UFL/COEL2001/016
FIELD MEASUREMENTS OF TURBULENCE AND
WAVEGENERATED RIPPLES
by
OLEG A. MOURAENKO
THESIS
2001
FIELD MEASUREMENTS OF TURBULENCE AND WAVEGENERATED 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
page
A CKN O W LED G M EN TS .............................................................................................. iii
LIST O F TA B LE S ...................... .................................................................................. vi
L IST O F FIG U R E S .......................................................................................................vii
K EY TO SY M B O LS ..................................................................................................... x
A B ST R A C T ............................... ............................. ........ ... .............................. xii
CHAPTERS
1 IN TR O D U C TIO N ................................... ...............................................................
Estim action of Turbulence .......................................................................................... 1
B edform s .................................................................................................................. 2
Summary of the SandyDuck'97 Data Set ......................................................... ..... 3
2 ESTIMATION OF TURBULENCE ...................................................................... 7
M easurem ent of Turbulence.............................. ................................................ 7
Separation in Frequency Domain........................................................................... 9
Initial Terms and Definitions ....................... ..................................... 9
C utoff M ethod......................................... ...................................................... 12
PV M ethod ................................................................................................... 13
V V M ethod....................................................................................................... 14
Comparison of Cutoff, PV and VV Methods................................... .......... ... 15
Separation in Tim e D om ain ................................................................................... 24
Errors in Measurement of Turbulence due to Frame Vibration................................. 28
3 BEDFORM MEASUREMENTS....................... ..... .......................... 32
Instrum ent and Data Processing.................................................. ......................... 32
Filtering of R aw D ata............................................................................................. 37
Short W ave R ipples................................................................................................ 43
D im tensions ........................................ .......................................................... 43
Approximation of Ripple Lengths........................................................................ 44
Approximation of Ripple Heights...................................................................... 49
4 RELATIONSHIPS BETWEEN TURBULENCE, SUSPENDED SEDIMENT
CONCENTRATIONS AND BEDFORMS .......................................................... ... 53
A analysis of R relations ........................... ............................................................. 53
TKE and Sediment Concentrations............................................................................ 53
TK E and B edform s................................................................................................ 55
Time Variations of TKE, Sediment Concentration, and Bedform Mobility .............. 59
5 C O N C LU SIO N S ............................................ ...................................................... 61
APPENDICES
A MATLAB PROGRAMS FOR FILTERING OF MTA DATA ................................ 64
B SHORT RIPPLES DURING THE SANDYDUCK'97 EXPERIMENT .................. 70
LIST OF REFEREN CES ............................................................................................. 79
BIOGRAPHICAL SKETCH ...................................................................... 80
LIST OF TABLES
Table Page
31: Filter description. ............................... ............................................................... 38
41: Coefficients of relationship between TKE and first moment of concentration for
different A D V 2 elevations. ....................... ..... ...... ....................................... ... 55
42: Coefficients of relationship between TKE and short ripple height for different
A D V 2 elevations. ............................................................ .................................. 57
43: Coefficients of relationship between TKE and short ripple length for different
A D V 2 elevations. ................................................................................................. 58
44: Coefficients of relationship between TKE and steepness of short ripples for
different A D V 2 elevations. ................... ..... .......... ........................................ ... 58
Bl: Analysis of short ripple form and migration...................................... ............. 70
B 2: Short ripple dim ensions....................................................................................... 74
LIST OF FIGURES
Figure Page
11: Beach profile on 09/27/97 and location of frame. Coordinate system relative to
coastline....................... ........ ... .......... ............... .... ........................ . . ..... 3
12: Instrument setup and dimensions....................... ................................................ 5
13: SandyDuck'97 offshore instrument setup.......................................... ............... 6
21: Instrum ent setup and dimensions. .................................................... ............... 8
22: The definitions of 'cutoff frequency as a point of inflection of crosschore (U)
velocity spectrum and point of steep descent of coherence function.................... 13
23: Spectra and coherence functions. Elevations of sensors above the bed: 15.8 cm for
ADV1 and 9.5 cm for ADV2; Hno 2.1 m, Tpeak 11.6 s, peak 78.50................ 16
24: Spectra and coherence functions. Elevations above the bed: 41.3 cm for ADVI
and 35.0 cm for ADV2; H,,,o 2.2 m, Tpeak 8.5 s, Opeak 64.6. ............................ 17
25: 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; Ho 2.1 m, Tpeak 11.6 s, peak 
7 8 .5 ...................... .. ................. .......................................................................... 1 8
26: 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
ADV1 and 35.0 cm for ADV2; H,o0 2.2 m, Tpek 8.5 s, peak 64.6. ................ 19
27: Full turbulent kinetic energy from PV and VV methods. a) Elevation of ADV2 is
9.5 cm; H,no 2.1 m, Tpeak 11.6 s, peak 78.50. b) Elevation of ADV2 is
35.0 cm; H,,o 2.2 m, Tpeak 8.5 s, Opek 64.60. ............................................... 21
28: Comparison of cutoff, PV and VV methods of estimation of TKE for 2 Hz data... 22
29: Time series of turbulent velocity components. Elevations above the bed: 14.3 cm
for ADVI and 8.0 cm for ADV2; Ho 1.2 m, Tpeak 12.8 s, 0pek 83............... 26
210: Time series of turbulent velocity components. Elevations above the bed: 28.5 cm
for ADV 1 and 22.2 cm for ADV2; Ho 1.3 m, Tpeak 11.1 s, Opek 600........... 27
211: Significant wave heights and mean values of frame tilts during the SandyDuck'97
experim ent .......... ........................... ........ ..... ....................................................... 29
212: Significant wave heights and STD of frame tilts during the SandyDuck'97
experim ent.................................. ....................................................................... 30
213: Spectra of velocity components and vibration rates for wave parameters: Hmo 
1.2 m, Tpeak 12.8 s, Opeak 830. a) Velocity spectra for ADV1 on elevation
15.8 cm; b) Velocity spectra for ADV2 on elevation 9.5 cm................................ 31
31: MTA structure and dimensions with an example of bedform profile..................... 33
32: Data from transducer #33, test #1. Despiked raw data points and their histogram... 35
33: Run #30 of Sandy Duck 97 data for transducer #33. Despiked raw data points and
data after applying filters.......................... ........................................................ 36
34: Histogram of percentage of removed data point............................................... ... 39
35: Magnitude and impulse response functions of FIR lowpass filter of 31 order with
cutoff frequency 2/30. .......................................................................................... 40
36: Raw and despiked signal (top), and filtered ofdespiked data (bottom). (*) FIR
lowpass filter of 31st order; (**) elliptic IIR lowpass filter of 5th order.................... 41
37: Approximation of ripples dimensions for one profile from run #30....................... 45
38: Approximation of ripples lengths by three methods for run #30.......................... 47
39: Comparison of methods of ripples lengths approximation ................................... 48
310: Approximation of ripples heights for run #30.................................. ............. .. 49
311: Comparison of methods of ripples heights approximation.....................................51
41: Relationship between TKE and first spatial moment of concentration (1) ............ 54
42: Relationship between short ripple height (HSR) and TKE for different elevations of
ADV2 (hADV2): R correlation coefficient, N number of data points ................. 56
43: Relationship between short ripple length (LsR) and TKE for different elevations of
sensor (hADV2): R correlation coefficient, N number of data points ..................... 57
44: Ripple crest positions, TKE, mean concentration and wave envelope for run #30:
start at 256.3589 in Julian days. ......................................... ... ........................... 59
KEY TO SYMBOLS
(ax,ay)
b
c(t,z)
CU
Chh()
c,( f)
,f
h(x)
hABS,ADVI,AI)V2
h(r),1(r)
H(f),L(f)
H, HSR
Hmo
i
L, LSR
N
Px
Qxy(f)
SQI(f)
R
S" (f)
Sxy (f)
SV (f)
S' (f)
t
At
T
Tpeak
U
V
v
[L] Amplitudes of vibration
Phase angle
[ML3] Suspended sediment concentration
[ML'] First moment of suspended sediment concentration
Autocorrelation function
Coincident spectral density function
[T'] Cyclical frequency
[L] Bed elevation from mean level
[L] Elevation of ABS, ADV ADV2 above the seabed
Unitimpulse response functions
Frequency response functions
[L] Ripple height, ripple height of short ripple
[L] Significant wave height determined from surface elevation
spectrum
/1, index
[L] Ripple length, ripple length of short ripple
[] Number of data points
[L] Pressure, normalized by water density and gravity
Average energy of signal
Quadrature spectral density function
Correlation coefficient
Autospectral density function
Crossspectral density function
[L2T1]
[L2T']
[T]
[T]
[T]
[T]
[LT']
[LT']
[LT']
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
Crossshore velocity component
Longshore velocity component
Velocity vector
V [LT']
V
W
(x,y,z)
x(t), y(t)
X(f),Y(f)
[*]
7,(f)
8
Efto,0,1.2..
Opeak
[LT']
[LT1]
[LT']
[LT']
[L]
Mean current and infragravity wave component of velocity
vector
Wind wave component of velocity vector
Turbulent component of velocity vector
Vertical velocity component
Crossshore, longshore and vertical coordinates
Time history records
Fourier transform of x(t), y(t)
Complex conjugate of[ ]
Coherence function
[L] Grid interval
Error source
Peak wave direction in degrees from positive longshore
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 WAVEGENERATED 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 wave
induced 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 'cutoff
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 mm. 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 highresolution 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: cutoff, PV, and VV. The cutoff method uses a 'cutoff 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 waveinduced 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 35250 cm and short wave ripples (SWR) with lengths 325 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 timerelated 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.
Beach profile (09/27/97) A7490
21
i2 I 
o 0
o Frame position o
U,2 \ +U
w CD
4
6 
100 200 300 400 500
Crossshore distance, m
Figure 11: 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 11.
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 12):
3D velocity measurements from two ADVs (acoustic Doppler
velocimeter);
Pressure measurements;
Onedimensional 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).
Onedimensional measurements of bedforms were carried out using 64element
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
I I
Figure 12: Instrument setup and dimensions.
The offshore instrument setup and dimensions are shown in Figure 13. The main
axis of the MTA was directed perpendicular to the shoreline and coincides with the x
direction 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.
4 .cm.
4 Ocm.
Figure 13: SandyDuck'97 offshore instrument setup.
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 frame, which can distort the flow;
Higher requirements for instruments, data acquisition 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 crossshore 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 ADV1 's sampling volume. The setup and dimensions of
instruments are shown on Figure 21.
Ocean
ADV2 ....
[Coast
Pressure I
ADV1 i1
'" 7
34.7cm.
1 18.0cm. tievatlon
18.0cm. 6.3cm. of pressure
I sensor
Elevation
Elevation 53.0cm.  ofADV1
of ADV2
Figure 21: 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 1%) 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
(crossshore) and transversal (longshore) directions. But using the TTC sensor (Tilt
TemperatureCompass) it is possible to estimate rolling (along crossshore direction) and
pitching (along longshore 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 frequencyfand inverse transform are given by
Equations 21':
+0o
X(f)= F{x(t)}= Jx(t)e'2,fidt
+(21)
x(t) = F'{X(f)}= X(f)e'2l/fdf
An average energy of signal is equal to
P = lim {x(t}2dt (22)
S 2T J
r
A spectral density function of signal x(t) is defined by
S.(f)= lim X(f)l, f ( 0,+00) (23)
According to Parseval's theorem:
{x(t)}2dt= iX(f)2 df (24)
The average energy of signal now can be expressed in term of spectral density
function:
1 All the equations can be found, for example, in the book of Bendat and Piersol, 1993.
+C +oo
+0 10
P= S, ()df = S,.(f)df (25)
0
To obtain an average energy of fluctuations for a frequency range the integral 25
should be evaluated only within this range:
/2
{fe[f,f2]}= f(f)df, ff2>0 (26)
Let two signals x(t) and y(t) have their Fourier transformations X(f) and
Y(f) correspondingly. Then the crossspectral density function between these signals is
defined by
S (f) = lim X(f)Y(f)= C,Y(f)iQ.(f), f (~o,+oo) (27)
7~ T
In general the crossspectral density function is a complex function. The real part
C,,(f) is called the coincident spectral density function or cospectrum, and the
imaginary part Q,,(f) is called the quadrature spectral density function or
quadspectrum.
Define the coherence function by
(f) = (28)
f Sxx (f ) SYY (f)
The coherence function, defined by the equation above, is a complex function, as
well as the crossspectral density function. Usually, a square of the magnitude of xy (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< ,(f) 1 (29)
The phase angle of coherence function is equal to
arg (,(f))=tan' Yj) (210)
I, ( f\
The velocity vector V could be written as a sum of three components:
V= +V+V' (211)
where V is a mean current and infragravity waves, V is a motion, induced by wind
generated 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:
Cutoff based on 'cutoff 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.
Cutoff Method
This is the most simple technique to separate the turbulent component of velocity
from waveinduced motion. The only problem is to find the 'cutoff 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 loglog 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 'cutoff 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 22. 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 bestfitted 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 'cutoff 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.
13
0.6
100 0.5
E
_~^0. 0.4
C 10 a) 0.3
CO 0_
0.2
104 .... ... 0.1
0
101 100 101 100
Frequency, Hz Frequency, Hz
Figure 22: The definitions of 'cutoff frequency as a point of inflection of crosschore
(U) velocity spectrum and point of steep descent of coherence function.
The turbulent kinetic energy (TKE) was calculated using Equation 26, wherefi is
a 'cutoff andf2 is Nyquist frequencies. The valuesfr=0.05 Hz andf2='cutoff 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 22 as example). This
property is commonly used to separate turbulent and wave components of velocity (see
Wolf, 1999). The coherence function for PVmethod (PressureVelocity) is given by
Equations 212:
y, (f)=0, 0< f <0.05
S,, (f) 2 (212)
fv (f)= (f) f 0.05
S,(f)S,( 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 213 and 214.
Sv = yVSv,, f > 0 (213)
Sv, = (1 7)Sv,, f > 0 (214)
where superscripts Wand T refer to waves and turbulent parts correspondingly.
The kinetic energy is estimated using Equation 26 withfi=0.05 Hz and
f2=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 m). As it is seen from
Figure 21 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 4 Vrms, 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 PV
method by Equations 215:
,,(f) =0, 0< f <0.05
S ,, 2 .5 (215)
S(f)SV)(f) f 0.05
where V is a crossshore, longshore or vertical component of velocity, and the index 1
and 2 refers to ADVI and ADV2 correspondingly.
The spectra for velocity components are given by Equations 216 and 217.
S: = r, SV,, f > 0 (216)
S, = ( Yv,2)SV,, f > 0 (217)
The kinetic energy is estimated using Equation 26 with f/=0.05 Hz and
f2=Nyquist frequency for both waves and turbulence.
Comparison of Cutoff, PV and VV Methods
The coherence functions and spectra after application of PV and VV methods are
shown on the next four figures. Figure 23 and Figure 24 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 23 the elevations were 9.5 cm for ADV2 and 15.8 cm for
ADV1. And for Figure 24 they were 35.0 cm and 41.3 cm for ADV2 and ADVI
correspondingly.
100 UADV1  ADV1 vs. Pres
SUADV2 UADV2
 Pressure  ADV1 ADV2
S104 ..
ci) ____'_._ o jj_
S 0 0.5 1 1.5 2 0 0.5 1 1.5 2
1
c 1 0 N I vs. Pres
0 10 VADV .0 VADV1
V vs. Press
VADV2 5 VADV2 V. P
O Pressure  ADV1 VS VADV2
Z 0.5
104 ..'. . : .
o 
0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
0,)
100 ADV WADV1 vs. Pres
t Fe q WADV2 WADV2VS. Pres
a  Pressure  WADV1s WADV2
V) 0.5
104 0.5
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz
Figure 23: Spectra and coherence functions. Elevations of sensors above the bed:
15.8 cm for ADVI and 9.5 cm for ADV2; H,,o 2.1 m, Tpeak 11.6 s, Opeak 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 crossshore, Vis a longshore
and W is a vertical components of velocity, in meters per second.
17
1 
100 A UADV u ADV vs. Pres
U1 u vs. Pres
 UADV2  UADV2vs Pres
Pr SU vsU
 Pressure  ADV1 VS ADV2
C1 0.5
E
.S 104A
CO 0
8 0 0.5 1 1.5 2 0 0.5 1 1.5 2
S( 1
10 V V vs. Pres
c 10 \ADV1 0, ADV1
S VADV2  VADv2 vs. Pres
S Pressure  ADV1 V. VADV2
S~0.5
104 .
o .
0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
:0.5
10 0 *W w vs. Pres
O of  W A W ADV2vs. Pres
a) ^^' Pressure ADVI ADV2
14 ~
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz
Figure 24: Spectra and coherence functions. Elevations above the bed: 41.3 cm for
ADVI and 35.0 cm for ADV2; H,,o 2.2 m, Tpeak 8.5 s, Opeak 64.6.
The coherence function between crossshore velocity and pressure (PU
coherence) is very high on wave frequencies (0.05 0.5 Hz). The situation is very
different for longshore 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.
0U
10 : ADV2
SWaves
 TKE
104
0 0.5 1 1.5 2
U)
C 0
o 10
 104
10
104
. 0 0.5
10)2
10 
v
ADV2
SWaves
TKE
1 1.5 2
100 ADV2
Waves
 TKE
104
44 r\ r
S U U.O I 1.50
Co
E
O 100 ADV
o Waves
2 TKE
)10
( 0 0.5 1 1.5 2
c,
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz
Figure 25: 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; Ho 2.1 m, Tpeak 11.6 s, peak 78.50.
For the vertical velocity component the PW and WW coherences are not as high
as for crossshore velocity. That difference could be explained by small elevation of
sensors above the seabed: inside the turbulent boundary layer the intensity of turbulent
E
*4 *1 C
2
19
motion greater than the intensity of waveinduced motion. Moreover, the magnitude of
vertical velocity is small.
SADV2
SWaves
^ , TKE
E
C,
c
ADV2 .
Waves
1  TKE
4 C
O3
7 i ADV2
I v I Waves
t~ t  TKE
0 0.5 1 1.5 2
0 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 26: 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
ADV and 35.0 cm for ADV2; Ho 2.2 m, Tpeak 8.5 s, Opek 64.6.
There is a small difference between coherence functions for ADV1 and ADV2.
However, the spectra of horizontal components of velocity are different (Figure 23).
C,
E
U,
C 0
0 100
_ 10
10
0
c
 104
a,
CO,
10'
10"
ADV2 was closer to the bed and the TKE is greater at high frequencies. Figure 24
indicates that the velocity spectra are about the same, when the sensors were located 35.0
and 41.3 cm above the bed.
Figure 25 and Figure 26 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 from the slope at high frequencies.
At a 9.5 cm elevation the turbulent spectrum of the longshore 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 nearbed turbulence.
The full turbulent kinetic energy, calculated by two methods, is shown on
Figure 27. 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 'cutoff 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  PV
100 1 :0 . . ..100 ..... .
E IE
U) U)
C+J> 2 C+j> 2
) 10  U) 10
104 104 "
102 10 102 10
Frequency, Hz Frequency, Hz
Figure 27: Full turbulent kinetic energy from PV and VV methods.
a) Elevation of ADV2 is 9.5 cm; H,,o 2.1 m, Tpeak 11.6 s, Opek 78.50. b) Elevation of
ADV2 is 35.0 cm; H,,no 2.2 m, Tpeak 8.5 s, ,peak 64.6.
ADV2
0.04~ J." .
0.02 ~*,:": y
0
0 1 2
Cutoff
0.02
0.015
> 0.01
0.005
0
0
0.08
0.06
> 0.04
0.02
0.08
0.06
0.04
3 4
x 103
1 2 3 4
Cutoff x 103
1 2 3 4
Cutoff 103
Cutoff x03
x 10
0 0.005 0.01 0.015 0 0.005
VV VV
0.015
Figure 28: Comparison of cutoff, PV and VV methods of estimation of TKE for 2 Hz
data.
0.1
0.08
0.06
* .
Ry = 29.9x
R = +0.85
jy = 5.1x
r' R = +0.96
ADV1

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 28. 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 'cutoff method estimates the minimum amount of total TKE, which
is approximately 5 times smaller than from VVmethod.
The PV method overestimates the total TKE in the longshore direction
and overestimates the full TKE. The TKE is estimated 6 times larger than
by VV method and 30 times larger than by the 'cutoff 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(f) its Fourier transformation, given by Equation 21. 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(z):
x, (t)= fh(r)x(t T)dt
(218)
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{x,(t)}= H(f)X(f), H(f)= F{h(t)}
(219)
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 'cutoff method and coherence functions for PV and VV
methods.
Let f. be a 'cutoff frequency, then
L(f) =, 0.05< f< (220)
L(f) = 0, If > f,
H(f) = 1 L(f) (221)
For PV and VV methods the functions H(f) and L(f) are given by
L(f)=O, 0< Jf 0.05
(222)
L(f) = (f), If > 0.05
H(f) = 1 L(f) (223)
where y(f) is a coherence function, given by Equation 224 for PV method and
Equation 225 for VV method:
( (f)=) (224)
VfS ,, Sp (f)
v, v,2 (f) = VsIV2 (f) (225)
1 SVV, (f)SV2V (f)
Finally, high and low frequency components of signal x(t) are defined by inverse
Fourier transform:
x,,(t)= F' {H(f)X(f)}
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 VV
method. The turbulent velocity components are plotted on Figure 29 and Figure 210
versus crossshore component.
The axes a and b of the ellipses were calculated as 3 ofor 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 crossshore direction.
ADV2
0.1
0.1
0.2 0.1 0 0.1 0.2
U', m/s
0.1
0.2
a = 0.16, b= 0.14, = 4.80
0.2 0.1 0 0.1 0.2
U', m/s
0.1 [
0
0.1
0.2
0.2 0.1 0 0.1 0.2
U', m/s
a = 0.15, b = 0.04, = 1.00
0.2 0.1 0 0.1 0.2
U', m/s
Figure 29: Time series of turbulent velocity components. Elevations above the bed:
14.3 cm for ADV1 and 8.0 cm for ADV2; H,o 1.2 m, Tpeak 12.8 s, Opeak 83.
a = 0.10, b = 0.08, = 4.60
a = 0.10, b = 0.04, a = 0.30
ADV1
ADV1
a = 0.07, b = 0.06, a = 7.70
0.2 0.1 0 0.1 0.2
U', m/s
a = 0.06, b = 0.04, a =1.20
0.2 0.1 0 0.1 0.2
U', m/s
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, a = 1.4
0.2 0.1 0 0.1 0.2
U', m/s
Figure 210: Time series of turbulent velocity components. Elevations above the bed:
28.5 cm for ADV 1 and 22.2 cm for ADV2; H,o 1.3 m, Tpeak 11.1 s, Opeak 600.
Figure 29 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
0.2
0.1
0
0.1
0.2
a = 0.06, b = 0.05, a = 2.00
ADV2
turbulence is close to uniform, only the magnitude changes with elevation. For higher
elevations (Figure 210) 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 (crossshore) and transversal (longshore) 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 l
in (x, y) plane. All three angles were measured simultaneously with other parameters,
such as velocity and pressure. Therefore, the time series of angles are available. Figure 2
11 show the mean value for two (0,0) angles during the SandyDuck'97 experiment. It
can be seen, that the angle 0 did not change significantly during the experiment, but 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.
The standard deviations of the time series of angles were calculated and plotted
on Figure 212. 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.
/10
r
09/20
~FC, ,
09/10
0.5 
1.5
09/10
09/20
09/20
09/30 10/10
10/20
10/30
*r
09/30 10/10
09/30
10/10
Julian days, day
10/20
10/20
10/30
10/30
11/09
11/09
11/09
Figure 211: Significant wave heights and mean values of frame tilts during the
SandyDuck'97 experiment.
For small angles the amplitudes (ax,a,) of vibration in x and y directions can be
approximated by
a, =AOr
aj = A(Z*r
(227)
3
E 2
0,
I 1
0
09,
1
i i
II
0)
. "'
c. 
x
0)
0,
(0i Q.
) I
2,.
>
1
f"
L~i CI~~L~r, ;~~~rr
where (AO,AZ) are the deviations from mean angles. They can be estimated
conservatively as 3 aof 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.
3
E 2
09/20 09/30
09/20 09/30
10/10
10/10
10/20 10/30
10/20
10/30
09/10
09/10
09/20 09/30 10/10 10/20
Julian days, day
10/30
11/09
Figure 212: Significant wave heights and STD of frame tilts during the SandyDuck'97
experiment.
The rates of vibration are given by Equations 228.
dax dO da d d
__A_ r; __ r
dt dt dt dt
The spectrum of vibration rates can be calculated as follows:
(228)
(1
09/10
0.2
U
09/10
0.2 
0.1
0,1
11
/09
a)
CO
.c 0
'i
0)
c,D
a
I
(/N
>>
. . . . . . . .. . . . ... . .. .. . . .
IA.
<^: L jIqm AA^
11/09
. . . . . . .
^:.Mi
Ih~,...~ 4.... .....~Cr
Sj, (f) = (2'f)2 S (f) (229)
The results are shown on Figure 213. The errors generated by the frame vibration
at all frequencies are much smaller (12 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
0
C
_0
o
S 10
0. 10
c 0
0
S100
0 0
_ 10
C 0
0
C
ca 10
(n 0
Figure 213: Spectra of velocity components and vibration rates for wave parameters:
H,o 1.2 m, Tpeak 12.8 s, 0peak 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 1.4 1.6 1.8 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 onedimensional 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 32element 50 cm length
MTA has 5MHztransducers 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 31 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
1 16 17 48 49 6 I4
6.0cm. 1.5cm. 4.0cm.
98.1cm.  50.0cm. 98.1cm.
Figure 31: 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.
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 MTA reads a signal from the transducer, and a single measurement is recorded
with 1 mm 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 problem, 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 32 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 MTA 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
S318
C
.U)
0 IIn
I
320
321
0
Test# 1: start = 42.4076 end = 42.4133;At = 2.0 s; xducer #33
fl 4 N
H + ++ +4*Ht+HHi'+l H +1 +++ ++ H +t+
I II I +
Hi + i + +
SNormal F
+ MTA data points 31(
 Modal filter = 1.
Lowpass filter
100 200 300 400 5000
Time, sec
0.2
PDF
Figure 32: Data from transducer #33, test #1. Despiked raw data points and their
histogram.
Two additional lines on the left plot of Figure 32 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.
I

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 'falsebed' 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
518 I
+ MTA data points
519  Modal filter
Lowpass filter
520 + + +
E521 + + + + +
522 + + 1++ 4+++ \H+ + + +
I
522 I4 +4 + 4+H + 44 ++ ++ 4+4+ +
E
8 524 H /iW4i wi' '
\
S525 + ++ + ++H 44 +H+++ W+++ +Hi+
526 + +++ ++4 ++ +++++ ++ +
527 4 + +
Normal PDF:
528 + + + 'I = 523.7
a = 2.0
529
0 100 200 300 4000 0.2 0.4
Time, sec PDF
Figure 33: Run #30 of Sandy Duck 97 data for transducer #33. Despiked raw data points
and data after applying filters.
Figure 33 contains the same information as Figure 32, 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 ID 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 1218 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, E8,,, is produced by several independent sources
of errors:
E,,, = Eo + + 2 + 3 +... (31)
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 nonlinearity, 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 31: Filter description.
r. AA Sandy Duck'97
Order Filter description Sandy Duck' Routine
settings
Remove data points with values less then Sm
SmallestDistance:
1 minimal distance (SmallestDistance) between 300 mm mta_proc
MTA and the bed
Remove data points, which deviations from
Mean exceed maximum value (MaxDeviation). MaxDeviation:
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)
Sis 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 Nelement N: 30
4 block of data, if the standard deviation of the StDevLevel: mta_proc
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. iner mtainterp
interpolation. 
Table 31 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 34 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%
5
U)
04
3
E
I2
z
1
U
0 
0 103 data files have less than
0 15% of removed points _
0  . . . . .. . . . . ..
7 lF] FI F ii F r1
0 10 20 30 40 50 60 70 80 90
Percent of removed points
Figure 34: 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 35.
FIR lowpass filter; Order: 31; Cutoff: 2/30
20
0)
40
C
2 60
0 0.1 0.2 0.3
Normal
0.08
20.06
S0.04 :
 0.02 
0 5 10
0.4 0.5 0.6 0.7 0.8 0.9
ized frequency (Nyquist=1)
15
Data points
20 25 30
Figure 35: 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 36 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 36 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 = 3.0s xducer #63
0 100 200 300 400 500
0 100 200 300 400 500
Time, sec
Figure 36: Raw and despiked signal (top), and filtered of despiked data (bottom). (*) FIR
lowpass filter of 31st order; (**) elliptic IIR lowpass filter of 5th order.
Figure 36 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 32 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 32 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 34150 mm and heights of 224 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 bestfit 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)= Hsin 2x+b (32)
2 (L )
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 onedimensional profile only. Obviously, if the real
bedforms in two dimensions have periodical shape with parallel crests, then any cross
section will have periodic structure. The height of measured onedimensional ripples will
be the same as original, but the length will depend on angle between normal to the crest
and direction of crosssection line. In case of threedimensional 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
x
X
or for discrete series
Nk
Chh(k) = N Z h,h,+k (34)
=I
where x is offset or lag. In discrete case offset is equal to
(35)
for grid interval S.
If the profile shape is defined by Equation 32 then the autocorrelation function is
H 2 28 o
C,,, = cos 
8 L
(36)
and its maximas are found at 5 = 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 34.
Run#30; Time 258.3589; Length=70.0mm; H =4.4mm; H =5.4mm
mean max
4
E
E 2
t
0
5 0
U 2
4
C
c 1
o
00
t
c 0.5
2
00
8 0.5
1
Distance along MTA, mm
0 20 40 60 80
Offset, mm
100 120 140
Figure 37: Approximation of ripples dimensions for one profile from run #30.
k = k8
Figure 37 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 minimums and maximums. Threshold for smallest
vertical deviation between two successive extremums was used. It was taken to be equal
to 0.2 where ois 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 38 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 10th and 27th 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 38.
Run# 30: start = 258.3589 end = 258.3844
Crests positions
U
E
E 100
c 200
5 0 300
1 400
E70
E
60
Length as 'mean'
E 70
E60
Length as 'mode'
o o
0 .... 0 7. 0 
70 o o
E e o. .....on c o. o o...
600 0 o o o0o
Correlation coefficient
1
0.5
0 5 10
15 20
Time, min
25 30 35
Figure 38: Approximation of ripples lengths by three methods for run #30.
...... ..... _ __ .. .. .. 1. _.
.. .... .... ...... ...... .
.., 
m ,__ m
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 39 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
E120
100
o 80
0
460
40
40 60 80 100 120 140
Mean length, mm
:%
. /
S y = 1.09x:
. . R=+0.62:
40 60 80 100 120 140
Modal length, mm
....... ..
y = 1.03x
S :: R = +0.69
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 39: Comparison of methods of ripples lengths approximation.
140
E 120
E
100
 80
"a
60
4 60
40
....
Sy =:0.89x
.R =:+0.64
140
E
E120
4C
a.
100
o 80
80
H 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 cresttrough 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 heights
6 .. .
2
Mode of heights
0 0 0
6
E 4 o o o o o
2E o o o o o o
2
6 0 0
0 0 0 0 0 00
2 0 0 . .. ..o. A O .. 0 . .. '
Maximeumei
___________Significant heights , ,
E I o o o Ooo<
 4 1. :. o .. ." ..... :o . .o
0 5 10 15 20 25 30 35
Time, min
Figure 310: 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 310 shows an example of ripple height approximations for the same data
as on Figure 38. 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 10th and 27th minutes the ripples were shifted along the MTA as
a result of some event. The decrease of ripple heights was observed during those events.
On Figure 311 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 mm. 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
E20
E
5 .
S15 15
:" .6 ,,
y =0.83X y= 166x
F 0. .. R .r:
+ 0.73 1 R = +0.91
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
E15
) R correlation coefficient
10 .. Solid line: Y= bX
10 ..
.. Dash line: Y = X
.2)
) 5 ....'... y.= O.85x
R = +0.9.1
5 10 15 20
Max height, mm
Figure 311: 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 1.52 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 B1) and estimated ripple
scales (Table B2) 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 threedimensional. 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 measurements in laboratory flumes 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:
kABS
= J zc(t,z)dz (41)
0
The TKE was calculated by VV method (see Chapter 2). The relationship is given
by Equation 42 and demonstrated on Figure 41 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.
logo, = a (TKE)/2 +b, a =23.4, b = 3.9 (42)
The first moment of concentration profile relates to potential energy of suspended
sediments. Thus, Equation 42 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 I 0.1
0.01 ." 0.01 .... .
0.001 ........ 0.001 . ... . .
.: y = 24.4x3.9 y = 23.4x3.9
S R = +0.86 I R = +0.85
0 0.05 0.1 0.15 0 0.05 0.1 0.15
1/2 1/2
TKE12, m/s TKE12, m/s
Figure 41: Relationship between TKE and first spatial moment of concentration (E).
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 42 is shown in
Table 41 for these fits.
Table 41: Coefficients of relationship between TKE and first moment of concentration
for different ADV2 elevations.
Elevation of Correlation Number of data
a b
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 41 shows that the correlation coefficients are high at all elevations and the
coefficients a and b of Equation 42 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= 10h (Hs )" or log,,(TKE)=alog,o(Hs,)+b
(43)
TKE= Oh(Lsh)" or log, (TKE)=alog, (LsR)+b
TKE= 1O Hs '
Ls,
or logio(TKE)=alogo Hs" +b
\LsR)
where HSR is ripple height; LSR is ripple length; a and b are some coefficients.
3.5'

hADV2<1 5.5 cm
y = 0.7x4.7
R = 0.74
SN=298
S:
'
2.5 2
h D=17.0..18.0 cm
y = 0.3x3.6
R = 0.29
2.5 , ..*N =177
3
3.5
4
3 2.5 2 1
hADV2=20.0..23.0 cm
1
y =1.1x5.6
R = 0.69
N = 270
2 .
':.
3 2.5 2
logl0(HSR)
1.5
2
2.2
2.4
2.6
3
hADV2=15.5..17.0 cm
y = 0.6x4.5
; R= 0.50
N=282
2.5
hADV2=18.0..20.0 cm
y = 0.4x3.6
R = 0.27
N =245
S. * Si
: I ; :. *' : "
5J
2.5 2
hADV2>23.0 cm
2.5 2
loglo(HSR)
1.5
1.5
Figure 42: Relationship between short ripple height (HsR) and TKE for different
elevations of ADV2 (hADv2): R correlation coefficient, N number of data points.
(44)
(45)
y = 0.1x2.0
R = +0.29
...... .. . N 75
:
i
Table 42: Coefficients of relationship between
ADV2 elevations.
TKE and short ripple height for different
Elevation of Correlation Number of b
a b 10
ADV2, cm coefficient data point
<15.5 0.74 298 0.71 4.71 1.97*10
15.5...17.0 0.50 282 0.63 4.47 3.36*10
17.0...18.0 0.29 177 0.30 3.60 2.51*104
18.0...20.0 0.27 245 0.36 3.57 2.70*104
20.0...23.0 0.69 270 1.08 5.56 2.78*10
>23.0 +0.29 75 0.10 2.00 9.94*10'
hADV2 <15.5 cm
2
y = 1.8x5.1
.: : R = 0.72
5 p ,* .... N=298
4 
4
1.4 1.2 1 C
hADV2=17.0..18.0 cm
2
y = 1.8x5.1
R = 0.55
5 : .:" . N=177
1.4 1.2 1 0.8
hADV2=20.0..23.0 cm
1
y = 3.1x6.6
R = 0.74
N = 270
2 ";
Ii.
3
4
1.4 1.2 1 0.8
loglo(LsR)
1.4 1.2 1
hADV2=18.0..20.0 cm
1.4 1.2 1
hADV2>23.0 cm
2.6
1.4 1.2 1
loglO(LsR)
Figure 43: Relationship between short ripple length (LSR) and TKE for different
elevations of sensor (hADv2): R correlation coefficient, N number of data points.
hADV2=15.5..17.0 cm
y = 1.8x5.0
R= 0.56
^ .3. N=282
:r'
0.
y =1.8x4.9
R = 0.49
N N=245
I s': a
8
8
0.
y = 0.0x2.3
R = 0.02
N =75
* I: 
0.8
2.2
2.4
Table 43: Coefficients of relationship between TKE and short ripple length for different
ADV2 elevations.
Elevation of Correlation Number of
ADV2, cm coefficient data point a
<15.5 0.72 298 1.82 5.13 7.48*106
15.5...17.0 0.56 282 1.75 5.01 9.77*106
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*105
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
Figures 42 and 43 show the relationship between turbulent kinetic energy and
height and length of short wave ripples correspondingly. The coefficients of bestfitted
lines are included into Tables 42 and 43. Table 44 shows the coefficients and
correlations coefficients for the relation between TKE and steepness of short wave
ripples. The relationship is given by Equation 45 and has the same form as for ripple
length and height.
Table 44: Coefficients of relationship between
different ADV2 elevations.
TKE and steepness of short ripples for
Elevation of Correlation Number of jb
a b 10
ADV2, cm coefficient data point
<15.5 0.65 298 0.90 4.10 7.94*10
15.5...17.0 0.35 282 0.56 3.60 2.50*104
17.0...18.0 0.13 177 0.17 3.05 8.81*104
18.0...20.0 0.11 245 0.19 2.89 1.29*103
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*103
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 43 and 44 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
0<
0
CO
Crests positions
 __
00,
7
x 103 TKE = (u')2+(V,)2+(W')2
x1
E 0.5
0
0.02
Vertically averaged concentration
I0.01
0
Wave envelope
0.4 
0.2 i Alji Al li .1".1l
20
Time, min
Figure 44: 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 44. 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 27th
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 cutoff method defines a single frequency that
separates turbulence from waves. The 'cutoff 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 method). 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 cutoff method estimates the minimum total TKE, which is approximately
5 times smaller than from VV method. The PV method overestimates turbulence due to
longshore fluctuations and also overestimates the full TKE. The estimated TKE is 6
times larger than the VV method and 30 times larger than the cutoff 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 MTAPROC(FileName,DirIn, DirOut);
%
% This routine for processing MTA data. It generates new data files,
% which include the next variables:
% Light
% Variable Function save Comment
despike *
mkmtal23 *
mkmtal23 *
duckhist *
mkprofx *
*
Raw MTA1 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
Xaxis for MTA
Xasis 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
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
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 TART E N 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((il)*n+l:i*n,:);
tmp(:) = modetrend(tmp(:)',100,MaxDeviation);
mtal23e((il)*n+l:i*n,:) = tmp;
end;
% remove extreme values mean +/ 5*MaxDeviation mm
meanmta = nanmean(mtarl23(:));
mtal23e(find(abs(mtal23emeanmta) > 5*MaxDeviation))=NaN;
% call despike function
mtal23d=despike(mtal23e(:,l:end1),SpikeLevel,SpikeDuration,0); % in places of spikes NaN
values
% Correct date of experiment in mtatime
jdst = datenum(ExperimentYear,hex2dec(FileName(2)),1)datenum(ExperimentYear,1,1);
% 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*(il)+l:N*i));
% if stdev of block big  bad data. Remove them.
if isnan(stdN)  (stdN > StDevLevel)
mtal23d(j,N*(il)+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, Nnumber of points per smallest 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 = mtainterp(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')';
% 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 standard 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
S deviations for the first derivative threshold, otherwise
% 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)>l
for i = l:size(x,l)
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(end29:end));
else
mn b = mean(x);
mn e = mn b;
end;
x=[mnb x mne];
dx=x(2:end)x(l:end1);
if stdflag == 1
dx=dx/std(dx);
end;
% Presize matrix
xns=zeros(1,lx) ;
i=1;
while(i <= lx)
% Spike should have first derivative > threshold.
spkwidth=0;
dxsum=dx(i);
while (spkwidth <= maxwidth) & (i+spkwidth<= lx1) & (abs(dxsum) > thold)
spkwidth = spkwidth+1;
dxsum=dxsum+dx(i+spkwidth);
end;
if spkwidth == 0
xns(i) = x(i+l);
i=i+l;
else
for j=l:spkwidth; xns(i+j1)=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: INTERP1
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 xaxis 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 Bl: Analysis of short ripple form and migration.
R# Julian Duration, At, Bedfoms Migration
Run# Quality (onshore
start time mmin 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 Bl: continued.
n D Bedforms Migration
Julian Duration, At, Qai
Run# Quality (onshore
start time m sec ality Flat Noise 2D 3D (onshore
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 on
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 B1: continued.
SBedforms Migration
Julian Duration, At,
Run# Julian Duration, At, Quality (onshore
start time min sec Flat Noise 2D 3D
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 yes 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
166 292.9282 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 Bl: continued.
Bedforms Migration
Run# Julian Duration, At, Qu
Run# Quality (onshore
start time min sec Flat Noise 2D 3D (on
__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
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 yes 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 yes
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 yes
211 304.4315 169 3 Good yes yes
212 304.6040 339 6 Good yes
213 304.8756 678 12 Good yes
214 305.4127 508 9 Good yes
215 305.8653 678 12 Good yes
Table Bl: continued.
Bedforms Migration
Julian Duration, At,
Run# Julian Duration, At, Quality (onshore
start time mm sec Flat Noise 2D 3D
offshore)
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 B2: Short ripple dimensions.
Number Length Length Height Height Height
Length, Corr. Height,
Run# of (hist.), (corr.), C (hist.), (sign.), (max),
mm 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 B2: continued.
Number ngthLength Leng Corr. Height,
Number Length, Length Length Corr Height Height Height Height
Run# of (hist.), (corr.), m (hist.), (sign.), (max),
mm coef mm
profiles mm 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 5
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 79 79 0.34 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 B2: continued.
Number Length Length Co HeightHeight Height Height
Run# of (hist.), (corr.), (hist.), (sign.), (max),
mm coef mm
profiles mm mm 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 >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 B2: continued.
Number Length Length Cor. Height Height Height
NubrLength, Corr. Height,
Run# of (hist.), (corr.), (hist.), (sign.), (max),
mm 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 B2: continued.
Number Length Length Cor. Height Height Height
R umb r Length, Corr. Height,
Run# of Ln (hist.), (corr.), (hist.), (sign.), (max),
mm 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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thesis, Univ. of Florida, Gainesville, 1999
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Hanes, D.M., V. Alymov, Y. Chang, C.D. Jette, Wave formed sand ripples at Duck,
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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.
