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Field measurements of turbulance and wave-generated ripples

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Title:
Field measurements of turbulance and wave-generated ripples
Series Title:
Field measurements of turbulance and wave-generated ripples
Creator:
Mouraenko, Oleg A.
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Language:
English

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University of Florida
Holding Location:
University of Florida
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All applicable rights reserved by the source institution and holding location.

Full Text
UFL/COEL-2001/016

FIELD MEASUREMENTS OF TURBULENCE AND WAVE-GENERATED RIPPLES by
OLEG A. MOURAENKO

THESIS

2001




FIELD MEASUREMENTS OF TURBULENCE AND WAVE-GENERATED RIPPLES

By
OLEG A. MOURAENKO
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

2001




In loving memory of my mother.




ACKNOWLEDGMENTS

I wish to express my gratitude to Daniel M. Hanes, the chairman of my graduate committee, for the support and freedom granted to me while pursuing my research interests. I also thank the members of my graduate committee, Robert G. Dean and Robert J. Thieke, for their great teaching and unending assistance.
I thank my parents for their love and trust. I thank my friends for their support,
encouragement and help. I thank the faculty members for their knowledge and attention. I also thank the students with whom I have studied and for the great times we were shared.
Special thanks go to Vadim Alymov, Vladimir Paramygin, Yeon Sihk Chang, Jamie Macmahan, Chris Bender, Justin Davis, Becky Hudson, Helen Twedell, Sidney Schofield, Jim Joiner for their help, support and patience.
I thank the Coastal Science Program, US Office of Naval Research provided the financial support for this research through the NICOP and NOPP programs.




TABLE OF CONTENTS
pM.ge
ACKNOWLEDGMENTS........................................................................ ii
LIST OF TABLES............................................................................... vi
LIST OF FIGURES .............................................................................. vii
KEY TO SYMBOLS.............................................................................. x
ABSTRACT .................................................................................... xi
CHAPTERS
1 INTRODUCTION............................................................................. I
Estimation of Turbulence ...................................................................
Bedforms ..................................................................................... 2
Summary of the SandyDuck'97 Data Set................................................... 3
2 ESTIMATION OF TURBULENCE......................................................... 7
Measurement of Turbulence.................................................................. 7
Separation in Frequency Domain ............................................................ 9
Initial Terms and Definitions ............................................................ 9
Cut-off Method........................................................................... 12
PV Method .............................................................................. 13
VV Method .............................................................................. 14
Comparison of Cut-off, PV and VV Methods ........................................ 15
Separation in Time Domnain................................................................. 24
Errors in Measurement of Turbulence due to Frame Vibration ........................ 28
3 BEDFORM MEASUREMENTS........................................................... 32
Instrument and Data Processing ............................................................ 32
Filtering of Raw Data........................................................................ 37
Short Wave Ripples.......................................................................... 43
Dimensions .............................................................................. 43
Approximation of Ripple Lengths...................................................... 44
Approximation of Ripple Heights...................................................... 49




4 RELATIONSHIPS BETWEEN TURBULENCE, SUSPENDED SEDIMENT
CONCENTRATIONS AND BEDFORMS ............................................................ 53
A nalysis of R elations ............................................................................................. 53
TKE and Sediment Concentrations ......................................................................... 53
T K E and B edform s .................................................................................................. 55
Time Variations of TKE, Sediment Concentration, and Bedform Mobility ........... 59
5 C O N C L U SIO N S ................................................................................................... 6 1
APPENDICES
A MATLAB PROGRAMS FOR FILTERING OF MTA DATA ............................. 64
B SHORT RIPPLES DURING THE SANDYDUCK'97 EXPERIMENT ................ 70
LIST O F R EFER EN C ES ............................................................................................ 79
BIO G RA PH ICA L SK ETCH ........................................................................................ 80




LIST OF TABLES

Table Page
3-1: Filter description ............................................................................ 38
4-I: Coefficients of relationship between TKE and first moment of concentration for
different ADV2 elevations ................................................................. 55
4-2: Coefficients of relationship between TKE and short ripple height for different
ADV2 elevations ............................................................................ 57
4-3: Coefficients of relationship between TKE and short ripple length for different
ADV2 elevations ............................................................................ 58
4-4: Coefficients of relationship between TKE and steepness of short ripples for
different ADV2 elevations ................................................................. 58
B-I: Analysis of short ripple form and migration ............................................. 70
B-2: Short ripple dimensions .................................................................... 74




LIST OF FIGURES

Figure PaMge
1-1: Beach profile on 09/27/97 and location of frame. Coordinate system relative to
c o a stlin e ..................................................................................................................... 3
1-2: Instrum ent setup and dim ensions ......................................................................... 5
1-3: SandyDuck'97 offshore instrument setup ............................................................ 6
2-1: Instrum ent setup and dim ensions ......................................................................... 8
2-2: The definitions of 'cut-off frequency as a point of inflection of cross-chore (U)
velocity spectrum and point of steep descent of coherence function ................... 13
2-3: Spectra and coherence functions. Elevations of sensors above the bed: 15.8 cm for
ADVI and 9.5 cm for ADV2; H 0- 2.1 m, Tpeak- 11.6 s, Oeak -78.50 ................. 16
2-4: Spectra and coherence functions. Elevations above the bed: 41.3 cm for ADVI
and 35.0 cm for ADV2; H,,,0 2.2 n, Tpeak 8.5 s, 0p,,,k 64.6 ............................. 17
2-5: Separation of wave and turbulent components in frequency domain by PV method
(left plots) and VV method (right plots). Elevations of sensors above the bed: 15.8 cm for ADV I and 9.5 cm for ADV2; H.o 2.1 m, Tpeak 11.6 s, 0peak
7 8 .50 .......................................................................................................................... 18
2-6: Separation of wave and turbulent components in frequency domain by PV method
(left plots) and VV method (right plots). Elevations above the bed: 41.3 cm for
ADVI and 35.0 cm for ADV2; Hm0 -2.2 m, Tpeak- 8.5 s, 0, ,ek -64.60 .......... 19
2-7: Full turbulent kinetic energy from PV and VV methods. a) Elevation of ADV2 is
9.5 cm; Ho 2.1 in, Tpeak- 11.6 s, 0Iek 78.5'. b) Elevation of ADV2 is
35.0 cm ; Hm0 2.2 In, Tp,,k 8.5 s, Olvak -64.60 ................................................ 21
2-8: Comparison of cut-off, PV and VV methods of estimation of TKE for 2 Hz data... 22




2-9: Time series of turbulent velocity components. Elevations above the bed: 14.3 cm
for ADV I and 8.0 cm for ADV2; H..0 1.2 in, Tpeak 12.8 s, op,,k 830 ............... 26
2-10: Time series of turbulent velocity components. Elevations above the bed: 28.5 cm
for ADV I and 22.2 cm for ADV2; H,,.o 1.3 in, Tpeak 1 I. 1 S, 011k 600 ............. 27
2-11: Significant wave heights and mean values of frame tilts during the SandyDuck'97
ex p erim en t ................................................................................................................. 2 9
2-12: Significant wave heights and STD of frame tilts during the SandyDuck'97
ex p erim en t ................................................................................................................. 3 0
2-13: Spectra of velocity components and vibration rates for wave parameters: Hmo
1.2 m, Tp,,ak- 12.8 s, 01!11k -83'. a)Velocity spectra for ADVI on elevation
15.8 cm; b) Velocity spectra for ADV2 on elevation 9.5 cm ................................ 31
3-1: MTA structure and dimensions with an example of bedform profile .................. 33
3-2: Data from transducer #33, test #1. Despiked raw data points and their histogram... 35 3-3: Run #30 of Sandy Duck 97 data for transducer #33. Despiked raw data points and
data after applying filters ...................................................................................... 36
3-4: Histogram of percentage of removed data point ................................................... 39
3-5: Magnitude and impulse response functions of FIR lowpass filter of 31 order with
cutoff frequency 2/30 .......................................................................................... 40
3-6: Raw and despiked signal (top), and filtered of despiked data (bottom). (*) FIR
lowpass filter of 31st order; (**) elliptic IIR lowpass filter of 5t" order ............... 41
3-7: Approximation of ripples dimensions for one profile from run #30 ..................... 45
3-8: Approximation of ripples lengths by three methods for run #30 ......................... 47
3-9: Comparison of methods of ripples lengths approximation ................................... 48
3-10: Approximation of ripples heights for run #30 ..................................................... 49
3-11: Comparison of methods of ripples heights approximation ................................... 51
4-1: Relationship between TKE and first spatial moment of concentration (E) ..... 54 4-2: Relationship between short ripple height (HsR) and TKE for different elevations of
ADV2 (hADV2): R correlation coefficient, N- number of data points ................ 56




4-3: Relationship between short ripple length (LsR) and TKE for different elevations of
sensor (hADI,2): R correlation coefficient, N- number of data points ................ 57
4-4: Ripple crest positions, TKE, mean concentration and wave envelope for run #30:
start at 256.3589 in Julian days ............................................................................. 59




KEY TO SYMBOLS

(ax,a,,)
b
c(t,z)
CI
C f )
h(x)
hABS,AI)1W,A)V2
h(r),1(r) H(f),L(.f) H, HSR m0
i
L, LS'R
N
P,
Q,(f)
R
Sr,(f) S,,,(f)
Sf1. (f)" s[,,/ (.f)
t
At
T
Tpeak
U
V
F

[L] Amplitudes of vibration

[ML ]
[T-M']
[L]U
[L]
[L] [L]
[L] [-]
[L]
[L2T'] [L2T-1] [T] IT] [T] [T] [LT-'] [LT ] [LT1]

Phase angle
Suspended sediment concentration First moment of suspended sediment concentration Autocorrelation function Coincident spectral density function Cyclical frequency Bed elevation from mean level Elevation of ABS, ADVI, ADV2 above the seabed Unit-impulse response functions Frequency response functions Ripple height, ripple height of short ripple Significant wave height determined from surface elevation spectrum
-1, index
Ripple length, ripple length of short ripple Number of data points Pressure, normalized by water density and gravity Average energy of signal Quadrature spectral density function Correlation coefficient Autospectral density function Cross-spectral density function Turbulent part of autospectral density function of velocity Wave part of autospectral density function of velocity Time variable
Sampling interval Record length, period Peak wave period determined from surface elevation spectrum Cross-shore velocity component Long-shore velocity component Velocity vector




Mean current and infragravity wave component of velocity vector
Wind wave component of velocity vector Turbulent component of velocity vector Vertical velocity component Cross-shore, long-shore and vertical coordinates Time history records Fourier transform of x(t),y(t) Complex conjugate of[ ] Coherence function

V
V/
V'
W
(x,y,z) x(t), y(t) X(f), Y(f)
[*]
6
Elot,0,1,2.. Opeak
I 02

[LT-']
[LT-'] [LT-'] [LT-'] [L]

[L] Grid interval
Error source
Peak wave direction in degrees from positive long-shore
direction
Mean value
Standard deviation
Variance




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 FIELD MEASUREMENTS OF TURBULENCE AND WAVE-GENERATED RIPPLES By
Oleg A. Mouraenko
August 2001
Chairman: Daniel M. Hanes
Major Department: Civil and Coastal Engineering
The SandyDuck'97 experiment data set was analyzed to estimate the intensity and frequency content of turbulence near the seabed in the nearshore region and to obtain the bedform dimensions at the position of measurements. The measurements of hydrodynamics were obtained with two acoustic Doppler velocimeters (ADV) and a pressure sensor in water depths of approximately 4 meters under a variety of wave conditions, with seabed conditions ranging from flat to rippled.
Three previously published techniques of separation of turbulent and waveinduced flow motion were analyzed. Qualitatively similar results were found for all the techniques, though quantitative values varied by one order of magnitude. It was established that the minimum of turbulent kinetic energy was estimated by 'cut-off frequency method and the best estimation of turbulence was provided by a method based on coherency between the signals from two velocity sensors that were separated in space.




A new filtering technique was developed to obtain a better estimate of short wave ripples. Several methods were used to obtain the ripple scales. The accuracy of ripple height measurements was found to be less than 2 mnm. Short wave ripples were found to exist more frequently than believed from previous analysis technique.
The estimated turbulent kinetic energy was compared to other measured
parameters to find empirical relationships. A high correlation was found between TKE and first moment of suspended sediment concentration profiles.




CHAPTER 1
INTRODUCTION
Estimation of Turbulence
Turbulence is an important phenomenon in coastal processes, which has only
recently become possible to measure due to the development of high-resolution velocity sensors. Some factors that complicate the measurement of turbulence intensity in the field include surface waves and the topography of the seabed. Different techniques are commonly used to separate the turbulent components of velocity from fluctuations induced by surface waves. Three such techniques are applied and evaluated here.
The intensity and frequency content of turbulence near the seabed in the nearshore region have been estimated from field measurements from SandyDuck'97 by using three different methods: cut-off, PV, and VV. The cut-off method uses a 'cut-off frequency as a criterion of separation of wave and turbulent components of velocity. This is a widely used technique (e.g. Kos'yan et al., 1996).
The PV method uses the coherence function between pressure and velocity to separate turbulence from waves (for example, see Wolf, 1999). Linear wave theory provides the relationship between pressure and velocity for wave-induced component. This method does not incorporate the effect of nonlinear waves or a sloping bottom. The VV method (Trowbridge, 1998) is based on measurements of velocity from two sensors, separated from each other by the distance much smaller than the surface wavelength but




2
larger then the correlation scale of turbulence. The coherence between sensors is then assumed to reflect wave induced motion.
Acoustic Doppler velocimeters (ADV) were used for velocity measurements during the SandyDuck'97 experiment. Voulgaris and Trowbridge (see Voulgaris and Trowbridge, 1998) verified this type of instruments for turbulence measurements by comparison with laser Doppler velocimeter (LDV). ADV showed a low noise level and a good agreement with turbulence measurements by LDV.
Bedforms
The presence of bedforms on the seabed affects the turbulence intensity, primarily through the process of flow separation.
Alymov (1999) and Hanes et al. (2001) analyzed the bedforms during the
SandyDuck'97 experiment and found two types of ripples. Long wave ripples (LWR) with lengths 35-250 cm and short wave ripples (SWR) with lengths 3-25 cm were both found to be present. However, SWR were only found in 31 runs from 164, and for 111 runs a flat bed conditions were identified. This low occurrence of SWR might have resulted because the measurement and analysis techniques did not have sufficient resolution. Therefore a new filtering procedure has been developed to make more accurate evaluation of SWR for SandyDuck'97 bedform measurements. Due to better accuracy of the new procedure, SWR were found present in most in most cases. Visually flat bed conditions were found only during 71 runs, and the existence of SWR has been established for 54 cases. The time resolution of new filtered data also provides the opportunity to study some short time-related effects. The migration of ripples, the




appearing and disappearing of ripples under wave groups, the reconstruction of ripple shape, and the variation of linear scales can now be analyzed.
Summary of the SandyDuck'97 Data Set
The SandyDuck'97 experiment took place in Duck, NC at the Army Corps of Engineers Field Research Facility from September 11 to November 10, 1997. Measurements include hydrodynamics, bedforms, profiles of suspended sediment concentrations, video images, and some other parameters. The total duration of all records is 44 days, which were made in various wave conditions, including several storm events.

2
0
0
' -2 LU
-4
-6
10c

Beach profile (09/27/97)

0 200 300 400 500
Cross-shore distance, m

kU

Figure 1-1: Beach profile on 09/27/97 and location of frame. Coordinate system relative to coastline.
A frame with instruments mounted on it was placed by scuba divers at a distance about 390 meters away from the shoreline and 1000 meters along the shoreline according to the FRF coordinate system. The depth at the site location was about 3.5 meters at low

\




tide. The beach profile with the frame position and coordinate system in (x,y)-plane are shown on Figure 1-1.
The acquisition system used in the SandyDuck'97 experiment (see Thosteson, 1997) allowed measuring and recording data from several instruments simultaneously. All data were collected with one of three sampling frequencies: 1, 2, or 4 hertz. The data from each run were stored in several 34 minutes files. These data include (see also Figure 1-2):
* 3D velocity measurements from two ADVs (acoustic Doppler
velocimeter);
* Pressure measurements;
* One-dimensional vertical profile of suspended sediment concentrations
from 1, 2.25, and 5 MHz ABS (acoustic backscatter);
* Tilt and compass data.
* Bedform measurements from a multiple transducer array (MTA).
One-dimensional measurements of bedforms were carried out using 64-element MTA (see Jette and Hanes. 1997). The highest time resolution for MTA data was 0.5 Hz or one profile per 2 seconds. Other rates were sometimes used to increase the length of the record. The MTA data were collected separately from hydrodynamic data, but were synchronized in time. Unfortunately, the bedform measurements are not available for all of hydrodynamic data due to both sampling limitation and biofouling of the MTA.




Pressure Sediment
concentrations

Figure 1-2: Instrument setup and dimensions.
The offshore instrument setup and dimensions are shown in Figure 1-3. The main axis of the MITA was directed perpendicular to the shoreline and coincides with the xdirection for velocity measurements. The elevations of the instruments were estimated from ABS profiles and recalculated according to their positions relative to ABS transducers. For some data the elevation of the MTA above the seabed are known, therefore other instrument elevations can be measured more accurately.




Ocean

6.0cm

62 1cm.

of MTA

ABS (3 frequencies) 3 2cm TTC

18 0cm
6 3cm
-JV-

ADV1
Elevation of ADV2

Vt-

e70.7cm. -53.0c
98.1cm. -4
Figure 1-3: SandyDuck'97 offshore instrument setup.

MTA2

64
4.0cm

98 1cm

Coast




CHAPTER 2
ESTIMATION OF TURBULENCE
Measurement of Turbulence
The successful measurement of turbulence depends highly on the capability of
instrumentation used. The frequency range of turbulent fluctuations is extremely wide. It extends from fractions of hertz up to hundreds. The instruments should allow measurements to be carried out with sufficient spatial accuracy and time resolution. Difficulties arise when measurements are taken in the nearshore zone, where many additional factors affect the results. Some of these factors are as follows:
* Difficulties in mounting and maintaining the instruments, especially
during storms;
* Energetic flow conditions cause vibration of instruments;
* Requirement of instrument stability leads to heavier and stronger
supported frane, which can distort the flow;
* Higher requirements for instruments, data acqusition and recording
systems.
During the SandyDuck'97 experiment two 5MHz ADVOcean probes (acoustic Doppler velocimeter) and a pressure sensor were used to measure hydrodynamic parameters. Two ADVs were placed with 6.3 cm difference in elevations and with 53 cm separation distance in the cross-shore direction. Sampling volumes of ADVs are located in 18 cm from the acoustic transmitters. The pressure sensor had an elevation of 34.7 cm




8
above the position of the ADVI's sampling volume. The setup and dimensions of instruments are shown on Figure 2-1.
Ocean [Coast
Pressure
* ADVI '
V ......... ..... .. ..I A ........ 7i,3 7
ADV2
S -18.0cm. Elevation
18.0cm. 6.3cm. of pressure
A Isensor
I LElevation
Elevation 53.0cm. of ADV1
of ADV2 WO
Figure 2-1: Instrument setup and dimensions.
Voulgaris and Trowbridge examined the suitability of acoustic Doppler
velocimeters (ADV) for turbulence measurements (see Voulgaris and Trowbridge, 1998). They found good agreement with measurements, made by laser Doppler velocimeter, stated very small errors (within I%) in estimation of mean flow and Reynolds stresses, and reasonable agreement with other methods of estimation of turbulent kinetic energy.
The frame with instruments mounted on it was fixed on the seabed with pipes. No measurements were made to estimate the vibration under wave forcing in longitudinal (cross-shore) and transversal (long-shore) directions. But using the TTC sensor (TiltTemperature-Compass) it is possible to estimate rolling (along cross-shore direction) and pitching (along long-shore direction) oscillations. These oscillations could distort the measurements of turbulence. The analysis will be made later in this chapter.




Separation in Frequency Domain Initial Terms and Definitions
A component of velocity vector can be represented as a sum of sinusoidal
fluctuations with different frequencies and phases. Fourier transform is commonly used to obtain such decomposition. Let x(t) be a signal, measured with time t. Then its direct Fourier transform X(f) as a function of frequency f and inverse transform are given by Equations 2-11:
X(f) = F{x(t)} = Jx(t)e-i2 'dt +(2-1) x(t) = F {X(f)} = X(f)e 2.if x~t)X(f)e f~df
An average energy of signal is equal to
= lim- {x(t)}2dt (2-2)
T 2Tj
A spectral density function of signal x(t) is defined by
S, (Jf) = lim X(f)2, fe (oo,-i-oo) (2-3)
/ 7-- T1
According to Parseval's theorem:
J{x(t)}2 Idt= jlX(f)2 df (2-4)
The average energy of signal now can be expressed in term of spectral density function:

SAll the equations can be found, for example, in the book of Bendat and Piersol, 1993.




= s' (f)df = s ,(f)df (2-5)
2 -_ 0
To obtain an average energy of fluctuations for a frequency range the integral 2-5 should be evaluated only within this range: {f E [f, f2 ]} = fS. (f)df, fl./2 > 0 (2-6)
I
Let two signals x(t) and y(t) have their Fourier transformations X(f) and
Y(f) correspondingly. Then the cross-spectral density function between these signals is defined by
S. (f) = li x(f)Y(f)=,,(f)- iQ,(f), fe (-c,+c) (2-7)
7 -- T
In general the cross-spectral density function is a complex function. The real part C.,,(.f) is called the coincident spectral density function or cospectrum, and the imaginary part ,,(f) is called the quadrature spectral density function or quadspectrum.
Define the coherence function by
S," (f) (2-8)
The coherence function, defined by the equation above, is a complex function, as well as the cross-spectral density function. Usually, a square of the magnitude of ,,(f) is used as a definition of coherence function. But in current work both the complex value and its magnitude are used. Note, that the magnitude of coherence function has a value between 0 and 1:




0 _< 7,(f) 1 (2-9)
The phase angle of coherence function is equal to
arg(,:, (f)) = -tan' t (2-10)
The velocity vector V could be written as a sum of three components:
V =V +V +V' (2-11)
where V is a mean current and infragravity waves, V is a motion, induced by windgenerated surface gravity waves, and V' is a turbulent motion. The easiest way to separate these components is to set their frequency ranges. The mean current and infragravity waves cover the lowest frequencies from 0 Hz up to 0.025 0.05 Hz. The fluctuations, induced by wind waves, extend from upper limit of infragravity waves up to approximately 0.5 0.8 Hz. High frequency fluctuations are associated with turbulence. Its range extends up to hundreds of hertz. This method only works, if these three components are defined as fluctuations of particular frequencies. In general, infragravity, wind waves, and turbulence have different physical origins. This does not guarantee clear separation in frequencies and means that their frequency ranges could overlap.
The lower limit of frequencies for wind waves was taken to be 0.05 Hz. Further investigation is devoted to the problem of separation of waves and turbulence.
There are three methods, which were used to solve the problem of separation of wave and turbulent components of velocity:
" Cut-off- based on 'cut-off frequency between wave and turbulent
fluctuations;
* PV based on coherence function between pressure and velocity signals;




VV based on coherence function between velocity signals from two
sensors separated in space.
Cut-off Method
This is the most simple technique to separate the turbulent component of velocity from wave-induced motion. The only problem is to find the 'cut-off frequency, which separates two types of motion. Two different approaches are commonly used to find it. One is based on assumption that the velocity spectrum, plotted in log-log scale, changes slope at this frequency. Another way involves the assumption that the velocity and pressure are coherent only at wave frequencies, but noncoherent at higher frequency fluctuations. Thus the 'cut-off' frequency could be defined as the frequency of steep descent of the coherence function between pressure and velocity. Examples of application of two definitions are shown on Figure 2-2. In all field measurements to be presented these definitions give almost the same results.
The point of inflection of the velocity spectrum curve was found by fitting two lines. Both lines are best-fitted lines for the high frequency part of the spectrum and for the wave part of the spectrum. The slope of the spectra characterizes the rate of energy dissipation.
For the SandyDuck'97 experiment data the mean value of the 'cut-off frequency was found to be 0.5 Hz with standard deviation of 0.1 Hz. It was estimated from 173 data records with sampling frequency of 4 Hz of all three components of velocity from both ADVs.




100 0.5
o ~0.4 ...
C:
10 _2 . .. .., 0 .3 ...
E a, 0.4
CI) 4
-10 -c)0.1
. . .. ..0
o : : : : : :. 0 .2 : :.: ::. . . .. . .
8 o 0.1ii ::
: : : : : :. . :0 . . . .
10-1 100 10-1 100
Frequency, Hz Frequency, Hz
Figure 2-2: The definitions of 'cut-off frequency as a point of inflection of cross-chore
(U) velocity spectrum and point of steep descent of coherence function.
The turbulent kinetic energy (TKE) was calculated using Equation 2-6, wherefl is a 'cut-off andf2 is Nyquist frequencies. The values J=0.05 Hz andfi='cut-off were used for estimation of wave kinetic energy.
PV Method
The value of the coherence function between pressure and velocity signals is high at wave frequencies and very low at higher frequencies (see Figure 2-2 as example). This property is commonly used to separate turbulent and wave components of velocity (see Wolf, 1999). The coherence function for PV-method (Pressure-Velocity) is given by Equations 2-12:
7y,,, (f) = 0, 0 < f < 0.05
S ,,) S / V (.f )1 f 0 .0 5 (2 -12 )
" ()=s",(Dfs (f)




where p is a pressure signal and V is one of three components of velocity. Note, that only magnitude of coherence function is used here. Spectra for velocity components are given by Equations 2-13 and 2-14.
S,, =V f >0 (2-13)
S,, 0 1-7,.) ,,.. > 0 (2-14)
where superscripts W and T refer to waves and turbulent parts correspondingly.
The kinetic energy is estimated using Equation 2-6 with fl=0.05 Hz and 13=Nyquist frequency for both waves and turbulence.
VV Method
Another method of separation of wave and turbulent components of velocity was suggested by Trowbridge (1998). This method is based on measurements of velocity from 'two sensors, separated from each other by the distance much smaller than the surface wavelength but larger then the correlation scale of turbulence'. Usually, the wavelength during the SandyDuck'97 experiment was approximately 75 m (estimated by linear theory for a wave period of 12 seconds and depth of 4 in). As it is seen from Figure 2-1 the distance between two ADVs is 53 cm, which is much smaller than the wavelength. The correlation scale of turbulence will depend on many parameters including the magnitude and frequency of flow fluctuations. The significant velocity, defined as 4V..., during the storm was about 1 m/s. Assuming a frequency of 0.5 Hz the length scale is equal to 0.5 m, which is comparable with distance between sensors. In reality, the turbulent velocity is expected to be less than the significant velocity, so the distance of 53 cm is larger, than the scale of turbulence.




The coherence function between two velocity signals is given similar to PVmethod by Equations 2-15:
(.f) =0, 0< f<0.05
S'(f) =(2-15) y~ (f) f 0.05
- S,1., (f)S,1, (f)'f>05
where V is a cross-shore, long-shore or vertical component of velocity, and the index I and 2 refers to ADVI and ADV2 correspondingly.
The spectra for velocity components are given by Equations 2-16 and 2-17.
1, = y ,, S,.. f > 0 (2-16)
S= (1 YV, )Sv, f> 0 (2-17)
The kinetic energy is estimated using Equation 2-6 with Jf=0.05 Hz and 13=Nyquist frequency for both waves and turbulence.
Comparison of Cut-off, PV and VV Methods
The coherence functions and spectra after application of PV and VV methods are shown on the next four figures. Figure 2-3 and Figure 2-4 demonstrate the initial spectra of pressure and velocity components on the left plots. The coherence functions between pressure and velocity and between two velocity signals from different sensors are shown on the right plots. The main difference between two figures is in elevation of ADVs above the seabed. For Figure 2-3 the elevations were 9.5 cm for ADV2 and 15.8 cm for ADVI. And for Figure 2-4 they were 35.0 cm and 41.3 cm for ADV2 and ADVI correspondingly.




100 UADV1 UADVl vs. Pres
u vs.Pres
- UADV2 ADV2vs. Pres
S sure UADV1 vs. UADV2
U) 0.5
E
10-4
U)
C/ 0
Q,
L 0 0.5 1 1.5 2 0 0.5 1 1.5 2
c\E 0 C: 1 s P
c 100 ADV1 .0 1 V PADVi res
- V-ADV2 C VADV2 vs. Pres
S- Pressure I _ VADVVS. VADV2
0
-a)o 0 .5 . . . . . . .
10-4
o "- =.c-!
-0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
CU)
a) 1
10 0 W vs. Pres
t- W[ADV2~ WADV2 vs. Pres
1 - Pressure - WADV1 VS. WADV2
CI) 0.5
10-4
0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz
Figure 2-3: Spectra and coherence functions. Elevations of sensors above the bed: 15.8 cm for ADVI and 9.5 cm for ADV2; Ho 2.1 m, Tpeak 11.6 s, Op,,,k 78.5'.
The pressure (p) was normalized by water density and gravity, thus measured in
meters. The velocity vector is V = (U, V, W), where U is a cross-shore, V is a long-shore
and W is a vertical components of velocity, in meters per second.




17
1 *
100 UADV1 UADV1 vs. Pres
S UADV2 UADV2vs. Pres
UU ADAVsU
- Pressure - UADV1 Vs. UADV2
C1 0.5
E
- 10U)
(n 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
0.
S10 VV vPe
100 V vADV1A VS. Press i
AOV
.1 VADV2 ... VADV2 vs. Press
U- Pressure - VADV1 VS. VADV2
0
0.5
C 10-4
00
0
0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
U)
1 00 D1W WAV1 vs. Pres
- 10 I D1AV
SWADV2 WADV2 vs. Pres
0
) - Pressure WADV1 VS. WADV2
-4) 0.5 1
10-4
0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz
Figure 2-4: Spectra and coherence functions. Elevations above the bed: 41.3 cm for ADVI and 35.0 cm for ADV2; H0o 2.2 m, Tpeak 8.5 s, Opek 64.6o.
The coherence function between cross-shore velocity and pressure (PU
coherence) is very high on wave frequencies (0.05 0.5 Hz). The situation is very
different for long-shore components of velocity. The PV coherence is about half
compared with the VV coherence at the peak wave frequency and is ever less for the rest
of wave frequencies.




i ': ] ADV2
.. ....W aves
- TKE
J 0.5 1 1.5 2
.. .. ADV2
Waves
~- TKE

0.5 1

1.5 2

0 0.5 1 1.5
Frequency, Hz

100 UADV2
.Waves
~- TKE
10-

CI)
E
CI)
10
o 10
C-)
C
0 10-4
CL C)

0 0.5 1 1.5 4
... .. .. .. .. VADV2
.......W aves
~~TKE

0 0.5 1 1.5 2

0 0.5 1 1.5
Frequency, Hz

Figure 2-5: Separation of wave and turbulent components in frequency domain by PV method (left plots) and VV method (right plots). Elevations of sensors above the bed: 15.8 cm for ADVI and 9.5 cm for ADV2; H o-2.1 in, Tpeak- 11.6 s, Opeak -78.50.
For the vertical velocity component the PW and WW coherences are not as high as for cross-shore velocity. That difference could be explained by small elevation of sensors above the seabed: inside the turbulent boundary layer the intensity of turbulent

CI)
E
C6)
o 100
0
.2
0 10-4
U)




19
motion greater than the intensity of wave-induced motion. Moreover, the magnitude of vertical velocity is small.

-UADV2
KWaves
0TKE .
0 0.5 1 1.5 2
0 0.5 1 1.5 2

100
104
E
(6
C 0
o 10
D
-0 10-4 CL U) 0) C.
o0

0 0.5. UADV2
; : .......... W aves
- "::, -- TKE
J 0.5 1 1.5 ,c

0.5 1 1.5 2

0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz
Figure 2-6: Separation of wave and turbulent components in frequency domain by PV method (left plots) and VV method (right plots). Elevations above the bed: 41.3 cm for ADVI and 35.0 cm for ADV2; Ho 2.2 i, Tpeak- 8.5 s, O,,,k 64.60.
There is a small difference between coherence functions for ADVI and ADV2. However, the spectra of horizontal components of velocity are different (Figure 2-3).

C,)
E
C o 10
C
"U
C
0)
- 10
CO.
0

-v
ADV2
Waves
- TKE

o




ADV2 was closer to the bed and the TKE is greater at high frequencies. Figure 2-4 indicates that the velocity spectra are about the same, when the sensors were located 35.0 and 41.3 cm above the bed.
Figure 2-5 and Figure 2-6 show the spectra of wave and turbulent components of velocity from ADV2. The spectra on the left plots were calculated using PV method and on the right using VV method. There are several evident differences:
" The slopes of the turbulent spectra at wave frequencies for the PV method
are different front the slope at high frequencies.
* At a 9.5 cm elevation the turbulent spectrum of the long-shore component
of velocity has larger values at wave frequencies than the spectrum of the
wave component. At 35.0 cm elevation both turbulent and wave spectra
wave are nearly the same. This is a result of small values of PV coherence,
which was mentioned before.
* For PV method the magnitude of turbulent spectra for horizontal
components differs from vertical by about a factor of 10.
" The turbulent spectra from VV method of all components of velocity have
nearly the same shape and magnitude, which supports the hypothesis of
homogeneous turbulence.
" The turbulent and total spectra of the vertical component of velocity are
about the same. Only a small part of the energy result from wave motions;
most of the vertical fluctuations are caused by near-bed turbulence.
The full turbulent kinetic energy, calculated by two methods, is shown on Figure 2-7. The plots show the TKE at 9.5 and 35.0 cm elevations above the seabed




correspondingly. PV and VV methods provide the same results on high frequencies, because coherence functions in both cases were very low at these frequencies. However, in the wave frequency range the TKE estimated by PV method is much higher than the TKE estimated using the VV method. Moreover, the slope of the PV spectrum changes, then the curve goes through 'cut-off frequency. There is no such inflection on PP spectrum.
Significant wave heights for both cases were almost the same and the bottom had small ripples with 45 mm length and 5 mm height. PV method shows approximately the same magnitudes of TKE at wave frequencies, but VV method reflects the difference in elevation.
a) b)
PV P
- PV PV
10- VV10 - VV
1 0 . . . . . . 1 0
10-4 10-4
E E\
U) U)
C > -2 Ci> -2A
U) 10 f U) 10
ttwo
U) U)
10-2 100 10-2 100
Frequency, Hz Frequency, Hz
Figure 2-7: Full turbulent kinetic energy from PV and VV methods. a) Elevation of ADV2 is 9.5 cm; H,,,o 2.1 m, Tpeak 11.6s, 9 e,,k 78.5o. b) Elevation of ADV2 is 35.0 cm; H,,,o 2.2 m, Tpeak 8.5 s, O0Pek -64.60.




ADV1
0.1
0.08 0.06
0.04 .
y =30.5x
0.02
+O+.81
0
0 1 2 3 4
Cut-off X 10-3
0.02
0.015
> 0.01
0.005 y 5.lx
R +0.96
0
0 1 2 3 4
Cut-off X 10-3
0.08
0.06
0.04 ,
0.02 . .. .: -. .

0.02 0.015 > 0.01
0.005

ADV2

Cut-off X 10-3

0 1 2
Cut-off

0 0.005 0.01 0.015 0 0.005
VV VV

4
X 10-3

0.015

Figure 2-8: Comparison of cut-off, PV and VV methods of estimation of TKE for 2 Hz data.

y y5.lx
R =+0.97




All three methods were applied to calculate the full turbulent kinetic energy for all data collected at a rate of 2 Hz data. Processing involved 1347 data records. The results are shown on Figure 2-8. The estimated TKE is plotted in pairs by methods. The functional dependencies between methods were approximated by linear regression. The correlation coefficients (R) were calculated as well.
To summarize the results of the comparison several conclusions can be made:
* All three methods of separation of turbulence from wave motion provide
qualitatively similar results, which follows from high correlation
coefficient between estimations of TKE by the methods described.
* The 'cut-off method estimates the minimum amount of total TKE, which
is approximately 5 times smaller than from VV-method.
* The PV method overestimates the total TKE in the long-shore direction
and overestimates the full TKE. The TKE is estimated 6 times larger than
by VV method and 30 times larger than by the 'cut-off method. This is
probably because a large amount of energy is the wave frequency band is
erroneously identified as turbulence.
" The VV method provides the best estimation of turbulence in the wave
frequency band. The power spectrum of the turbulence has the same slope
over both wave and turbulent frequencies.




Separation in Time Domain
The methods described in previous section can be used for the separation of wave and turbulent components of velocity in the time domain. Let x(t) be an initial signal and X(J) its Fourier transformation, given by Equation 2-1. Then high or low frequency components of the signal x(t) can be extracted as a convolution integral of signal with some weighting functions h(r) and 1(r):
x, (t) = h(r)x(t -r)dt
(2-18)
x, (t) = l(r)x(t r)dt
Fourier transform of convolution integral is a product of Fourier transforms of the signal and weighting function: F{xj(t)} = H(f)X(f), H(f) = F{h(t)} (2-19)
(2-19)
F{x,(t)}= L(f)X(f), L(f)= F{l(t)} The Fourier transforms H(f) and L(f) of the weighting functions will be
defined using step functions for 'cut-off method and coherence functions for PV and VV methods.
Let f be a 'cut-off frequency, then
L(f)= 1, 0.05 < j f. (2-20)
L(f)= 0, fl >.
H(f) = I- L(f) (2-21)
For PV and VV methods the functions H(f) and L(f) are given by




L(f) = 0, O < f < 0.05 (2-22)
L(f) = y(.f), f > 0.05 H(f) = 1 L(f) (2-23)
where y(f) is a coherence function, given by Equation 2-24 for PV method and Equation 2-25 for VV method: ,f S" (f) (2-24)
Sill, (.f).S,,,,
S (f)
,, (f) = (f) (2-25)
S ",, (f)SV,2 ('f)
Finally, high and low frequency components of signal x(t) are defined by inverse Fourier transform:
x,,(t) = F-' {H(f)X(f)} (2-26)
x,(t) = F-' {L(f)X(f)}
Two data records with different elevations of sensors above the seabed were taken to demonstrate the results of separation of turbulent component of velocity by the VVmethod. The turbulent velocity components are plotted on Figure 2-9 and Figure 2-10 versus cross-shore component.
The axes a and b of the ellipses were calculated as 3afor each direction, so that the ellipses contain most of points (about 99%). The angle a is an angle of inclination of main axis of ellipse relatively to cross-shore direction.




ADV2

0
-0.1
-0.2 a = 0.10, b = 0.08, = -4.60
-0.2 -0.1 0 0.1 0.2
U', m/s

-0.1
-0.2

0.1

0
-0.1
-0.2

-0.2 -0.1 0 0.1 0.2
U', m/s

a = 0.16, b = 0.14, oa = -4.80
-0.2 -0.1 0 0.1 0.2
U', m/s

- a = 0.15, b = 0.04, c = -1.00
-0.2 -0.1 0 0.1 0.2
U', m/s

Figure 2-9: Time series of turbulent velocity components. Elevations above the bed: 14.3 cm for ADVI and 8.0 cm for ADV2; Hno- 1.2 mn, Tpeak- 12.8 s, 01,eck 830.

a = 0.10, b = 0.04, c = 0.30

ADV1




ADV2

0.2 0.1
0
-0.1
-0.2

-0.2 -0.1 0 0.1 0.2
U', m/s

a = 0.06, b =0.04, c = 1.20
-0.2 -0.1 0 0.1 0.2
U', m/s

0.2 0.1
0
-0.1
-0.2

a = 0.06, b = 0.05, c, = -2.00
-0.2 -0.1 0 0.1 0.2
U', m/s

a = 0.06, b = 0.04, a = 1.40
-0.2 -0.1 0 0.1 0.2
U', m/s

Figure 2-10: Time series of turbulent velocity components. Elevations above the bed: 28.5 cm for ADVI and 22.2 cm for ADV2; H,,,0- 1.3 in, Tpeak 11.1 S, 0 ,ak 600.
Figure 2-9 shows that close to the bottom the difference in intensity of the
directional component of the turbulence significantly varies with elevation of sensor. The ratio of vertical to horizontal amplitudes depends upon elevation above the seabed. The distortion of the ellipse (ratio a/b ) in the vertical plane is greater than in the horizontal plane when the sensor is closer to the bottom. However, in the horizontal plane the

ADV1




turbulence is close to uniform, only the magnitude changes with elevation. For higher elevations (Figure 2-10) the ellipses are nearly circles for all projections. This means that turbulent fluctuations have amplitudes that are approximately equal in the horizontal directions.
Errors in Measurement of Turbulence due to Frame Vibration
The frame and the instruments mounted on it may vibrate under the wave forcing. The amplitude and frequency of this vibration can affect velocity measurements and therefore our estimations of turbulence. There are no measurements to estimate the amplitude of longitudinal (cross-shore) and transversal (long-shore) vibration. However, they can be evaluated indirectly from tilt measurements by the TTC sensor.
The TTC measures three angles: 0- in (x, z) -plane, 0- in (y,z) -plane, and ,8in (x, y) -plane. AllI three angles were measured simultaneously with other parameters, such as velocity and pressure. Therefore, the time series of angles are available. Figure 211 show the mean value for two (0, 0) angles during the SandyDuck'97 experiment. it call he seen, that the angle 0 did not change significantly during the experiment, hut the angle 0 reflects wave activity, especially during storm on 10/ 18/97. Note that this angle reverts back to the value it had before the storm. It means that the inclination of the frame was most likely caused by increased wave forcing, but was not a result of any construction displacement or permanent deformation.
Thle standard deviations of the time series of angles were calculated and plotted on Figure 2-12. Both (0, 0) angles show the instability of the frame during the




experiment. The frame vibrated under waves and the amplitudes of all vibrations are clearly related to the wave activity; and the largest values are reached during the storms.

09/20

09/30 10/10

p'.~b 'b

10/20

10/30

* ,
. . 1 . .
It

11/09

09/10 09/20

09/30

10/10

10/20

10/30

10/10
Julian days, day

11/09
11/09

Figure 2-11: Significant wave heights and mean values of frame tilts during the SandyDuck'97 experiment.
For small angles the amplitudes (a,, a,) of vibration in x and y directions can be approximated by

a, AO r a, AO r

(2-27)

3
2
1
0 09/
-1

E
0) CT
a -

10

i.
-:V
- t ," .i .l .. .. ......" :
: ..... ...V.%- : f

0, a,
C 0
~ a, ~ c
CU
ai ~zr




where (AO, Ab) are the deviations from mean angles. They can be estimated conservatively as 3o-of corresponding angles. The radius r is a distance from TTC sensor center of rotation to point of interest. For ADVI and ADV2 the radiis are approximately equal to 0.6 m and 0.8 m.

09/20 09/30

09/20 09/30

10/10

10/10

10/20 10/30

10/20

10/30

0
09/10

09/20 09/30 10/10 10/20
Julian days, day

10/30

11/09

Figure 2-12: Significant wave heights and STD of frame tilts during the SandyDuck'97 experiment.

The rates of vibration are given by Equations 2-28.
da dO daY do
- r ; - r
dt dt dt dt
The spectrum of vibration rates can be calculated as follows:

(2-28)

3
E 2
)
T 1

11

V9 V" ..... \M N.
EC;

09/10
0.2

U

0
09/10 0.2 -

0.1

11

/09

0) Co
0 2
) I >1
03
o a

11/09

. . . . . . . . . . . . . . . m : . . . . .




S,,, (f) = (2'f)2 S,, (f) (2-29)
The results are shown on Figure 2-13. The errors generated by the frame vibration at all frequencies are much smaller (1-2 order in magnitude), than the turbulent fluctuations. Thus, the frame vibration did not affect turbulence estimations significantly.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 b)

E 100 C
.o
0
.2
10
01
-o
C
_ 10
a. 10 C) 0
Ci)
E 0 Ci) l
0
t5 t 10 C-)
-"
a- 10 U) 0

1.4 1.6 1.8 2

Figure 2-13: Spectra of velocity components and vibration rates for wave parameters: Ho 1.2 m, Tpeak 12.8 s, 0,,,k 830. a) Velocity spectra for ADVI on elevation 15.8 cm; b) Velocity spectra for ADV2 on elevation 9.5 cm.

0.2 0.4 0.6 0.8 1 1.2 Frequency, Hz




CHAPTER 3
BEDFORM MEASUREMENTS
Instrument and Data Processing
The Multiple Transducer Array (see Jette and Hanes, 1997) was used during the SandyDuck'97 experiment to obtain one-dimensional measurements of bedforms. The MTA is an acoustic instrument. It consists of a line of acoustic elements, situated with fixed spacing. The entire array has three MTAs. The middle 32-element 50 cm length MTA has 5MHz-transducers with 1.5 cm spacing between them. Each transducer has an acoustic footprint on the seabed of approximately 2.5 cm if the array is 50 cm above the seabed. Two other 100 cm length MTAs have 16 transducers with 6 cm intervals. The frequency of transducers is 2MHz and the footprint is 4.5 cm for 50 cm elevation of instrument above the seabed. The middle MTA has better spatial resolution, because of higher operating frequency and overlapping of footprints of adjacent transducers. Figure 3-1 shows dimensions and order of transducers of the MTA. The dots on the bed profile, shown on the figure, correspond to the centers of the footprints of transducers along the measured profile.
The minimum time resolution of the instrument is one profile every two seconds. This limit results from using only one circuit to as a transceiver for all the transducers. Therefore some time is needed for switching between two successive transducers.




MTA3 MTA1 MTA2
1617 48 49 64
I I i i I I I I I I llliiiiiiiiiiiiii
, .6.0cm. 1.5cm. .- 4.0cm.
98.1cm. 50.Ocm. 98.1cm.
Figure 3-1: MTA structure and dimensions with an example of bedform profile.
The MTA has a flexible control system. Most of settings can be changed remotely during the experiment. Each MTA has its own data logger, but the data can be collected on a remote computer as well. The capacity of the internal loggers is large enough to collect 2 hours of data with a sampling frequency of 0.5 Hz.
The MTA was designed to measure bedforms of two different scales. Ripples with lengths from 12 cm up to 238.5 cm are measured by the entire array. Ripples with lengths from 3 up 46.5 cm are discerned by the central MTA only.
Unfortunately, like any other measuring systems the MTA produces errors in
measurements. Understanding the possible sources of errors might help to develop better data filtering algorithms and evaluate the precision of the instrument.
The errors in MTA measurements can be separated into three groups:
* System errors related to the usage of acoustic elements, system design,
and methods of signal preprocessing by the MTA before recording the
data.




* Environment related errors caused by influences specific to the
environment, such as the mobility of the bed, the presence of suspended
sediments, or the vibration of instruments.
0 The data interpretation errors.
The 2 and 5 MHz transducers emit sound with wavelengths of 0.75 and 0.3 mm correspondingly. These are the lower limits of resolution for a single measurement. To obtain more precise measurements, several successive data points are needed. This version of MITA reads a signal from the transducer, and a single measurement is recorded with I mnm resolution, whereupon reading device switches to next transducer. This switch sometimes could cause a jump in voltage, resulting in a spike in data record. During the filtering process, these spikes are removed, but the time resolution of data becomes less. To solve this problems, it is advised to collect more data during each session of reading from one transducer.
Laboratory tests were conducted at the University of Florida Coastal and
Oceanographic Engineering Laboratory (see Jette, 1997; Alymov, 1999). These tests indicate that even if the MTAs are used in still water without suspended sediments, the recorded data contains noise and spikes.
The left plot on Figure 3-2 shows an example of despiked data record from
Test #1 (see Alymov, 1999) for transducer #33. On the right plot the histogram is shown with normal probability density function curve with mean of 316.9 mm and standard deviation of 1 1 mm. This test was conducted in still water without suspended sediments, and the elevation of the MITA above the sloped bed was fixed. As indicated by the plot,




the system itself has a high level of noise. This noise is roughly normally distributed and could be removed by standard filtering procedures.

315

E 316
E
317
E
0
o318
- 1

320

Test# 1: start = 42.4076 end = 42.4133; At = 2.0 s; xducer #33
+ ..1 [ H- + + +-+ +++ +
+HER +--Hi+f-{ i +-Hi-M++++ 44H ....
I I It 1 1
1 v I 1
F I 4- _t-tH *f-Hj1H I H h~--4 - : d,'i J ilJ Ii 4 -. + :? I'I 'I
Normal F
+ MTA data points = 31(
- Modal filter a= 1.
- Lowpass filter

0 100 200 300 400 5000
Time, sec

0.2 PDF

Figure 3-2: Data from transducer #33, test #1. Despiked raw data points and their histogram.
Two additional lines on the left plot of Figure 3-2 present two results of data filtering. One of the filtering methods was used in previous works (see Jette, 1997; Alymov, 1999). It is based on taking the histogram mode, calculated for each group of successive data points. On the figure it is shown by a dashed line and called modal filter. The lowpass filtering is a new method, which was developed to improve previous filter. It will be described later.

L




It is difficult to distinguish the errors of measurements, when the MTA is used in a specific environment, such as oscillating flow motion, presence of suspended sediments, bedload sediment transport, or bed 'sheet' flow. The MTA was designed to be able to prevent 'false-bed' response from higher elevations. But this kind of data points usually looks like spikes, and can be successfully removed. The motion of sediments near the bed causes the biggest problem. For some sets of data they do not show position of the bed, which could be expected for particular flow conditions. For example, the measured position of the seabed rises with increasing sediment concentration.

Run# 30: start = 258.3439 end = 258.3485; At = 2.0s xducer #33
+t MTA data points
-- Modal filter Lowpass filter I
+ + 4

4000

200
Time, sec

0.2 PDF

Figure 3-3: Run #30 of Sandy Duck 97 data for transducer #33. Despiked raw data points and data after applying filters.




Figure 3-3 contains the same information as Figure 3-2, except the data were
taken from Run #30 of the Sandy Duck'97 experiment, when the bed position was nearly stable. Similar to the first case, the distribution of data points is approximately normal, but now the standard deviation is larger.
The MTA measures I D bedform profiles with spatial resolutions of 1.5 and 6 cm. Theoretically, shortest periodic features with lengths 3 and 12 cm could be measured, based on 3 data points. In real measurements these limits are not attainable: four or more points are needed to estimate ripple length more accurate. For the MTAs with 6 cm intervals presence of ripples with lengths less then 12 cm could lead to incorrect estimation of short ripples due to aliasing. Ripples with lengths of 12-18 cm could be estimated correctly by full MTA only if the same scales appear at the middle MTA (see Alymov, 1999).
Filtering of Raw Data
The raw data consist of time series of distances between the MTA and seabed for each transducer. The data from the three MTA's were collected separately, so synchronization of records in time was made first.
Let's assume, that the total error, e,,,,, is produced by several independent sources of errors:
EtOt 0 + El +1 E2 +i E 3 +'" (3-1I)
where each of E, is an error of a specific type. In general case all these errors could correlate with each other, making relations more complex due to non-linearity, but for current analysis these types of errors will be neglected. The linearity of the error sources




means that each error could be removed by applying of certain filter successively. A set of filters, used for current work, includes despiking and digital filter and is followed by restoration of removed data points.

Table 3-1: Filter description.
Order Filter description Sandy Duck'97 Routine
settings
Remove data points with values less then SmallestDstance:
SmallestDistance:
S minimal distance (SmallestDistance) between 300 mm mta_proc
MTA and the bed
Remove data points, which deviations from
mean exceed maximum value (MaxDeviation). MaxDeviation:
2 The mean distance calculated as mean of all 150 mm mtaroc
values for entire run.
Despiking. Remove each block of points, if the
first point in the block has a value, different
from previous data point by a value larger than threshold. The block duration (SpikeDuration)
is defined by number of successive data points, SpikeLevel: 6 mm
which have close values and deviations less SpikeDuration: 10 despite
then threshold (SpikeLevel). The threshold could be defined as a number of standard deviations of the data series, or as maximal possible deviation during one time period.
Block processing. Remove each N-element N: 30
4 block of data, if the standard deviation of the StDevLevel: mtaproc
block exceeds threshold (StDevLevel). 10 mm
FilterOrder: 31
5 FIR lowpass filter with Hamming window. CutOff: 2/30 mta_proc
Linear
6 Interpolate removed values. Linear mtainterp
interpolation. m




Table 3-1 describes all the filters that were applied to the raw MTA data and
particular settings for Sandy Duck'97 data. The column 'Routine' has a name of function that reproduces the algorithm. All the functions were written in Matlab, and their listings are included in Appendix A.
The first four filters remove prominent values from the data. The threshold for
instantaneous change in the bed elevation was chosen as 6 mm per sampling period (2, 3, 4, 7, 8, 9, 10, 12, 60 seconds). It was possible, because the mobility of the seabed was small. Block processing is needed for bad data. If standard deviation for the block is large, then the error is comparable with height of measured bedforms. It was found experimentally, that the threshold value of 10 mm for standard deviation is acceptable for this data set.
Figure 3-4 presents a histogram of percentage of removed data points from the data. The mode of histogram is 10%. The histogram also shows, that about 63% of all runs have 15% or less data points, removed by despiking. The runs, which have more then 40% of removed data, are usually bad.
164 MTA data files; Mode = 10%
60 .... I
50 .103 data files have less than
Ci)
2C40 15% of removed points
E 30 ....
0
0 10 20 30 40 50 60 70 80 90
Percent of removed points
Figure 3-4: Histogram of percentage of removed data point.




For digital filtering the finite impulse response (FIR) lowpass filter with
Hamming window was used. The order of filter was 31 and normalized cutoff frequency was 2/30. The main characteristics of this filter are shown on Figure 3-5.

FIR Iowpass filter; Order: 31; Cutoff: 2/30

-20
-40 0)
CU
2 -60

0 0.1 0.
0.08
U)
E 0.060
CL
ci)
0.04
U)
0-0.02
0 5

2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized frequency (Nyquist=l)
Ia I I I

10

15
Data points

20 25 30

Figure 3-5: Magnitude and impulse response functions of FIR lowpass filter of 31 order with cutoff frequency 2/30.
The FIR filter was chosen because of linear phase response and larger transition width in magnitude response. The phase shift was removed by applying the filter in both directions. That resulted in squared magnitude response. The other filters with different parameters were tested. The bottom plot on Figure 3-6 shows an example of applying of elliptic infinite impulse response (IIR) filter of order 5 with cutoff normalized frequency of 2/20. Taking into consideration the analysis of error sources and expected accuracy




from the previous section, it is hard to evaluate, which filter provides the better results. As follows from Figure 3-6 the difference between two trends is about 1 mm, which is comparable with the magnitude of system error. So both trends are close in terms of expected error. On the other hand, the large cutoff frequencies lead to appearance of higher fluctuations for one transducer, which are not correlated with the data from the neighbor transducers. That results in random fluctuation of full MTA profile. The FIR filter with parameters described above provides more reasonable results.

Run# 78: start = 270.5433 end = 270.5502; At = 3.Os xducer #63

100 200 300 400 500

E
E
I545
E
2 550
0

100 200 300 400 500
Time, sec

Figure 3-6: Raw and despiked signal (top), and filtered of despiked data (bottom). (*) FIR lowpass filter of 31 st order; (**) elliptic IIR lowpass filter of 5th order.
Figure 3-6 shows an example of the filtering process. Raw and despiked data are shown on the top plot. Raw data (thin line) has a number of large spikes. Those spikes




were successfully removed by despiking. The dots present the remaining data points. Those points are shown on the bottom plot together with trends, calculated by applying three different filters. The thick line presents a result of filtering, which will be used in estimation of dimensions, mobility and migration of bedforms in the following sections.
The method of filtration, used in previous works (Jette, 1997; Alymov, 1999), was based on the modal distance to the bed from the group of several data points, usually 10. It was noted before, that the data from the MTA is recorded with 1 mm step, although the true position of the bed could be inside the 1 mm interval. Such discreteness of data allows this method to define the bed position well, but only on weakly noisy data. Figure 3-2 shows the result of filtering by the modal filter (dash line) for a stable bed. The jumps up to 2 mm of the trend show instability of this method in presence of noise. To get better approximation more data points are required for mode calculation. For the raw data with 2 seconds sampling filtered record will have at least 20 seconds time resolution, which is not enough for study of migration and mobility of bedforms under the waves.
The 'lowpass filter' method has several advantages:
" Higher stability. The prominent points have less influence on a trend.
* Higher accuracy. The system error is about normally distributed. The filter
removes noise more accurately (see Figure 3-2 as example).
* Higher time resolution. The result of filtering has the same time step as
initial raw data.
* Smoothly changing data. The bed changes gradually, but not stepwise.
The new method approximates a stable bed position ignoring short jumps.




The accuracy of filtered data could be evaluated only in comparison with other data or from the expected behavior of the measured bedforms under flow effects. In the section below 'Short Wave Ripples' it will be shown, that migrating ripples with height of 2 mm are well distinguishable. So the accuracy of the measurements is less then 2 mm in the vertical scale.
Short Wave Ripples
Dimensions
Short wave ripples (SWR) with lengths of 34-150 mm and heights of 2-24 mm were observed during the SandyDuck'97 experiment (Hanes et al, 2001). Only 22% of runs have SWR, during other runs flat bed conditions were established. Their analysis of dimensions was based on data filtered by 'modal filter' method. Using new filtration algorithm, these results can be improved and ripple dimensions can be established in most cases.
Dimension analysis was made for data from middle MTA only. The interval between transducers is 1.5 cm, number of points is 32 and full length of profile is 46.5 cm. From each profile a best-fit parabolic trend was removed first. To increase the precision, the data for each profile was interpolated on a 0.3 cm grid. There is no direct method to evaluate bedform scales less than 1.5 cm from the MTA measurements; therefore these scales were ignored.
The ripple lengths and heights were approximated. These types of dimensions imply periodicity of bedform shape, which roughly can be reproduced by some periodic function with certain parameters, for example sine function:




h(x) = Hsin2 x + bIJ (3-2)
where h(x) is bed elevation from mean level; H is ripple height; L is ripple length; b is a phase angle.
Note that the MTA measures one-dimensional profile only. Obviously, if the real bedforms in two dimensions have periodical shape with parallel crests, then any crosssection will have periodic structure. The height of measured one-dimensional ripples will be the same as original, but the length will depend on angle between normal to the crest and direction of cross-section line. In case of three-dimensional ripples, there is no way to approximate their length. In spite of this, attempts to estimate ripple dimension were made for each recorded profile.
Approximation of Ripple Lengths
Three different techniques were used to estimate ripple lengths:
* Autocorrelation.
Distances between crests or troughs for each profile.
* Mode of distances between crests or troughs for blocks of several profiles.
The autocorrelation function is defined as
'V
Chh ( ) =lim 2XI fh(x)h(x + )dx (3-3)
-X
or for discrete series
N-k
C (k) N k hhi+k (3-4)

where is offset or lag. In discrete case offset is equal to




(3-5)

for grid interval 1.
If the profile shape is defined by Equation 3-2 then the autocorrelation function is

H 2 2fr Chh = Cos
8 L

(3-6)

and its maximas are found at = nL, n e Z. If n = 1, then offset is equal to length of ripples.
This property is used for estimation of ripple lengths, which are equal to the offset at first local maximum of autocorrelation function, calculated from Equation 3-4.

Run#30; Time 258.3589; Length=70.0mm; H =4.4mm; H =5.4mm mean max

4
E E2
C
0
P 0 Ca W-2
-4
1
.2
8 -0.5
0
0
0 o -0.5
0
-1

Distance along MTA, mm

0 20 40 60 80
Offset, mm

100 120 140

Figure 3-7: Approximation of ripples dimensions for one profile from run #30.

(k = k,5




Figure 3-7 shows an example of interpolated profile on top plot and normalized by variance autocorrelation function for this profile on bottom plot. The dashed line indicates offset position of local maximum. The profile shape is highly periodic. This property could be described by a value of normalized autocorrelation function at maximum, which is equal to correlation coefficient between initial and shifted profiles. The correlation coefficients for each profile were calculated also.
Two other methods are commonly used in of estimation of wavelengths of
periodic signals, which are based on distances between extremes. The positions of crests and troughs were found as local irninii-nums and maxim-umns. Threshold for smallest vertical deviation between two successive extremums was used. It was taken to be equal to 0.2, where a is standard deviation of profile. After the crests and troughs were found, the mean of distances between successive crests or troughs was calculated as ripple length. The usage of crests or troughs is defined by the amount of each. Also the distances between crests or troughs were collected for blocks of 30 profiles for calculation of their mode.
Figure 3-8 show time series of estimated ripple lengths by each of three described methods. The crest positions on the top plot allow evaluation of the accuracy of the methods. At the beginning, seven crests are initially seen, which give a length of about 66 mm. For eight crests at the end the length of ripples is about 58 mm. No one method provides smooth variations of estimated quantity; all of them have spikes and scatter in values. In spite of this, the approximations are very close to each other, and show the tendency in changing of ripples lengths toward the end.




The correlation coefficients, shown on bottom plot, are larger, than 95% level of significance for 30 degrees of freedom. Consequently, the ripples have highly periodic shape. It is also supported by visual analysis. On the top plot two zones of ripples instability could be distinguished at 10t" and 27t" minutes. The profiles look shifted during small periods of time. The correlation coefficient shows the time of these shifts better than other 3 methods shown in Figure 3-8.

0
E
E 100
(D 1'- 200
300
m 400
70
E E
60

Run# 30: start = 258.3589 end = 258.3844
Crests positions
. . . . . . . .

Length as 'mean' 70
60 Length as 'mode' 00
7 0. . .i 0 . .
E 70 0o000 0
000
E 0 0 0 0 0 0 0
60 00.. .... 0 0 0.0 ...
Correlation coefficient
0.5
0 I I I I

0 5 10 15 20
Time, min

25 30 35

Figure 3-8: Approximation of ripples lengths by three methods for run #30.




After the lengths were evaluated, the modal values for each data file were
calculated. The mode was calculated on a grid with 3 mm intervals. Figure 3-9 presents the results of comparison of three methods. Good correlation is found. Note, as follows from the plots, the 'mode' method slightly underestimates the ripple lengths, compared with 'mean' and 'autocorrelation' methods. The estimation of ripple lengths by mean of distances between crests or troughs was taken to be basic for further analysis.

140
E
E 120
-cJ
C 100
5 80
0
< 60
40

40 60 80 100 120 140
Mean length, mm

40 60 80 100 120 140
Modal length, rmm

Y =1.03x R = l0.69
40 60 80 100 120
Mean length, mm

Number of data points = 1017 Number of lengths > 160 mm = 13 R correlation coefficient Solid line: Y = bX Dash line: Y = X

Figure 3-9: Comparison of methods of ripples lengths approximation.

140
E 120
E
0 100
- 80 "0
0
2E60
40

Z,
. ":::,.x' ..
y = 0.89x ., ........" .R. .
.=+0.64.

140
E
E 120
C100
o 80
0
0
< 60
40




Approximation of Ripple Heights
The approximation of ripples heights was made for each measured profile and for
groups of successive profiles. Analogous to estimation of ripple lengths, described in the
previous section, the positions of crests and troughs along the profile were found. For
each crest-trough pair the difference in elevations was calculated and stored for
evaluation of the next parameters:
* Mean of ripple heights for each profile.
* Maximum of ripple heights for each profile.
* Modes of ripple heights for groups of several profiles.
* Significant heights for groups of several profiles.
Run# 30: start = 258.3589 end = 258.3844 Mean heic hts 6
E
E 4
2
Mode of heights
6 . . . . . . . . . . . .! . . .
E 00o I o 0 0 0
E 4 0 . 0 .. ...... 0. 0 :.o ao 0 0..o .. 0 :
0 0 0 a 00 00
2-0 00 0 0
Maximum heights
6
E 6 .... . . . . .+ . . . . . .
2 I I I I
Significant heights
86 0 0 O .:. . .! . .i. .... :....... :. .. "
E 4 0 .. .. 0x 0 -o .0 ..... O0 O 0 o -0o. - - .. . o
E. .. 0.O: o o :: o : :
0
2 . . . . .. . . . ... ; . . . . i . . . .
0 5 10 15 20 25 30 35
Time, min

Figure 3-10: Approximation of ripples heights for run #30.




The significant height is defined here as a mean of 1/3 of largest excursions for each group of 30 profiles. The maximum and significant heights describe characteristics of the most prominent ripples.
Figure 3-10 shows an example of ripple height approximations for the same data as on Figure 3-8. In spite of stable pattern of ripples, their heights can change rapidly in time. For the data shown, measured ripple height fluctuations have about 2 mm magnitudes. Not only true bed motion could cause them, but also suspended sediments. It was noted before, that on 1 0k" and 27" minutes the ripples were shifted along the MITA as a result of some event. The decrease of ripple heights was observed during those events.
On Figure 3-1 1 comparison of results of height approximation from four methods is shown. Each data point presents the modal value of ripple heights, estimated by one of described methods, for each data file. The mode was found with 0.5 mm precision. The significant height is about 1 .66 times larger than approximated by mean value. The high correlation coefficient and small scatter of data show good agreement of methods. The height, calculated as a mode of excursions, is not in very good agreement with mean heights. The mean and modal heights should have close values, but modal height is about
0.83 times the mean. The correlation coefficient is still high, but the data shows larger scatter, than in other cases. The maximal and significant heights are in good agreement too. The maximal height is usually 18% larger than significant ripple height.
The estimated ripple heights of 61 out of 1036 files from the SandyDuck'97 data were larger than 25 mmi-. Most of these data were from bad profile measurements, so they were excluded from comparison. The approximation of ripple heights based on mean of excursions provide reasonably good results and will be used as a basic estimation.




20
E 20 ..
E E
E
E15 -.
*u l .d 15 . .-.. ..." .
165
~K~. y=.8 x 5 : :., R+,.91
._ .:-.:.. R: =+0.73 R = +
5 10 15 5 10 15
Mean height, mm Mean height, mm
20 Number of data points = 1036
E / : Number of heights> 25 mm= 61
E
15 :",/ I- ...
- "R correlation coefficient
- 'Solid line: Y = bX
....:: Dash line: Y X
C
: .. y.= 0.85x
R =+0.9.1
5 10 15 20
Max height, mm
Figure 3-11: Comparison of methods of ripples heights approximation.
The accuracy of ripple length and height estimations is highly dependent on scales
of real bedforms, which were measured by the MTA. For small ripples, the error of
approximation is high and could be compared with accuracy of measurements. Therefore
presence of ripples with heights of 1.5-2 mm could be shown only from other
information, like ripple migration. Otherwise, flat bed conditions should be concluded.




52
The results of analysis of short ripple forms (Table B-I) and estimated ripple scales (Table B-2) are included in Appendix B. The ripple forms during each run were analyzed visually base on changing in time of bedform profiles, measured by MTA. The bedforms were stated to be two dimensional only if the profiles have sinusoidal form. Otherwise the bedforms were referred to three-dimensional. In cases of flat bed two characteristics were used. If there were no short ripples the 'flat' bed conditions were stated, but if some spikes were present the bedforms were referred to 'noise'. Those spikes were usually resulted from instantaneous sediment suspension.




CHAPTER 4
RELATIONSHIPS BETWEEN TURBULENCE, SUSPENDED SEDIMENT CONCENTRATIONS AND BEDFORMS Analysis of Relations
The purpose of this chapter is to develop relationships between turbulent kinetic energy other parameters. The relationships between turbulent kinetic energy (TKE), bedform scales and suspended sediment concentrations have been analyzed. All relations were found in form of linear regression and analyzed for different elevations of velocity sensor.
The importance of study and development of empirical relationships is
determined by complexity of theoretical description of such relations. The number of relationships can be estimated from mneasuremnents in laboratory flumres and tanks, but only field experiments can provide the most reliable environment of flow motion, wave activity, sediment transport. Availability of a large amount of field data gives an opportunity to establish empirical relations for different conditions.
TKE and Sediment Concentrations
The turbulent kinetic energy was compared to suspended sediment concentration data. The suspended sediment concentration profiles were measured by ABS simultaneously with velocity (see Chapter 1). Several statistics were calculated for each profile and for entire data files. One of the best correlations was found between TKE and mean of first spatial moment of concentration, calculated as follows:




h IJ.\
- f zc(t, z)dz (4-1)
0
The TKE was calculated by VV method (see Chapter 2). The relationship is given by Equation 4-2 and demonstrated on Figure 4-1 for both ADVs. The coefficients were calculated from 1347 data records of 2 Hz data, with each record covering 34 or 68 minutes of observations. The correlation coefficient is calculated to be 0.85.
log,,j,=a(TKE)'/2+b, a=23.4, b=-3.9 (4-2)
The first moment of concentration profile relates to potential energy of suspended sediments. Thus, Equation 4-2 provides the relationship between kinetic energy of turbulent motion and potential energy of sediments. The relation is not linear, and cannot be explained by a simple transfer of energy from one type to another. That demonstrates a complexity of real mechanisms of sediment suspension, which cannot be described from simple energy balance.
ADV1 ADV2
0.1 0.1
E E.
O l:, i O. l .. . .
...... 0...
0.001 0.01
y = 24.4x-3.9 y = 23.4x-3.9
R = +0.86 R +0.85
0 0.05 0.1 0.15 0 0.05 0.1 0.15
TKE 12, m/s TKE 12, m/s
Figure 4-1: Relationship between TKE and first spatial moment of concentration (U).




It should be noted that the TKE were estimated directly from measurements. The elevations of the velocity sensors may have changed during the experiment due to seabed erosion or accretion, but no corrections were made to recalculate TKE relative to one elevation. The regression was therefore repeated for subsets of the data during which the ADV was in certain range. The variation of coefficients in Equation 4-2 is shown in Table 4-1 for these fits.
Table 4-1: Coefficients of relationship between TKE and first moment of concentration for different ADV2 elevations.
Elevation of Correlation Number of data ADV2, cm coefficient point
<15.5 +0.86 298 26.85 -4.02
15.5... 17.0 +0.77 282 24.07 -3.93
17.0... 18.0 +0.69 177 20.20 -3.78
18.0...20.0 +0.88 245 19.70 -3.61
20.0...23.0 +0.89 270 20.87 -3.70
>23.0 +0.62 75 33.93 -4.55
all +0.85 1347 23.4 -3.9
Table 4-1 shows that the correlation coefficients are high at all elevations and the coefficients a and b of Equation 4-2 do not vary much with elevations of ADV2.
TKE and Bedforms
Scales of short wave ripples were compared with turbulent kinetic energy. The length and height of ripples were estimated as described in Chapter 3. TKE was calculated for each record from ADV2 by VV method. The relationships between turbulent kinetic energy and bedform scales have been found in the following form:

TKE= 10 (H,.)" or log,0 (TKE) =alog,0 (Hs,,,)+b

(4-3)




TKE=10"(Lss1)" or logfo(TKE)=aloglo(Ls;<)+b

TKE = 10r N
LS)?

or log0lo(TKE)=alogo0 Hsn N+b s )

where HsR is ripple height; LSR is ripple length; a and b are some coefficients.

-3.5 L
-3

hADV2<1 5.5 cm
y = -0.7x-4.7 R = -0.74 N = 298
. .. . .
* :l, ".:"

-2.5 -2
hADV2=17.0..18.0 cm

y = -0.3x-3.6 R = -0.29
-2.5 .:N =177
-3
-3.5
-4
-3 -2.5 -2 -1
hADV2=20.0..23.0 cm
-1 y = -1.1x-5.6
R = -0.69 N =270
-2
-3

-3 -2.5 -2
loglo(HsR)

-1.5

hADV2=1 5.5..17.0 cm
. y = -0.6x-4.5
* ; R =-0.50
.. N =282
. -2.5
hADV2=1 8.0..20.0 cm
y -0.4x-3.6
R = -0.27
N = 245
I : *
I. *

-2.5 -2
hADV2>23.0 cm

-2
-2.2
-2.4
-2.6
-3

-2.5 -2
logl0(HSR)

-1.5

-1.5

Figure 4-2: Relationship between short ripple height (HsR) and TKE for different elevations of ADV2 (hADV2): R correlation coefficient, N- number of data points.

(4-4) (4-5)

y = 0.1 x-2.0
R = +0.29
N =75




Table 4-2: Coefficients of relationship between TKE and short ripple height for different ADV2 elevations.
Elevation of Correlation Number of lb
a b 10b
ADV2, cm coefficient data point
<15.5 -0.74 298 -0.71 -4.71 1.97*10-5
15.5...17.0 -0.50 282 -0.63 -4.47 3.36*10-5
17.0...18.0 -0.29 177 -0.30 -3.60 2.51*10-4
18.0...20.0 -0.27 245 -0.36 -3.57 2.70*10-4
20.0...23.0 -0.69 270 -1.08 -5.56 2.78*106
>23.0 +0.29 75 0.10 -2.00 9.94*10-

-2 hADV2<1 5.5 cm
-2
y = -1.8x-5.1 : R = -0.72
-2.5 :. N-=298
-3. :. ,. "
-3.5
-4
-1.4 -1.2 -1 -0.
hADV2=17.0..18.0 cm
-2 AV
y = -1.8x-5.1 R = -0.55
-2.5 N177
-3
-3.5
_A

-1.4 -1.2 -1
hADV2=20.0..23.0 cm

-1.4 -1.2

-0.8

-1 -0.8

-2.2
-2.4
-2.6

loglo(LSR)

hADV2=1 5.5..17.0 cm
y = -1.8x-5.0
| R=-0.56
N 282
. .. . . . . . .
-1.4 -1.2 -1 -0.
hADV2=1 8.0..20.0 cm
y = -1.8x-4.9
R = -0.49 SN= 245
* : .

-1.4 -1.2 -1 -0.8
hADV2>23.0 cm
y = -0.0x-2.3
R = -0.02
N = 75
. . .. i.. . .. . ..
; : .=
-1.4 -1.2 -1 -0.8
loglO(LSR

Figure 4-3: Relationship between short ripple length (LsR) and TKE for different elevations of sensor (hADV2): R correlation coefficient, N- number of data points.

y = -3.1x-6.6
R = -0.74
N = 270




Table 4-3: Coefficients of relationship between TKE and short ripple length for different ADV2 elevations.
Elevation of Correlation Number of
ADV2, cm coefficient data point a b
<15.5 -0.72 298 -1.82 -5.13 7.48* 10-6
15.5...17.0 -0.56 282 -1.75 -5.01 9.77* 10-6
17.0...18.0 -0.55 177 -1.82 -5.11 7.80*10-"
18.0...20.0 -0.49 245 -1.76 -4.87 1.35* 10-5
20.0...23.0 -0.74 270 -3.07 -6.61 2.43* 10-'
>23.0 -0.02 75 -0.02 -2.25 5.56* 10"3
Figures 4-2 and 4-3 show the relationship between turbulent kinetic energy and
height and length of short wave ripples correspondingly. The coefficients of best-fitted
lines are included into Tables 4-2 and 4-3. Table 4-4 shows the coefficients and
correlations coefficients for the relation between TKE and steepness of short wave
ripples. The relationship is given by Equation 4-5 and has the same form as for ripple
length and height.

Table 4-4: Coefficients of relationship between different ADV2 elevations.

TKE and steepness of short ripples for

Elevation of Correlation Number of a l jo
ADV2, cm coefficient data point
<15.5 -0.65 298 -0.90 -4.10 7.94* 1015.5... 17.0 -0.35 282 -0.56 -3.60 2.50* 10-4
17.0...18.0 -0.13 177 -0.17 -3.05 8.81*10-4
18.0...20.0 -0.11 245 -0.19 -2.89 1.29* 10-3
20.0...23.0 -0.53 270 -1.10 -4.24 5.79* 10-'
>23.0 +0.20 75 0.08 -2.15 7.14*10-3
As it follows from figures and tables above, the TKE mainly decreases with an
increase of bedform scales. Only for elevations of ADV2 more then 23 cm the TKE
increases with increase of ripple height, but the TKE no longer depended on ripple length
(correlation coefficient is 0.02). The coefficients in relations 4-3 and 4-4 do not show




consistent dependence with ADV2 elevation. The highest correlation is found, when the velocity sensor was closest to the bottom (<15.5 cm). Unfortunately, the ADV2 elevation was less than 10 cm only for a few runs, for which bedform data are available.
Time Variations of TKE, Sediment Concentration, and Bedform Mobility

E E
C)
(n
0o

Crests positions
.- . .
.. .. .. .- _

x 10-3

TKE = (U,)2+(V)2 +(W')2

E 0.5
0
Vertically averaged concentration
0.02 ....... .
c0.01
0
Wave envelope
0.6
E02 1~ JI 1. x AA

20
Time, min

Figure 4-4: Ripple crest positions, TKE, mean concentration and wave envelope for run #30: start at 256.3589 in Julian days.




As example time series of ripple crest positions, turbulent kinetic energy,
vertically averaged concentration, and wave envelope are shown on Figure 4-4. The data were recorded during run #30. The same bedform data were shown on Figures 3.8 and
3.10 with ripple length and ripple height parameters. Notice that at the 10th and 27t" minute of the record the ripple profiles were shifted.
The wave envelope on the bottom plot shows, that at that times when the rippes shifted there were big groups of waves passing through. The wave group most likely caused the ejection of sediments into suspension and also caused an increase of turbulent intensity. This example demonstrates that not every large wave can significantly change the shape of bedforms. Even ripples disappear during passing of one wave group they almost immediately recover their shape.




CHAPTER 5
CONCLUSIONS
In this thesis the SandyDuck'97 experiment data set is analyzed with respect to the measurements of turbulence and the measurement of short wave ripples. Three techniques for estimating of turbulence were utilized. All three methods are based on frequency separation of velocity fluctuations, but each uses different assumptions to estimate the turbulence intensity. The cut-off method defines a single frequency that separates turbulence from waves. The 'cut-off frequency is found as a point of steepest descent of the coherence function between pressure and velocity, or alternatively, where the velocity spectrum changes its slope. This frequency was found for a large number of observations to be 0.5 Hz with standard deviation of 0. 1 Hz. Two other methods are based on the coherence between velocity and pressure (PV method) and two velocity signals from two sensors separated in space (VV methodd. All three methods were applied to data and results were compared.
The three methods of separation of turbulence from wave motion provide
qualitatively similar results. Estimations of TKE by the methods described are highly correlated. The cut-off method estimates the minimum total TKE, which is approximately
5 times smaller than from VV method. The PV method overestimates turbulence due to long-shore fluctuations and also overestimates the full TKE. The estimated TKE is 6 times larger than the VV method and 30 times larger than the cut-off method. The VV method provides the best estimation of turbulence in the wave frequency band. The




power spectrum of the turbulence has the same slope over both wave and turbulent frequencies.
The influence of frame vibrations on the measurement of turbulence was
investigated. The error of measurement of high frequency velocity fluctuations due to frame vibration was estimated from measurements of frame tilt and was found to be small (about 1%).
A new filtering technique based on the FIR filter was developed and applied to
the SandyDuck'97 dataset in order to improve the estimation of small wave ripples. Some advantages of this technique are as follows:
" Higher accuracy. Because the system errors are normally distributed, the
applied FIR filter removes noise more accurately.
" Smoothly changing data. The seabed most likely changes gradually rather
than stepwise. The new method approximates a stable bed position
ignoring short jumps.
" Study of short time effects becomes possible, such as the formation and
destruction of ripples during the passage of several large waves.
Flat bed conditions were found only during 71 out of 164 runs, and during 54 runs the SWR were found and their dimension were estimated.
Several methods were used for estimation of ripple scales. Good agreement
between the methods was found. The precision of ripple height measurements was found to be less than 2 mm, but for smaller ripples additional information, such as ripple migration, could be used, to prove their existence.




The estimated turbulent kinetic energy was compared to other measured
parameters to find empirical relationships. Good correlation was found between TKE and first spatial moment of suspended sediment concentration profiles. The first moment of concentration profile relates to potential energy of suspended sediments. Thus, the high correlation provides the relationship between kinetic energy of turbulent motion and potential energy of sediments.
The correlations between TKE and ripple scales were analyzed for different
elevations of velocity sensor. A high negative correlation was found between TKE and ripple heights and lengths when the velocity sensor was closer than 15.5 cm to the seabed. At higher elevations the tendency remains, but correlation coefficients become smaller.




APPENDIX A
MATLAB PROGRAMS FOR FILTERING OF MTA DATA
Function MTA PROC.
function [mtal23] = mta proc(FileName,DirIn, DirOut); % Procedure MTA PROC(FileName,DirIn, DirOut); % This routine for processing MTA data. It generates new data files, % which include the next variables:

Light Function save

despike mkmtal23 mkmtal23 duckhist *
mkprofx *

Comment
Raw MTAl data Raw MTA2 data Raw MTA3 data combined raw MTA data despiked MTA data as intermediate result full profiles filtered data time of measurements as Julian date full profiles histogram method time of averaged profiles time step of histogram profiles X-axis for MTA X-asis for middle part of MTA in mm time step for raw data and mtal23 profiles list of parameters

% PARAM is a structure includes name of parameter and its used value.
% ExperimentYear Year of experiment
% SmallestDistance In mm smallest distance from MTA to bottom % MaxDeviation In mm maximum deviation from mean bottom level
% SpikeLevel In mm maximum jump between two consecutive profiles
% SpikeDuration Maximum spike width in numbers of profiles
% PointsInBlock Process blocks with N points
% StDevLevel Level of standard deviation for good data
% DoFiltering Run filter (1 or 0)
% numavg Number of profiles to be averaged
% FilterOrder Set order of filter (set ODD number)
% DoHistogram Run histogram method (1 or 0)
% ProfilesInHistogram Use p profiles to get a historgam % SaveLight Save light file (set 1) or full file (0)
% Oleg Mouraenko 7/29/2000
% See also : MKMTA123, DUCKHIST, DESPIKE, MTA INTERP
%%%%%%%%%%%%%%%%%%% Parameters %%%%%%%%%%%%%%%%%%%%%%%
% Data
ExperimentYear = 1997; % set year of experiment
% Extreme values

%
% Variable
% mtarl % mtar2 % mtar3 % mtarl23 % mtal23d % mtal23 % mtatime % profmod % proftime % avg % profx % XMiddle % deltat % PARAM % - - -




SmallestDistance = 300; % (300) in mm smallest distance from MTA to bottom MaxDeviation = 30; % (150) in mm maximum deviation from mean bottom level
SpikeLevel = 6; % (6) in mm maximum jump between two consecutive profiles
(dispike function)
SpikeDuration = 10; % (10) maximum spike width in numbers of profiles (despike function)
% Block process (removing of full blocks if sddev is large) DoBlockProcess = 0; % (1) 1 or 0
N = 30; % (30) process blocks with N points
StDevLevel = 10; % (10) level of standard deviation for good data

% Filtering DoFiltering numavg = 30; FilterOrder

1; %
%
31; %

(1) 1 or 0
(30) number of profiles to be averaged filter cutoff
(31) set order of filter (set ODD number)

% Historgam method DoHistogram = 0; p = 10;
% Save variables SaveLight = 1;

% (0) 1 or 0
% (10) use p profiles to get a historgam
% (1) Save light file (set 1) or full file (0)

%%%%%%%%%%%%%%%%% S T A R T EN G I NE %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% save paremeters
PARAM = struct(..
'ExperimentYear',ExperimentYear ....
'SmallestDistance',SmallestDistance ....
'MaxDeviation',MaxDeviation ...
'SpikeLevel',SpikeLevel ....
'SpikeDuration',SpikeDuration ...
'DoBlockProcess',DoBlockProcess,..
'PointsInBlock',N,...
'StDevLevel',StDevLevel ....
'DoFiltering',DoFiltering ...
'numavg',numavg,...
'FilterOrder',FilterOrder ...
'DoHistogram',DoHistogram, ..
'ProfilesInHistogram',p, ..
'SaveLight',SaveLight);
% Start Engine
load(fullfile(DirIn,FileName), 'mtarl, 'mtar2','mtar3');
% deltat time step for MTA deltat=mtarl(2,2)-mtarl(2,1);
% profx variable X axis for MTA profx=mkprofx;
% XMiddle X axis for MTA1 in mm XMiddle = (0:31)*15;
% call mtal23 to form mtal23 and mtatime variables [mtarl23, mtatime]=mkmtal23(mtarl,mtar2,mtar3,'r'); % 'r' means form from mtar's variables
% remove extreme values mtal23e = mtarl23; mtal23e(find(mtarl23 < SmallestDistance))=NaN;
% remove extreme values mode +/- MaxDeviation mm n = 4;
for i=1:16
tmp = mtal23e((i-l)*n+l:i*n,:);




66
tmp(:) = modetrend(tmp(:)',100,MaxDeviation);
mtal23e((i-l)*n+l:i*n,:) = tmp; end;
% remove extreme values mean +/- 5*MaxDeviation mm meanmta = nanmean(mtarl23(:)); mtal23e(find(abs(mtal23e-meanmta) > 5*MaxDeviation))=NaN;
% call despike function mtal23d=despike(mtal23e(:,l:end-1),SpikeLevel,SpikeDuration,O0); % in places of spikes NaN values
SCorrect date of experiment in mtatime jdst = datenum(ExperimentYear,hex2dec(FileName(2)),l)-datenum(ExperimentYear,l,l);
% Check blocks with length N for bed of good data %N=30; %process blocks with N points; if DoBlockProcess
ly=fix(size(mtal23d,2)/N); % number blocks
for j=1:64;
for i=l:ly;
stdN = nanstd(mtal23d(j,N*(i-l)+l:N*i));
% if stdev of block big -- bad data. Remove them.
if isnan(stdN) I (stdN > StDevLevel)
mtal23d(j,N*(i-l)+l:N*i)=NaN;
end;
end;
end;
% correct length of mtal23, mtal23d, mtarl23 and mtatime
mtarl23 = mtarl23(:,l:N*ly); mtal23d = mtal23d(:,l:N*ly);
mtal23 = mtal23d;
% mtatime times of recording
mtatime = mtatime(:,l:N*ly)+jdst; % correct start in Julian date else
mtal23 = mtal23d;
mtatime = mtatime + jdst; % correct start in Julian date end;
% filtering of each transduser if DoFiltering
% Elliptic IIR lowband filter 9 order (should be odd) with cutoff fr=2*deltat/T
% For T=N*deltat: fr = 2/N, N-number of points per smalest harmonic; Rp=0.02, Rs=60;
% Sintax [b,a] = ellip(Order, Rp, Rs, Fr);
% [b,a] = ellip(Filterorder,0.005,40,2/numavg);
% FIR lowband filter with Hamming window
% Set variable numavg to change cut off frequency of filter
[b,a]=firl(FilterOrder,2/numavg)
for i=l:size(mtal23,1)
ind=find(-isnan(mtal23(i,:)))
if length(ind) > 3*numavg
mtal23(i,ind) = filtfilt(b,a,mtal23(i,ind));
end;
end;
% remove NaN values
try
mtal23 = mta interp(mtal23,'linear');
catch
disp('Error in removing NaN values! mtal23 was saved with NaN');
end;
end;
% call histogram method for profmod if DoHistogram
% p=10; % number of averaging profmod = duckhist(mtal23d,p);




67
% interpolation along profile remove NaN values
profmod = mta_interp(profmod')';
6 proftime time of each histogram profile
proftime = mtatime(l:p:end);
avg = deltat*p; else
profmod=[];
avg=[];
proftime=[]; end;
% save variables if exist(fullfile(DirOut,[FileName '.mat']))
append = '-append'; else
append =
end;
if SaveLight
%light save
if DoHistogram
save(fullfile(DirOut,FileName),'mtal23','mtatime','mtal23d','profx',...
'XMiddle', 'deltat','profmod', 'proftime','avg','PARAM',append);
else
save(fullfile(DirOut,FileName),'PARAM','mtal23','mtatime','mtal23d','profx' ....
'XMiddle','deltat',append);
end;
else
%full save
save(fullfile(DirOut,FileName),'mtarl','mtar2','mtar3','mtarl23','mtal23','mtal23d',...
'mtatime','profx','XMiddle','deltat','profmod','proftime','avg','PARAM',append) end;
return;
Function DESPIKE.
function xnsnan = despike(x,thold,maxwidth,stdflag)
% Function DESPIKE % Removes extraneous points from data time series. % Run
% y = despike(x); % y = despike(x,m); % y = despike(x,m,n); % y = despike(x,m,n,stdflag); % where
% y despiked data with NaNs % x initial data array. Process each row. % m theshold % n maximum spike width % stdflag using standart deviation
% y = despike(x) using 2.5 standard deviations as the first
% derivative threshold and a maximum spike width of 3 points.
%
% y = despike(x,m) uses m standard deviations for the first % derivative threshold
% y = despike(x,m,n) sets a maximum spike width of n points
% y = despike(x,m,n,stdflag) if stdflag = 1, then m standard
% deviations for the first derivative threshold, otherwise
S first derivative threshold is m.

Oleg Mouraenko, 7/28/2000




if (exist('thold') = 1)
thold=2.5; end
if (exist('maxwidth') -= 1)
maxwidth=3; end
if (exist('stdflag') -= 1)
stdflag = 1; end
if size(x,l)>l1
for i = 1:size(x,1)
xl = despike(x(i,:),thold,maxwidth,stdflag);
xnsnan(i,:)=xl;
end;
return;
end;
%%%%%%%%%% Begin lxnan=length(x); indnan = find(-isnan(x));
x=x(indnan); lx=length(x);
% Add first and last points to avoid spikes at the edges; if lx > 30
mn b = mean(x(l:30));
mn e = mean(x(end-29:end)); else
mn b = mean(x);
mnne = mnnb; end;
x=[mnb x mn e];
dx=x(2:end)-x(1:end-1);
if stdflag == 1
dx=dx/std(dx); end;
% Presize matrix xns=zeros(l,lx);
i=1;
while(i <= lx)
% Spike should have first derivative > threshold.
spkwidth=0;
dxsum=dx(i);
while (spkwidth <= maxwidth) & (i+spkwidthc<= lx-1) & (abs(dxsum) > thold)
spkwidth = spkwidth+l;
dxsum=dxsum+dx(i+spkwidth);
end;
if spkwidth == 0
xns(i) = x(i+1);
i=i+l;
else
for j=l:spkwidth; xns(i+j-l)=NaN; end;
xns(i+spkwidth) = x(i+spkwidth+l);
i=i+spkwidth+l;
end;
end

xnsnan=repmat(NaN, 1, lxnan); xnsnan(indnan)=xns;




69
Function MTA INTERP.
function newmta = mta_interp(mta,type);
% Function YY = mta interp(Y,type);
% Interpolation of NaN points. Data in rows. % Here 'type' mean type of interpolation
% or 'linear' linear interpolation
% 'nearest' nearest neighbor interpolation
% 'spline' cubic spline interpolation
% 'cubic' cubic interpolation
%
% Oleg Mouraenko, 7/30/2000
% See also: INTERPI
if -exist('type','var')
type = 'linear'; end;
newmta=repmat(nan,size(mta));
N = size(mta,2); XX = 1:N;
for j=l:size(mta,l)
Y2 = mta(j,:);
X = find(-isnan(Y2));
if length(X)>0.1*N
newmta(j,:) = interpl(X,Y2(X),XX,type);
end;
end;
return;
Function MKPROFX.
function profx = mkprofx;
% Function MKPROFX % Makes x-axis for MTA data. Use with mtal23 variable. % Run
% profx = mkprofx;
%
% Oleg Mouraenko, 07/24/2001
%
% See also: MKMTA123
profx=[linspace(0,90,16),linspace(96,96+46.5,32),linspace(148.5,238.5,16)];
return;




APPENDIX B
SHORT RIPPLES DURING THE SANDYDUCK'97 EXPERIMENT

Table B-i: Analysis of short ri pp form and migration.
Run# Julian Duration, At, QualityBedrms Migratione
start time min sec Flat Noise 2D 3D offshore)
12 253.7835 112 2 Good yes
14 254.4002 112 2 Good yes
16 254.6687 112 2 Good yes
18 255.3972 112 2 Good yes 20 255.6772 112 2 Good yes
22 256.4095 112 2 Good yes
24 256.6775 112 2 Good yes on
26 257.4111 112 2 Good yes
28 257.7149 112 2 Good yes
30 258.3358 112 2 Good yes on
31 258.4953 112 2 Good yes
34 259.3502 29 2 Good yes
35 259.6095 59 2 Good yes on
37 260.4434 59 2 Good yes
38 260.5282 59 2 Good yes
39 261.3528 59 2 Good yes
42 262.8117 112 2 Good yes
44 263.2964 112 2 Bad
46 263.4895 112 2 Bad
48 263.7181 169 3 Good yes
50 264.4523 169 3 Good yes
51 264.6049 169 3 Good yes on
54 265.4375 169 3 Good yes on
55 265.6221 169 3 Good yes on
56 265.7677 169 3 Good yes
58 266.3794 169 3 Good yes
60 266.6689 169 3 Good yes
62 267.3365 169 3 Good yes
63 267.5163 169 3 Good yes on->off
64 267.6738 169 3 Good yes off->on




Table B-i: continued.
Julian Duration, At, QuBedforrns Migration
Ru#start timre illi sec QaiyFlat Noise 2D 3D (osre
offshore)
65 267.8278 169 3 Good yes on
67 268.3167 169 3 Good yes on
68 268.4856 169 3 Good yes on
69 268.6429 169 3 Good __yes
70 268.8002 169 3 Good __yes_72 269.3345 169 3 Good yes __ __yes
73 269.5007 169 3 Good yes
74 269.6674 169 3 Good yes
75 269.8354 169 3 Good yes___77 270.3317 169 3 Good yes yes
78 270.5016 169 3 Good yes
79 270.6777 169 3 Good yes
80 270.8490 169 3 Good yes
82 271.3384 169 3 Good yes on
83 271.5007 169 3 Good yes on
84 271.6634 169 3 Good yes
85 271.8341 169 3 Good yes off
87 272.3370 169 3 Good yes
88 272.5038 118 3 Good yes
89 272.6833 112 2 Good __yes
91 273.3333 169 3 Good yes
92 273.5010 169 3 Good yes on
93 273.6599 226 4 Good yes on
95 274.3376 112 2 Bad_96 274.4586 112 2 Bad
97 274.6224 112 2 Good yes on
98 274.7461 226 4 Good yes on
100 275.3565 112 2 Good yes
101 275.4588 169 3 Good yes
104 276.5072 226 4 Good __yes on
108 278.4590 169 3 Good yes on
109 278.6337 112 2 Good yes
110 278.7509 226 4 Good yes ___112 279.3284 112 2 Good yes on
113 279.4592 169 3 Good __yes on
114 279.6257 112 2 Good yes_ on
115 279.7509 226 4 Good yes yes Oil
116 280.3389 112 2 Good yes on
117 280.4590 169 3 Good __yes off
118 280.6238 59 2 Good yes yes off
119 280.7111 226 4 Good yes yes off




Table B-i: continued.
R t ulan Duaton ABedforms Migration
un start time III 1 sec QaiyFlat Noise 2D 3D (osre
offshore)
124 281.5838 112 2 Bad
125 281.7509 169 3 Bad
127 282.3500 118 3 Bad
128 282.4592 169 3 Good yes____129 282.6323 112 2 Good yes yes ___130 282.7587 226 4 Good yes yes____132 283.3340 226 4 Bad
133 283.5418 226 4 Bad ___134 283.7507 226 4 Bad
136 284.3343 226 4 Bad____137 284.5471 226 4 Bad ______138 284.7524 226 4 Bad____140 285.3340 226 4 Bad __ ___141 287.3339 112 2 Good __ yes ___142 287.4595 169 3 Good yes____143 287.6429 112 2 Good yes ___144 287.7620 226 4 Good yes____145 287.9800 452 8 Good yes____146 288.4627 339 6 Good ye yes____147 288.7451 169 3 Good yes yes____149 289.3464 112 2 Good yes yes____150 289.4591 169 3 Good yes____151 289.6012 169 3 Good yes ___152 289.7382 169 3 Good yes yes____154 290.3630 112 2 Good yes
155 290.4712 169 3 Bad
156 290.6225 112 2 Bad
157 290.7390 169 3 Bad____158 290.8916 565 10 Bad
159 291.4592 339 6 Bad
160 291.7450 169 3 Bad
161 291.8950 565 10 Bad
162 292.3429 112 2 Good yes
164 292.5332 169 3 Good yes
165 292.7068 169 3 Bad yes _166 1292.9282 508 9 Good yes
167 293.3639 169 3 Good yes_168 293.5054 169 3 Good yes yes
169 293.6587 339 6 Good yes____170 293.9328 565 10 Good yes____171 294.4707 169 3 Good yes_____




Table B-I: continued.
Juia Draio, tBedforms Migration
Ru#start time IImm1 sec Qality Flat Noise 2D 3D (onshore______offshore)
172 294.6368 169 3 Good yes
173 294.7961 169 3 Good yes___________174 294.9529 508 9 Good yes
175 295.3652 169 3 Good yes_______176 295.5148 169 3 Good yes yes 1
177 295.6695 169 3 Good yes yes
178 295.8195 169 3 Good yes on
179 295.9765 508 9 Good yes on
180 296.3811 169 3 Good yes on
181 296.5261 169 3 Good ys on
182 296.6811 169 3 Good yes
183 296.8290 169 3 Good yes
184 296.9862 508 9 Good yes
185 297.4036 169 3 Good_ yes ye s
186 297.5827 169 3 Good yes yes on
187 297.7527 169 3 Good yes
188 297.9052 565 10 Good yes____189 298.3175 169 3 Good yes ___190 298.4765 339 6 Good yes
191 298.7506 169 3 Good yes
192 298.9049 565 10 Good yes
193 299.3509 169 3 Good yes yes on
194 299.5071 339 6 Good yes yes on
195 299.7911 169 3 Good yes on->off
196 299.9398 565 10 Bad
197 300.3846 169 3 Bad
198 300.5310 169 3 Good yes
199 300.6785 169 3 Good yes off->on
200 300.8253 678 12 Good yes on
202 301.5113 339 6 Good yes on
203 301.7853 678 12 Good yes on
204 302.3591 169 3 Good yes on
205 302.5446 169 3 Good yes on
206 302.7076 169 3 Good yes on
207 302.8920 678 12 Good yes on
210 303.7850 678 12 Good ye s
211 304.4315 169 3 Good yes yes
212 304.6040 339 6 Good es_213 304.8756 678 12 Good yes
214 305.4127 508 9 Good yes
215 305.8653 678 12 Good Iyes _________




Table B-1: continued.
Bedforms Migration
Run# Julian Duration, At, Quality(osre
start time rin sec Flat Noise 2D 3D (onshoreoffshore)
216 306.4027 169 3 Good yes on
217 306.5388 339 6 Good yes on
218 306.8468 678 12 Good yes yes on
219 307.5247 452 8 Good yes on
220 307.8913 678 12 Good yes 221 308.4083 1424 30 Good yes on
222 309.4260 2849 60 Good yes 223 311.9171 678 12 Good yes
224 312.4537 508 9 Bad
225 312.8467 678 12 Good yes 226 313.3570 169 3 Good yes on

Table B-2: Short ripple dimensions.
Number Length, Length Length Corr. Height Height Height Height Run# o Lengt (hist.), (corr.), (hist.), (sign.), (max),
1111m coef mm
profiles mm mm mm mm mm
12 3360 46 31 37 0.05 1.5 0.5 3 3
14 3360 43 37 37 0.06 3 1.5 4.5 5.5
16 3360 46 34 37 0.06 1.5 1 2.5 3
18 3360 43 31 34 0.08 1.5 0.5 2.5 2.5
20 3360 43 31 34 0.08 1.5 0.5 2 2.5
22 3360 58 64 76 0.26 2.5 3 3.5 4
24 3360 64 61 67 0.36 2.5 3 3.5 4
26 3360 52 31 70 0.23 1.5 0.5 2.5 2.5
28 3360 67 64 67 0.36 2.5 2.5 3.5 4
30 3360 61 61 61 0.44 4 4 5 5
31 3360 67 61 67 0.31 2.5 2.5 3.5 4
34 870 79 85 76 0.05 7 9.5 10 10
35 1770 73 67 67 0.06 6.5 7.5 9 12.5
37 1770 91 88 109 0.25 7 7 9 9.5
38 1770 94 91 142 -0.16 9.5 4 17 19
39 1770 82 58 142 0.22 8 5.5 13 17.5
42 3360 79 61 >160 0.10 6 1 10.5 13
44 3360 64 37 >160 0.20 >25 >25 >25 >25
46 3360 82 64 >160 0.26 >25 >25 >25 >25
48 3390 46 34 40 0.08 1.5 0.5 2.5 2.5




Table B-2: continued.
NubrLength, LntLeghCorr. Height, Height Height Height Run# of 1111 (hist.), (corr.), 'of m (hist.), (sign.), (max),
profiles mmn mm mm mm mm
50 3390 70 64 70 0.46 2.5 3 4 4
51 3390 61 61 64 0.39 2.5 2.5 3.5 3.5
54 3390 64 64 67 0.45 3.5 3.5 4.5 4.5
55 3390 61 67 64 0.35 3.5 3 5 15
56 3390 67 64 67 0.28 2.5 3 3.5 4.5
58 3390 46 34 40 0.04 1.5 0.5 2 2.5
60 3390 61 70 73 0.28 2.5 2.5 3.5 4
62 3390 58 34 76 0.19 1.5 0.5 2.5 2.5
63 3390 76 179 79 0.34 1 2 2 3 3
64 3390 76 76 76 0.37 3 3.5 4.5 4
65 3390 70 76 82 0.45 3.5 3 4.5 5
67 3390 67 61 64 0.12 5 4 6.5 7
68 3390 73 61 >160 0.01 5 4.5 8.5 11.5
69 3390 79 58 >160 -0.08 6.5 2.5 11.5 13
70 3390 73 79 73 0.13 4.5 4.5 6 6.5
72 3390 70 61 67 0.12 1.5 1.5 3 3
73 3390 49 34 34 0.08 1 .5 0.5 2.5 2.5
74 3390 49 37 >160 0.07 2 1.5 4 8
75 3390 46 34 37 0.07 1.5 0.5 2.5 3
77 3390 43 31 34 0.06 1.5 1 2.5 3
78 3390 40 34 34 0.06 1.5 1 2.5 3
79 3390 49 34 34 0.12 1.5 0.5 2.5 3
80 3390 46 31 73 0.14 1.5 0.5 2 2.5
82 3390 70 88 76 0.05 7 4 9.5 10
83 3390 79 >160 >160 0.16 6 6 15.5 17.5
84 3390 79 79 109 0.23 5 6.5 9.5 11
85 3390 85 67 91 0.04 7 7.5 10 10.5
87 3390 115 >160 >160 -0.10 14.5 12 19 20
88 2370 79 70 >160 0.11 10.5 2.5 18 >25
89 3360 76 76 76 0.16 7 4 11 12.5
91 3390 139 >160 >160 0.10 9.5 >25 >25 >25
92 3390 82 61 >160 0.07 6 3.5 12 10
93 3390 70 70 67 0.13 4.5 3.5 8 8.5
95 3360 67 67 70 0.22 2 2 3 >25
96 3360 64 46 73 0.28 2.5 1.5 3.5 >25
97 3360 70 73 70 0.44 2.5 2.5 3.5 3.5
98 3390 61 61 61 0.47 3 2.5 4 4.5
100 3360 85 >160 >160 0.16 11 >25 20 >25
101 3390 82 70 106 0.14 7.5 6.5 13.5 12.5
104 3390 70 >160 >160 0.17 4.5 5 6.5 7
108 3390 61 31 64 0.21 3 3.5 5 5




Table B-2: continued.
Number Length Length Height HegtHeight
Run# of Length, (hist.), (corr.), Cor'egt (hist.), (sign.), (max),
Profiles mi rm mm ce m mm mm mm
109 3360 43 31 34 0.10 1.5 0.5 2.5 3.5
110 3390 49 31 64 0.14 1.5 1.5 2.5 3
112 3360 70 67 70 0.42 4.5 4.5 5.5 6
113 3390 61 64 67 0.22 4 5 6 6
114 3360 61 61 61 0.25 3.5 4 5 5.5
115 3390 61 61 64 0.35 3.5 3 4 5
116 3360 67 64 67 0.44 3 3 5 5
117 3390 61 58 70 0.31 3 3.5 5 5.5
118 1770 64 67 70 0.24 3 3.5 4 5
119 3390 64 61 67 0.33 2.5 3 4 4.5
124 3360 43 31 34 0.09 1.5 1.5 2.5 3
125 3390 43 34 34 0.10 1.5 1 2.5 2.5
127 2370 109 37 34 0.16 >25 >25 >25 >25
128 3390 55 31 61 0.05 2 1 3.5 4.5
129 3360 61 34 >160 0.06 3 1 6 11
130 3390 49 34 34 0.04 2 1.5 4 5.5
132 3390 67 31 34 0.24 >25 >25 >25 >25
133 3390 55 37 37 0.10 4.5 >25 >25 >25
134 3390 58 52 40 0.16 >25 >25 >25 >25
136 3390 58 34 >160 0.20 4.5 >25 >25 >25
137 3390 61 34 37 0.01 2.5 1 4.5 >25
138 3390 58 34 >160 0.10 5.5 1 10 >25
140 3390 bad bad bad bad bad bad bad bad
141 3360 64 64 >160 0.08 3.5 2.5 5 6
142 3390 58 64 73 0.08 2 1.5 3 3.5
143 3360 70 70 76 0.21 1.5 0.5 2.5 3
144 3390 58 43 >160 0.04 2 1 4 3
145 3390 46 37 37 0.06 1.5 0.5 2.5 2.5
146 3390 46 34 40 0.09 2 1.5 3 3.5
147 3390 46 34 40 0.10 2 1.5 3 3
149 3360 49 34 37 0.08 1.5 0.5 2.5 2.5
150 3390 46 34 37 0.12 2 1 3 3.5
151 3390 40 34 37 0.10 2.5 2 3.5 4.5
152 3390 46 34 37 0.06 2 1 3 3.5
154 3360 46 34 40 0.06 1.5 1 2 2
155 3390 49 37 >160 0.08 >25 >25 >25 1>25
156 3360 64 94 >160 0.29 >25 >25 >25 >25
157 3390 46 34 40 0.18 4.5 2.5 >25 >25
158 3390 46 43 43 0.14 4.5 2.5 5 >25
159 3390 bad bad bad bad bad bad bad bad
160 3390 bad bad bad bad bad bad bad bad




Table B-2: continued.
Number Length Length Height Height Height
Run# of Length (hist.), (corr.), Corr. Height, (hist.), (sign.), (max),
1m1m coef mm
profiles mm mm mm mm mm
161 3390 46 37 43 0.17 >25 >25 >25 >25
162 3360 46 37 40 0.05 3 2 5 6.5
164 3390 46 40 40 0.14 4.5 1.5 5 6.5
165 3390 46 40 40 0.05 3.5 2 6 >25
166 3390 46 37 37 0.09 3 2 6 6
167 3390 46 34 37 0.06 2.5 1 4.5 4
168 3390 43 37 40 0.09 3 2 4.5 4
169 3390 46 31 40 0.06 3 2 4.5 6
170 3390 46 37 34 0.08 1.5 1.5 2.5 3
171 3390 49 31 37 0.09 1.5 0.5 2.5 2.5
172 3390 46 40 40 0.09 1.5 1 2.5 3
173 3390 49 34 40 0.09 1 0.5 2 2
174 3390 49 40 40 0.13 1 0.5 2 2
175 3390 52 34 70 0.19 1 0.5 2 2
176 3390 67 67 70 0.42 3 3 3 4
177 3390 67 64 67 0.37 2.5 3 4 4
178 3390 67 70 67 0.42 3 3 4 4.5
179 3390 61 61 61 0.37 3.5 3.5 4.5 5
180 3390 70 64 70 0.03 5.5 4.5 9.5 10.5
181 3390 79 70 >160 0.07 5.5 2.5 13 12
182 3390 97 >160 >160 0.19 10 >25 >25 >25
183 3390 76 37 >160 -0.01 5.5 >25 9.5 >25
184 3390 61 31 >160 0.11 2 1 3 3
185 3390 43 31 31 0.13 1.5 0.5 2.5 3
186 3390 61 31 70 0.24 3 2.5 4.5 4.5
187 3390 49 34 64 0.07 2 1 4.5 4
188 3390 67 31 73 0.18 2 0.5 3.5 4.5
189 3390 58 34 >160 0.10 2.5 1 5 4.5
190 3390 49 34 34 0.09 2.5 1.5 >25 >25
191 3390 52 34 >160 0.04 2 1 4.5 3
192 3390 43 31 31 0.10 1.5 0.5 2 2.5
193 3390 43 31 31 0.18 1.5 0.5 3 3.5
194 3390 55 64 64 0.17 2.5 3 4.5 5
195 3390 61 64 67 0.30 4 3 5 5.5
196 3390 79 >160 >160 0.21 >25 >25 >25 >25
197 3390 76 37 >160 0.19 >25 >25 >25 >25
198 3390 49 43 43 0.15 1.5 1 2.5 2.5
199 3390 70 70 70 0.35 2 3 3.5 3.5
200 3390 61 61 64 0.33 3.5 3.5 5 5
202 3390 67 64 64 0.18 5 4.5 7.5 7.5
203 3390 73 79 88 0.00 7 4.5 11 12




Table B-2: continued.
Number Length Length Height Height Height
Run# of Len (hist.), (corr.), Corr Hg (hist.), (sign.), (max),
Imm coef mm
profiles mm mm mm mm mm
204 3390 70 85 88 0.16 12 12 12 12
205 3390 85 64 100 0.10 6.5 5 9.5 10.5
206 3390 73 61 >160 0.02 6 5 10.5 15
207 3390 70 67 >160 0.08 6.5 6.5 6.5 6.5
210 3390 43 34 34 0.13 1.5 1 2.5 3
211 3390 43 31 34 0.10 1.5 1.5 3 3.5
212 3390 43 31 34 0.08 1.5 1 2.5 2.5
213 3390 46 31 34 0.05 1.5 1 2.5 3
214 3390 43 31 34 0.06 1.5 0.5 2.5 3
215 3390 49 31 67 0.11 2 0.5 3.5 4
216 3390 64 61 64 0.19 4 4 6 6.5
217 3390 58 64 67 0.19 3 2.5 4.5 5
218 3390 52 34 67 0.11 2.5 2 4 4.5
219 3390 52 34 64 0.12 3 3.5 3.5 5
220 3390 64 37 >160 0.14 3 >25 >25 >25
221 2850 52 34 >160 0.03 1.5 1 2.5 2.5
222 2850 46 37 37 0.07 2 1.5 3.5 >25
223 3390 49 31 37 0.11 1.5 1.5 2.5 2.5
224 3390 58 61 67 0.24 3 3.5 4 5
225 3390 61 61 64 0.18 3 2.5 4.5 5
226 3390 64 67 73 0.35 3 3 4 4.5




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BIOGRAPHICAL SKETCH

Oleg A. Mouraenko was born the second son of Nadezhda and Alexander
Mouraenko in 1974 in Myaundzha, Magadan region, northeast of Russia. In 1987 his family moved to Barnaul, Russia. In 1991 he finished high school with a silver medal and entered the Mathematical Department of the Altai State University, Barnaul. During the study he found his interests in algebra and applied mathematics. Being a student, he started working in 1993 at the bookkeeping office on campus, where he got an excellent opportunity to apply his knowledge and skills in computer programming. In 1996 he graduated with honor and received the bachelor's degree in applied mathematics. That year he entered the graduate school at the Institute for Water and Environmental Problems of the Russian Academy of Science, Barnaul. In 1999 he was invited by Daniel Hanes to continue his research in coastal engineering at the University of Florida. Currently, he resides in Gainesville, Florida, where he continues his study in pursuit of a doctoral degree.