1, h=3.5m A Group T=6.5, h=4m & Group T=6.5, h=3m
80 Group T=9.1, h=4m
0 Group T=9.1, h=3m
E Random T=6.5, h=4m
< 60 Random T=9.1, h=4m
E x
U U Random T=9.1, h=3m
t 40
0
C. X
I
0 20
0 0
4) 0 *
A
0- *. A
00 0.2 0.8 1.0 1.2 1.4 1.6 18
-20
-40
Wave Height (m)
Figure 4-9. Plot of the averaged transport rate vs. the wave height for various wave conditions and depths.
The effect of the wave period on transport was investigated by comparing the transport
rates of 9.1-sec waves to those of 6.5-sec waves holding the water depth and other wave
parameters constant. In six out of ten cases the longer period wave experienced greater
transport rates. Figure 4-10 illustrates this trend. The Jonswap random waves comprised




three of the instances in which the shorter period waves resulted in a larger transport. This may indicate a possible effect of the wave type on transport.
By observation of the plotted transport rate calculations (Appendix B), the highest transport occurred under the 9.1-sec monochromatic waves of a 1.5 m wave height. These waves were generated during phase 2 for which sheet flow conditions were achieved. As is expected, the transport rates during phase 1 are considerably lower than those of phase 2 often not exceeding 10 cm2/min.
70
- GEA
60. GFA
GGA
GHA
50 GIA
"E
10
0
- 3 0 /", f \
Location Along the Tank (cm) Figure 4-10. Plot of transport rate of natural group waves of varying wave height and period. GEA -T=9.ls, H=O.8m, GFA -T=9.ls, H=O.7m, GGA -T-6.5s, H=0.7, GHA -T=6.5s,
H=O. 8m, and GIA- T=6.5 s, H=lmi.
The trend relating wave type to transport was difficult to discern. Never did all three wave-types experience the same wave conditions. When comparing Jonswap random




waves and natural group waves under the same conditions, the results were inconclusive. Both indicated a higher transport rate 50% of the time. The natural group waves (6.5-sec period, 1 m wave height), however, did produce a greater transport rate when compared to 6.5-sec monochromatic waves of 1 m. The conditions of the 9. 1-sec monochromatic waves were never the same for a different wave type.
Transport rate is expected to increase with increasing Shields roughness parameter, as this is an indication of the shear stress at the bed. Figure 4-11 illustrates this trend. The transport rates are relatively low for the conditions during phase 1 for low Shields roughness numbers. A gradual increase in transport is observed until sheet flow conditions are met at a Shields roughness parameter of approximately 0.8. A much greater increase in the transport rate is apparent after this point. The higher degree of scatter in transport at the higher Shields numbers is also apparent. Effect of Water Depth
In determining the effect of water depth on transport, runs of the same wave
conditions that were conducted both at a water depth of 3 m and 4 m are compared. Out of the seven times that this occurred, four of the cases resulted in a clear increase in the transp ort rate with a decrease in water depth. Of the three remaining instances, the difference between the transport rates for the given water depths was never greater than 1 cm2/min. A decrease in the water depth is associated with an increase in the shear stress at the bed. As sediment transport is dependent on the shear stress, it is expected to increase with decreasing water depth.




140120100.
80
E 60t 40
0
20 .
0
0.2V 0.4 0.6 *0.8 1 1.2 1.4 16
-20 *
-40
Shields Roughness Parameter
Figure 4-11. Plot showing relationship between Shield roughness parameter and transport rates.
Effects of Bed Profile
The effect of the bed geometry on transport is difficult to quantify. The transport rate
plots with respect to the tank location (Appendix B) often mimic each other in shape as can be seen in Figure 4-10. This suggests the shape of the bed or the flow conditions at
certain locations may. be responsible for the high or low transport rates at those locations.
Comparing the transport rate profile of GEA to the bed profile following the run,
similarities in the profile shapes are observed. Lower transport occurs at the troughs,
while higher transport occurs at the crests. This creates similar profiles of the transport rate and the sand bed. For many transport profiles a large transport is calculated at the




beginning of the sand bed around 90 m. This is also the location of the erosion pit indicating good agreement between the calculated results and the observations.

Number of Ripples
Figure 4-12. Plot of transport rate versus number of ripples.

The number of ripples between 90 and 130 m was plotted against the averaged
transport rate in figure 4-12 to determine if the bed shape might have an observable effect on transport. This figure suggests a decrease in sediment transport as the number of ripples increases. This corresponds to the observation that the highest rates of transport occurred during phase 2 where the bed was for the most part flat. A greater amount of suspension over the rippled bed may have occurred, but due to the timing of the suspension related to the wave motion no net transport resulted from this. This suggests




p
4 4
4
4 4*
4
4
4
7.: 4 4
4
* 4 4 4
4 *4~* S ~ *4 4
a
0.1200 0.1~00

1.0600 0.0800

*4 0.0200 0.0400

-20
-40
Ripple Steepness
50
40
30
*4
20
E*
44 S10 4
0
a.
1! *4 4
. C ,* 4
0.0 )00 0.0200 4 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1
-10
-20
-30
Ripple Steepness
Figure 4-13. Plot of averaged transport rate vs. ripple steepness. a) All runs. b) Phase 1 only.

0.1000

0.1400

0.1200

0.1000




that the bed profile is not the dominant parameter in determining transport. Figure 4-13 is a plot of the transport rate against ripple steepness for a) both phase 1 and phase 2 and b) only phase 1. An obvious trend is not apparent from this comparison. The highest transport calculated for phasel was for run RBB. This is most likely an error, due to the slipping of the MTA prior to or during this run.
Two non-sequential runs of the same wave parameters and water depth were compared to gain a better understanding of the effect of the bed on transport. Only one example of this exists 9.1-sec Jonswap random waves of 0.8 mn wave height, runs RFB and RFD. The ripple steepness prior to the runs differs by 66% indicating a good potential for comparison. The averaged transport rates for both runs, however, were very low with the originally steeper bed having a smaller and negative transport rate. Plotting the transport rates along the tank against each other (fig. 4-14 c) reveals that the transport for the steeper bed (R.FD) varies along the profile, while the smoother bed has a relatively steady transport rate. Although, the averaged transport rate is less, the greater fluctuation in the transport rate along the bed may indicate that the steeper ripples contributed to sediment suspension.
The stability of the bed may also be a factor affecting sediment transport under
identical wave conditions. The bed prior to run REB is more irregular than the bed prior to rn RFD, suggesting that the bed is more susceptible to readjustment. As only one example is available for comparison, it is impossible to recognize a trend in the data.




20 -

101-

- I t 0
1, .1).

0.85 0.9 0,95 1 1.05 1.1 1.15
Location Along the Tank (cm)

1.2 1.25 1.3 .35 X 10

Figure 4-14. Profiles and transport rates for 9.1-sec Jonswap random waves of 0.8 m wave height. a) Bed profile prior to run RFB. b) Bed Profile prior to run RFD. c) Transport rates of RFB and RFD.

5
o~

-20i

-10
-15




Sources of Error
Many possibilities of error exist for collection and processing of the data, as well as the interpretation of the results. The most obvious error in data collection occurred during the runs m0702-1 a and m07O2-2a. Sometime prior to the collection of file 0702la the NITA slipped so that it was rotated 26.1' from the horizontal. The rotation of the MTA from the horizontal is obvious in the raw data of these two files, but it is not known when the slipping began. A data collection error may also have existed in the repeated raising and lowering of the crane arm. Although the repeatability of MTA lowering was tested and found to be insignificant (+/- OX), tension in the cables may have loosened over time resulting in a larger variation. The carriage is also assumed to travel at a constant velocity during data collection. However, variations in the velocity could be felt during data collection as a result of inconsistencies in the carriage track. It is expected that the same variations in velocity were experienced for every run.
The data underwent substantial processing to derive the ripple dimensions and
transport rate calculations. Some of the steps are subjective relying on the researcher's interpretation of the data. Therefore, many possibilities for human error existed. Several assumptions were made in creating the averaged profile that was used in all of the data analysis. The bed was assumed to be two-dimensional for a 45 cm width. Although there is no evidence to refute this assumption, the spatial distribution of the bed is not known. It was also assumed that the last ping of a given transducer on the beach-side block occurred at the edge of the block nearest the sand bed. The beach-side block ('firstblock') was used as a reference for the x-axis. The last ping of a specified transducer of the block was assigned the x-coordinate location of 135.5 in. The distance between pings




of an individual transducer, however is approximately 6.5 cm. Therefore, depending on the location of the last ping on the block, the x-coordinate could be off by as much as 6.5 cm. This could affect the averaging of the profiles from the thirty-two transducers and the sediment transport rate calculations that find the difference between bed elevation for a given location of two sequential runs. Ideally, the averaged profiles should line up perfectly so that the paddle-side and the beach-side edge of the sand traps would be in the same location for each run. This was not the case. For this reason, the paddle-side sand trap edges were aligned before the sediment transport rates were calculated. In most cases aligning the paddle-side edge resulted in a discrepancy of location for the beachside sand trap edge. This could be due to the inaccuracy in assigning the x-coordinate, or it could be the result of the varying velocity of the carriage and a corresponding variation in the calculated velocity of, the MTA for each run. A third assumption is that the MTA was changed to a 45*angle. The exact orientation of the MTA, however, is not known as the positioning of the MTA was an eyeball approximation. This assumption may also result in a misrepresentation of the bed
The ripple dimensions are based on the averaged profile of the thirty-two transducers. During this averaging the smaller ripples that have been shown in previous research to affect suspension may have been averaged out (fig. 3-10). A careful comparison of the averaged profile to the unaveraged profiles revealed that the smaller fluctuations in the averaged bed profile are not observed on the individual profiles. For this reason, the smaller fluctuations or 'ripples' were considered to be a product of averaging and therefore, not real. Smaller ripples that affect sediment suspension may exist, but are not located due to averaging.




Several assumptions and corrections to the bed profiles were made in order to
determine sediment transport rates. The sediment transport calculations are based on the assumption that no sand is transported into the test section. As only asphalt t is present on the paddle-side of the test section, this is a reasonable assumption although it cannot be verified.
A great deal of fine sediment was present in the water that was pumped in from a nearby navigation channel. This sediment left a thin coat on the test section and the instruments. The duration of the wave generation compared to the cohesive properties of this fine sediment is thought to negate any effect the fine sediment would have on suspension.
The bed profiles were corrected for the erosion pit that developed in phase 2.
Although care was taken to closely resemble the bed profile in replacing the out of range data, this most probably had an impact on the transport rate calculations.




CHAPTER 5
CONCLUSIONS
The Seatek Multi-Transducer Array (MTA4) is effective in determining the bed
response to various wave conditions and water depths. The bedforms were examined to determine the bed response to a variation in wave period, height, and type, and water depth. Several trends in the data are observed. The ripple length appeared to be a function of wave period with shorter period waves resulting in shorter ripple lengths. This is as expected, as ripple length is dependent on the semi-excursion of the water particle.
For the Jonswap random and natural group 6.5-sec period waves, an increase in wave height caused an increase in ripple steepness. The 9.1-sec period waves of the monochromatic and Jonswap random wave type showed the opposite trend as the wave height increased, the ripple steepness decreased. This is most probably the result of the ripple crests being sheared off under higher energy waves as described by Willis et al. (1992). Under sheet flow conditions, the bed responded as is expected. As the wave height increased, creating a larger Shields roughness parameter, the ripple steepness and the number of ripples decreased.
Decreasing the water depth also had an observable effect on the ripple dimensions.
The ripple length was longer for shallower water depths given the same wave conditions. Not only does the shear stress at the bed increase as the water level is decreased, the




shape of the wave becomes increasing g*ly nonlinear. The longer, flatter wave trough as illustrated in fig. 3-2 will cause a larger orbital diameter at the bed, and therefore a larger ripple length will result. By examining the bed profiles in sequential order, as well as comparing the non-sequential profiles of the same wave conditions and water depth, the bed appeared to be heavily influenced by the previous bed shape. The difference in the initial bed profiles is believed to contribute to the large degree of scatter that exists in the data. No trend was apparent for the bedform response to differing wave types. Nielsen's model and Miller and Komar's model cannot be accurately applied to this data set as the mobility number or d1d ratio exceeds the acceptable values.
The sediment transport rates are also compared to the wave height, type, and period, as well as water depth. Higher sediment transport rates were observed under sheet flow conditions of phase 2. The transport rates were often a factor of five or more greater than those experienced during phase 1. The bed profiles of phase 1 can typically be classified as rippled beds, while the bed profiles of phase 2 can be considered flat. This perhaps indicates that the bed shape is not the dominant parameter in determining transport. The transport rate plots of phase 1, however, showed more variation in transport than the flat beds of phase 2. This suggests the bed profile influences the timing of sediment suspension and the direction of transport. Comparing changes in wave height, wave period, and water depth, a greater transport rate was observed for 9. 1 -sec period waves, of a larger wave height and shallower water depth. These trends are also consistent with theory. As wave energy is proportional to the wave height squared, under higher wave conditions the potential for suspending sediment is higher. The shear stress at the bed is




also. increased under shallower water depths resulting in higher sediment transport rates. No noticeable trend was observed regarding wave type.
For a better understanding of the influence of the above parameters, a larger sample space is needed. Many observations of the bed response are based on only a few examples. To improve the confidence level of the statements made and trends observed, more repeated conditions are needed. It would also be beneficial to. examine the bedform dimensions of the individual transducers'profiles. A better description of the smaller ripples could be gained from this, as well as removing the uncertainty of the twodimensional assumption. Errors did exist in the data processing. This is apparent from overlaying consecutive runs, as the permanent structures (sand traps) often do not line up. This error might be diminished if the location and coordination between the start of data collection with the MTA and the initiation of the carriage motion are the same from run to run. A better processing technique, such as using the transducer whose ping is closest to the edge of the block in determining the x-coordinate positions, might also reduce this error. The misalignment of the profiles is significant for the transport rate calculations. These calculations depend on finding the change in elevation of the bed at each 2 cm location along the bed. A misalignment of the profiles will result in an erroneous transport rate prediction. Another suggestion for improving the data processing would include the use of the angle of repose in determining spikes or erroneous points in the data.
The data set relating bedforms, wave conditions and transport rates presented here has great value as a comparison for existing data and models and as a input for the derivation of new models. The noted trends and conclusions drawn based on this data are meant as




a guide for further, more detailed study. Incorporating the data collected from the other instruments deployed during the SISTEX99 experiments could lead to a better description of the near-bed processes and the bed response to wave conditions. A comparison of the ripple dimensions to the measured nearbed velocity from the ADV and a comparison of the measured suspended sediment data from the Transverse Suction Sample or the Acoustic Back Scatter are just a few avenues that can be explored further. The concentration based on CCM measurements and the near-bed velocity from the ADV can be used to estimate sediment transport in bed load based on the cu integral (eq. 2.15). Combining this information with the suspended load transports based on the TSS or ABS data, an approximation of the total transport can be calculated. This estimate can then be compared to the calculated sediment transport rates based on the continuity equation from the MTA data. The data can also be used to test the validity of existing models for ripple formation and transport as well as in the derivation of new models.




APPENDIX A
BED PROFILES AND BEDFORM DATA




90

55

0.95 1 1.05 1.1
Location Along the Tank (cm)

1.15 1.2 1.25 1.3
X04

Figure A-1. Averaged profile with peaks and troughs indicated of file m0629- 1 a profile
following run TEC.

400

600
Ripple Length (cm)

800

2 3 4 5 6 7
Ripple Height (cm)

Figure A-2. Histograms of bedforms of file m0629-1 a profile following run TEC.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

I I I
~1

a,
1.5
0 1
-o
E 0.5
0
0




451 12
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) X 104
Figure A-3. Averaged profile with peaks and troughs indicated of file m0629-2a profile
following run TEE.

10
8
6
4
2
0
0 20 40 60 80
Ripple Length (cm)

6 8
Ripple Height (cm)

IUU

120 140

10 12 14

Figure A-4. Histograms of bedforms of file m0629-2a profile following run TEE.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) X 104
Figure A-5. Averaged profile with peaks and troughs indicated of file m0630-1a profile
following run MAA.

0 L.
20

du
Ripple Length (cm)

1 U U

5 10 15
Ripple Height (cm)

20 25

Figure A-6. Histograms of bedforms of file m0630-1a profile following run MAA.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




C)
75
70
a
60
55 50
45 L L
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 104
Figure A-7. Averaged profile with peaks and troughs indicated of file m0630-2a profile
following run MBB.

]

5

100 150 200 250
Ripple Length (cm)

10 15 20 25 30
Ripple Height (cm)

Figure A-8. Histograms of bedforms of file m0630-2a profile following run MBB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




1.05 1.1 1.15
Location Along the Tank (cm)

1.3 x 104

Figure A-9. Averaged profile with peaks and troughs indicated of file m0630-3b profile
following run MCB.

3
2.5
2
1.5
0.5
0
50 100

200 250
Ripple Length (cm)

40

20
Ripple Height (cm)

Figure A-10. Histograms of bedforms of file m0630-3b -profile following run MCB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




1.05 1.1 1.15
Location Along the Tank (cm)

1.3 x 104

Figure A- 11. Averaged profile with peaks and troughs indicated of file m070 1-1 a profile
following run MAD.

50 100

150 200 250 300 35C
Ripple Length (cm)

8 ,I

10 15 20 25 30
Ripple Height (cm)

Figure A- 12. Histograms of bedforms of file m070 1-la profile following run MAD.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

I
0




0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 104
Figure A- 13. Averaged profile with peaks and troughs indicated of file m0701-2a profile
following run GAA.

150 200
Ripple Length (cm)

AN& i

15 20
Ripple Height (cm)

25 30 35

Figure A- 14. Histograms of bedforms of file m0701-2a profile following run GAA.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




65 It
60 55
50
45 I
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 10
Figure A-15. Averaged profile with peaks and troughs indicated of file m0701-3a profile
following run GAB.

50 100

Zuu
Ripple Length (cm)

20
Ripple Height (cm)

Figure A-16. Histograms of bedforms of file m0701-3a profile following run GAB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

300




60 65 55
50
4 5 L
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 104
Figure A-17. Averaged profile with peaks and troughs indicated of file m0701-4a profile
following run RBA.

100 150 200 250
Ripple Length (cm)

300 350

15
Ripple Height (cm)

Figure A-18. Histograms of bedforms of file m0701-4a profile following run RBA.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

3 2.5
2 1.5
I 0.5
0 50
3
2.5
2 1.5
1 0.5
0




1.05 1.1 1.15 1.2 1.25 .1
Location Along the Tank (cm) X 104

Figure A- 19. Averaged profile with peaks and troughs indicated of file m0702-1 a profile
following run RBB.

5
4 3 =
2
1
0 100
50 100

150 200 250
Ripple Length (cm)

300 350 400

5 10 15
Ripple Height (cm)

- U -

Figure A-20. Histograms of bedforms of file m0702-la profile following run RBB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

45L0.9

I

I I I




60 Il
55w
50
45 L I I
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) X 104
Figure A-2 1. Averaged profile with peaks and troughs indicated of file m0702-2a profile
following run RBD.

100

150
Ripple Length (cm)

2UU

I

R1
Ripple Height (cm)

300

30

Figure A-22. Histograms of bedforms of file m0702-2a profile following run RBD.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

0 50

I I

I I I




100
95 90 85 80
75 70 65 60
55 50
45
0.9

1.2 1.25 1.3

Location Along the Tank (cm) x 10,
Figure A-23. Averaged profile with peaks and troughs indicated of file m0706-1 a profile
following run RCA.

Eu

100 150 200 250
Ripple Length (cm)

300 350 400 450

I.E

2 4 6 8 10
Ripple Height (cm)

12 14 16 18

Figure A-24. Histograms of bedforms of file m0706- 1 a profile following run RCA.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

0.95 1 1.05 1.1 1.15

0

M. M




0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 10 4

Figure A-25. Averaged profile with peaks and troughs indicated of file m0706-2a profile
following run RCB.

150
Ripple Length (cm)

OM I

2 4 6 8 10
Ripple Height (cm)

- ,-

12 14 16 18

Figure A-26. Histograms of bedforms of file m0706-2a profile following run RCB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




100
95 90
85 80 C 75 Ca
> 70
w
65 60
55 50
45 L I L L L
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) X 104
Figure A-27. Averaged profile with peaks and troughs indicated of file m0706-3a profile
following run GBA.

3 2.5
2 1.5
1
0.5
0 50

150 200 250 300
Ripple Length (cm)

0 2 4 6 8 10 12 14 16 18
Ripple Height (cm)
Figure A-28. Histograms of bedforms of file m0706-3a profile following run GBA.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

I I I I I I




1 1.05 1.1 1.15
Location Along the Tank (cm)

1.2 1.25 1.3
x 104

Figure A-29. Averaged profile with peaks and troughs indicated of file m0707- 1 a profile
following run RDB

2l-

ILI
60 80 100
8 1 1

120 140 160 180
Ripple Length (cm)

200 220 240

2 4

8 10
Ripple Height (cm)

L_ M

12 14 16

Figure A-30. Histograms of bedforms of file m0707-la -profile following run RDB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

I1(if)

70 l-

45' 0.

0.95

ZOU

I I I I I I

I

9

I I




1.05 1.1 1.15
Location Along the Tank (cm)

1.3
x 104

Figure A-3 1. Averaged profile with peaks and troughs indicated of file m0707-2a profile
following run REB.

100 120 140 160 180
Ripple Length (cm)

0l

200 220

240 260

I I U

6 8 10
Ripple Height (cm)

12 14 16 18

Figure A-32. Histograms of bedforms of file m0707-2a profile following run REB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

3 2.5
2 1.5
1
0.5
0 80

6
5
4
3
2
0
0

I I




0.9 0.95

1 1.05 1.1 1.15
Location Along the Tank (cm)

1.2 1.25 1.3
x 104

Figure A-33. Averaged profile with peaks and troughs indicated of file m0707-3a profile
following run RFB.

0
50 100

200 250 300 3
Ripple Length (cm)

4 6 8 10 12 14
Ripple Height (cm)

Figure A-34. Histograms of bedforms of file m0707-3a profile following run RFB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

4 i v0i

d I' /'t




45 1 I 1 1
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) X 104
Figure A-35. Averaged profile with peaks and troughs indicated of file m0707-4a profile
following run RGA.

Jiii, -1
200 250 300 3 Ripple Length (cm)

6
4
2
0
0

6 8
Ripple Height (cm)

10 12 14

Figure A-36. Histograms of bedforms of file m0707-4a profile following run RGA.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 10
Figure A-37. Averaged profile with peaks and troughs indicated of file m0708- lax profile
following run RGB.

100 150 200 250 300 350 400
Ripple Length (cm)

450 500 550

. I.

2 4 6 8 10 12 14
Ripple Height (cm)
Figure A-38. Histograms of bedforms of file m07080-lax profile following run RGB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

6
6
4
2
0 50

I I N I I 1 111111-

I




0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) x 10'
Figure A-39. Averaged profile with peaks and troughs indicated of file m0708-2ax profile
following run BAB.

100

300

150
Ripple Length (cm)

0 5

15

Ripple Height (cm)

Figure A-40. Histograms of bedforms of file m0708-2ax profile following run BAB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




1.05 1.1 1.15
Location Along the Tank (cm)

1.3 x 104

Figure A-41. Averaged profile with peaks and troughs indicated of file m0708-3ax profile
following run BBB.

U,

80 100 120 140
Ripple Length (cm)

1-

160 180 200 220

5
4 I

10
Ripple Height (cm)

Figure A-42. Histograms of bedforms of file m0708-3ax profile following run BBB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.




4 5 ,
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Location Along the Tank (cm) X 104
Figure A-43. Averaged profile with peaks and troughs indicated of file m0708-4ax profile
following run BCB.

120 140 160 180
Ripple Length (cm)

IWONE

200 220 240

5 10
Ripple Height (cm)

Figure A-44. Histograms of bedforms of file m0708-4ax profile following run BCB.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

4
3
2
1
0 100
3
2.5
2 1.5
1
0.5
0
0




1.05 1.1 1
Location Along the Tank (cm)

1.2 1.25 1.3
X14

Figure A-45. Averaged profile with peaks and troughs indicated of file m0709- 1ax profile
following run RFD.
4 3
2
0
80 100 120 140 160 180 200 220 240 260
Ripple Length (cm)
5
4 3
2 1
0
2 4 6 8 10 12 14 16 18 20 22
Ripple Height (cm)
Figure A-46. Histograms of bedforms of file m0709- 1 a profile following run RFD.
a) Histogram of ripple lengths; b) Histogram of ripple heights.

100
95 90 85 80
S75
0 % 70
w
65 60 55 50