• TABLE OF CONTENTS
HIDE
 Half Title
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Key to symbols
 Abstract
 Introduction
 Estimation of turbulence
 Bedform measurements
 Relationships between turbulence,...
 Conclusion
 MATLAB programs for filtering of...
 Short ripples during the SandyDuck...
 Reference
 Biographical sketch














Title: Field measurements of turbulance and wave-generated ripples
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00091375/00001
 Material Information
Title: Field measurements of turbulance and wave-generated ripples
Series Title: Field measurements of turbulance and wave-generated ripples
Physical Description: Book
Language: English
Creator: Mouraenko, Oleg A.
Publisher: Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Place of Publication: Gainesville, Fla.
 Record Information
Bibliographic ID: UF00091375
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Table of Contents
    Half Title
        Half Title
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
        Page ix
    Key to symbols
        Page x
        Page xi
    Abstract
        Page xii
        Page xiii
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    Estimation of turbulence
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
    Bedform measurements
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
    Relationships between turbulence, suspended sediment concentrations and bedforms
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
    Conclusion
        Page 61
        Page 62
        Page 63
    MATLAB programs for filtering of MTA data
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
    Short ripples during the SandyDuck '97 experiment
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
    Reference
        Page 79
    Biographical sketch
        Page 80
Full Text




UFL/COEL-2001/016


FIELD MEASUREMENTS OF TURBULENCE AND
WAVE-GENERATED RIPPLES







by




OLEG A. MOURAENKO


THESIS


2001
















FIELD MEASUREMENTS OF TURBULENCE AND WAVE-GENERATED RIPPLES


By

OLEG A. MOURAENKO















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

UNIVERSITY OF FLORIDA


2001





























In loving memory of my mother.
















ACKNOWLEDGMENTS


I wish to express my gratitude to Daniel M. Hanes, the chairman of my graduate

committee, for the support and freedom granted to me while pursuing my research

interests. I also thank the members of my graduate committee, Robert G. Dean and

Robert J. Thieke, for their great teaching and unending assistance.

I thank my parents for their love and trust. I thank my friends for their support,

encouragement and help. I thank the faculty members for their knowledge and attention. I

also thank the students with whom I have studied and for the great times we were shared.

Special thanks go to Vadim Alymov, Vladimir Paramygin, Yeon Sihk Chang,

Jamie Macmahan, Chris Bender, Justin Davis, Becky Hudson, Helen Twedell, Sidney

Schofield, Jim Joiner for their help, support and patience.

I thank the Coastal Science Program, US Office of Naval Research provided the

financial support for this research through the NICOP and NOPP programs.

















TABLE OF CONTENTS

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 ut-off M ethod......................................... ...................................................... 12
PV M ethod ................................................................................................... 13
V V M ethod....................................................................................................... 14
Comparison of Cut-off, 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

3-1: Filter description. ............................... ............................................................... 38

4-1: Coefficients of relationship between TKE and first moment of concentration for
different A D V 2 elevations. ....................... ..... ...... ....................................... ... 55

4-2: Coefficients of relationship between TKE and short ripple height for different
A D V 2 elevations. ............................................................ .................................. 57

4-3: Coefficients of relationship between TKE and short ripple length for different
A D V 2 elevations. ................................................................................................. 58

4-4: Coefficients of relationship between TKE and steepness of short ripples for
different A D V 2 elevations. ................... ..... .......... ........................................ ... 58

B-l: Analysis of short ripple form and migration...................................... ............. 70

B -2: Short ripple dim ensions....................................................................................... 74
















LIST OF FIGURES


Figure Page

1-1: Beach profile on 09/27/97 and location of frame. Coordinate system relative to
coastline....................... ........ ... .......... ............... .... ........................ . . ..... 3

1-2: Instrument setup and dimensions....................... ................................................ 5

1-3: SandyDuck'97 offshore instrument setup.......................................... ............... 6

2-1: Instrum ent setup and dimensions. .................................................... ............... 8

2-2: The definitions of 'cut-off frequency as a point of inflection of cross-chore (U)
velocity spectrum and point of steep descent of coherence function.................... 13

2-3: Spectra and coherence functions. Elevations of sensors above the bed: 15.8 cm for
ADV1 and 9.5 cm for ADV2; Hno 2.1 m, Tpeak 11.6 s, peak 78.50................ 16

2-4: Spectra and coherence functions. Elevations above the bed: 41.3 cm for ADVI
and 35.0 cm for ADV2; H,,,o 2.2 m, Tpeak 8.5 s, Opeak 64.6. ............................ 17

2-5: Separation of wave and turbulent components in frequency domain by PV method
(left plots) and VV method (right plots). Elevations of sensors above the bed:
15.8 cm for ADV I and 9.5 cm for ADV2; Ho 2.1 m, Tpeak 11.6 s, peak -
7 8 .5 ...................... .. ................. .......................................................................... 1 8

2-6: Separation of wave and turbulent components in frequency domain by PV method
(left plots) and VV method (right plots). Elevations above the bed: 41.3 cm for
ADV1 and 35.0 cm for ADV2; H,o0 2.2 m, Tpek 8.5 s, peak 64.6. ................ 19

2-7: 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

2-8: Comparison of cut-off, PV and VV methods of estimation of TKE for 2 Hz data... 22










2-9: Time series of turbulent velocity components. Elevations above the bed: 14.3 cm
for ADVI and 8.0 cm for ADV2; Ho 1.2 m, Tpeak 12.8 s, 0pek 83............... 26

2-10: 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

2-11: Significant wave heights and mean values of frame tilts during the SandyDuck'97
experim ent .......... ........................... ........ ..... ....................................................... 29

2-12: Significant wave heights and STD of frame tilts during the SandyDuck'97
experim ent.................................. ....................................................................... 30

2-13: 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

3-1: MTA structure and dimensions with an example of bedform profile..................... 33

3-2: Data from transducer #33, test #1. Despiked raw data points and their histogram... 35

3-3: Run #30 of Sandy Duck 97 data for transducer #33. Despiked raw data points and
data after applying filters.......................... ........................................................ 36

3-4: Histogram of percentage of removed data point............................................... ... 39

3-5: Magnitude and impulse response functions of FIR lowpass filter of 31 order with
cutoff frequency 2/30. .......................................................................................... 40

3-6: Raw and despiked signal (top), and filtered ofdespiked data (bottom). (*) FIR
lowpass filter of 31st order; (**) elliptic IIR lowpass filter of 5th order.................... 41

3-7: Approximation of ripples dimensions for one profile from run #30....................... 45

3-8: Approximation of ripples lengths by three methods for run #30.......................... 47

3-9: Comparison of methods of ripples lengths approximation ................................... 48

3-10: Approximation of ripples heights for run #30.................................. ............. .. 49

3-11: Comparison of methods of ripples heights approximation.....................................51

4-1: Relationship between TKE and first spatial moment of concentration (1) ............ 54

4-2: Relationship between short ripple height (HSR) and TKE for different elevations of
ADV2 (hADV2): R correlation coefficient, N- number of data points ................. 56










4-3: Relationship between short ripple length (LsR) and TKE for different elevations of
sensor (hADV2): R correlation coefficient, N- number of data points ..................... 57

4-4: Ripple crest positions, TKE, mean concentration and wave envelope for run #30:
start at 256.3589 in Julian days. ......................................... ... ........................... 59
















KEY TO SYMBOLS


(ax,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
[ML-3] 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
Unit-impulse 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
Cross-spectral density function


[L2T-1]
[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
Cross-shore velocity component
Long-shore 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
Cross-shore, long-shore 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 long-shore
direction
Mean value
Standard deviation
Variance
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

FIELD MEASUREMENTS OF TURBULENCE AND WAVE-GENERATED RIPPLES

By

Oleg A. Mouraenko

August 2001


Chairman: Daniel M. Hanes
Major Department: Civil and Coastal Engineering

The SandyDuck'97 experiment data set was analyzed to estimate the intensity and

frequency content of turbulence near the seabed in the nearshore region and to obtain the

bedform dimensions at the position of measurements. The measurements of

hydrodynamics were obtained with two acoustic Doppler velocimeters (ADV) and a

pressure sensor in water depths of approximately 4 meters under a variety of wave

conditions, with seabed conditions ranging from flat to rippled.

Three previously published techniques of separation of turbulent and 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 'cut-off

frequency method and the best estimation of turbulence was provided by a method based

on coherency between the signals from two velocity sensors that were separated in space.










A new filtering technique was developed to obtain a better estimate of short wave

ripples. Several methods were used to obtain the ripple scales. The accuracy of ripple

height measurements was found to be less than 2 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 high-resolution velocity

sensors. Some factors that complicate the measurement of turbulence intensity in the field

include surface waves and the topography of the seabed. Different techniques are

commonly used to separate the turbulent components of velocity from fluctuations

induced by surface waves. Three such techniques are applied and evaluated here.

The intensity and frequency content of turbulence near the seabed in the nearshore

region have been estimated from field measurements from SandyDuck'97 by using three

different methods: cut-off, PV, and VV. The cut-off method uses a 'cut-off frequency as

a criterion of separation of wave and turbulent components of velocity. This is a widely

used technique (e.g. Kos'yan et al., 1996).

The PV method uses the coherence function between pressure and velocity to

separate turbulence from waves (for example, see Wolf, 1999). Linear wave theory

provides the relationship between pressure and velocity for wave-induced component.

This method does not incorporate the effect of nonlinear waves or a sloping bottom. The

VV method (Trowbridge, 1998) is based on measurements of velocity from two sensors,

separated from each other by the distance much smaller than the surface wavelength but







2

larger then the correlation scale of turbulence. The coherence between sensors is then

assumed to reflect wave induced motion.

Acoustic Doppler velocimeters (ADV) were used for velocity measurements

during the SandyDuck'97 experiment. Voulgaris and Trowbridge (see Voulgaris and

Trowbridge, 1998) verified this type of instruments for turbulence measurements by

comparison with laser Doppler velocimeter (LDV). ADV showed a low noise level and a

good agreement with turbulence measurements by LDV.



Bedforms

The presence of bedforms on the seabed affects the turbulence intensity, primarily

through the process of flow separation.

Alymov (1999) and Hanes et al. (2001) analyzed the bedforms during the

SandyDuck'97 experiment and found two types of ripples. Long wave ripples (LWR)

with lengths 35-250 cm and short wave ripples (SWR) with lengths 3-25 cm were both

found to be present. However, SWR were only found in 31 runs from 164, and for 111

runs a flat bed conditions were identified. This low occurrence of SWR might have

resulted because the measurement and analysis techniques did not have sufficient

resolution. Therefore a new filtering procedure has been developed to make more

accurate evaluation of SWR for SandyDuck'97 bedform measurements. Due to better

accuracy of the new procedure, SWR were found present in most in most cases. Visually

flat bed conditions were found only during 71 runs, and the existence of SWR has been

established for 54 cases. The time resolution of new filtered data also provides the

opportunity to study some short time-related effects. The migration of ripples, the











appearing and disappearing of ripples under wave groups, the reconstruction of ripple

shape, and the variation of linear scales can now be analyzed.



Summary of the SandyDuck'97 Data Set

The SandyDuck'97 experiment took place in Duck, NC at the Army Corps of

Engineers Field Research Facility from September 11 to November 10, 1997.

Measurements include hydrodynamics, bedforms, profiles of suspended sediment

concentrations, video images, and some other parameters. The total duration of all

records is 44 days, which were made in various wave conditions, including several storm

events.



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
Cross-shore distance, m


Figure 1-1: Beach profile on 09/27/97 and location of frame. Coordinate system relative
to coastline.



A frame with instruments mounted on it was placed by scuba divers at a distance

about 390 meters away from the shoreline and 1000 meters along the shoreline according

to the FRF coordinate system. The depth at the site location was about 3.5 meters at low










tide. The beach profile with the frame position and coordinate system in (x,y)-plane are

shown on Figure 1-1.

The acquisition system used in the SandyDuck'97 experiment (see Thosteson,

1997) allowed measuring and recording data from several instruments simultaneously.

All data were collected with one of three sampling frequencies: 1, 2, or 4 hertz. The data

from each run were stored in several 34 minutes files. These data include (see also

Figure 1-2):

3D velocity measurements from two ADVs (acoustic Doppler

velocimeter);

Pressure measurements;

One-dimensional vertical profile of suspended sediment concentrations

from 1, 2.25, and 5 MHz ABS (acoustic backscatter);

Tilt and compass data.

Bedform measurements from a multiple transducer array (MTA).

One-dimensional measurements of bedforms were carried out using 64-element

MTA (see Jette and Hanes, 1997). The highest time resolution for MTA data was 0.5 Hz

or one profile per 2 seconds. Other rates were sometimes used to increase the length of

the record. The MTA data were collected separately from hydrodynamic data, but were

synchronized in time. Unfortunately, the bedform measurements are not available for all

of hydrodynamic data due to both sampling limitation and biofouling of the MTA.















Pressure Sediment
concentrations
I I


Figure 1-2: Instrument setup and dimensions.



The offshore instrument setup and dimensions are shown in Figure 1-3. 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 1-3: 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 cross-shore direction. Sampling volumes of ADVs are located

in 18 cm from the acoustic transmitters. The pressure sensor had an elevation of 34.7 cm








8


above the position of the ADV1 's sampling volume. The setup and dimensions of

instruments are shown on Figure 2-1.


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 2-1: Instrument setup and dimensions.



Voulgaris and Trowbridge examined the suitability of acoustic Doppler

velocimeters (ADV) for turbulence measurements (see Voulgaris and Trowbridge, 1998).

They found good agreement with measurements, made by laser Doppler velocimeter,

stated very small errors (within 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

(cross-shore) and transversal (long-shore) directions. But using the TTC sensor (Tilt-

Temperature-Compass) it is possible to estimate rolling (along cross-shore direction) and

pitching (along long-shore direction) oscillations. These oscillations could distort the

measurements of turbulence. The analysis will be made later in this chapter.










Separation in Frequency Domain

Initial Terms and Definitions

A component of velocity vector can be represented as a sum of sinusoidal

fluctuations with different frequencies and phases. Fourier transform is commonly used

to obtain such decomposition. Let x(t) be a signal, measured with time t. Then its direct

Fourier transform X(f) as a function of frequencyfand inverse transform are given by

Equations 2-1':

+0o
X(f)= F{x(t)}= Jx(t)e-'2,fidt

+(2-1)
x(t) = F-'{X(f)}= X(f)e'2l/fdf


An average energy of signal is equal to


P = lim- {x(t}2dt (2-2)
S- 2T J
-r

A spectral density function of signal x(t) is defined by


S.(f)= lim X(f)l, f (- 0,+00) (2-3)


According to Parseval's theorem:


{x(t)}2dt= iX(f)2 df (2-4)


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 1-0
P= S, ()df = S,.(f)df (2-5)
0

To obtain an average energy of fluctuations for a frequency range the integral 2-5

should be evaluated only within this range:

/2
{fe[f,f2]}= f-(f)df, ff2>0 (2-6)


Let two signals x(t) and y(t) have their Fourier transformations X(f) and

Y(f) correspondingly. Then the cross-spectral density function between these signals is

defined by


S (f) = lim X(f)Y(f)= C,Y(f)-iQ.(f), f (-~o,+oo) (2-7)
7~- T

In general the cross-spectral density function is a complex function. The real part

C,,(f) is called the coincident spectral density function or cospectrum, and the

imaginary part Q,,(f) is called the quadrature spectral density function or

quadspectrum.

Define the coherence function by


(f) = (2-8)
f Sxx (f ) SYY (f)

The coherence function, defined by the equation above, is a complex function, as

well as the cross-spectral density function. Usually, a square of the magnitude of 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 (2-9)

The phase angle of coherence function is equal to


arg (-,(f))=-tan' Yj) (2-10)
I,- ( f\

The velocity vector V could be written as a sum of three components:

V= +V+V' (2-11)

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:

Cut-off- based on 'cut-off frequency between wave and turbulent

fluctuations;

PV based on coherence function between pressure and velocity signals;










*VV based on coherence function between velocity signals from two

sensors separated in space.



Cut-off Method

This is the most simple technique to separate the turbulent component of velocity

from wave-induced motion. The only problem is to find the 'cut-off frequency, which

separates two types of motion. Two different approaches are commonly used to find it.

One is based on assumption that the velocity spectrum, plotted in log-log scale, changes

slope at this frequency. Another way involves the assumption that the velocity and

pressure are coherent only at wave frequencies, but noncoherent at higher frequency

fluctuations. Thus the 'cut-off frequency could be defined as the frequency of steep

descent of the coherence function between pressure and velocity. Examples of application

of two definitions are shown on Figure 2-2. In all field measurements to be presented

these definitions give almost the same results.

The point of inflection of the velocity spectrum curve was found by fitting two

lines. Both lines are best-fitted lines for the high frequency part of the spectrum and for

the wave part of the spectrum. The slope of the spectra characterizes the rate of energy

dissipation.

For the SandyDuck'97 experiment data the mean value of the 'cut-off frequency

was found to be 0.5 Hz with standard deviation of 0.1 Hz. It was estimated from 173 data

records with sampling frequency of 4 Hz of all three components of velocity from both

ADVs.







13


0.6

100 0.5
E
_~^0. 0.4

C 10 a) 0.3
CO 0_
0.2

10-4 .... ... 0.1

0
10-1 100 10-1 100
Frequency, Hz Frequency, Hz


Figure 2-2: The definitions of 'cut-off frequency as a point of inflection of cross-chore
(U) velocity spectrum and point of steep descent of coherence function.



The turbulent kinetic energy (TKE) was calculated using Equation 2-6, wherefi is

a 'cut-off andf2 is Nyquist frequencies. The valuesfr=0.05 Hz andf2='cut-off were

used for estimation of wave kinetic energy.



PV Method

The value of the coherence function between pressure and velocity signals is high

at wave frequencies and very low at higher frequencies (see Figure 2-2 as example). This

property is commonly used to separate turbulent and wave components of velocity (see

Wolf, 1999). The coherence function for PV-method (Pressure-Velocity) is given by

Equations 2-12:

y, (f)=0, 0< f <0.05

S,, (f) 2 (2-12)
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 2-13 and 2-14.

Sv = yVSv,, f > 0 (2-13)

Sv, = (1 7)Sv,, f > 0 (2-14)

where superscripts Wand T refer to waves and turbulent parts correspondingly.

The kinetic energy is estimated using Equation 2-6 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 2-1 the distance between two ADVs is 53 cm, which is much smaller than the

wavelength. The correlation scale of turbulence will depend on many parameters

including the magnitude and frequency of flow fluctuations. The significant velocity,

defined as 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 2-15:

,,(f) =0, 0< f <0.05

S ,, 2 .5 (2-15)
S(f)SV)(f) f 0.05


where V is a cross-shore, long-shore 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 2-16 and 2-17.

S: = r, SV,, f > 0 (2-16)

S, = (- Yv,2)SV,, f > 0 (2-17)

The kinetic energy is estimated using Equation 2-6 with f/=0.05 Hz and

f2=Nyquist frequency for both waves and turbulence.



Comparison of Cut-off, PV and VV Methods

The coherence functions and spectra after application of PV and VV methods are

shown on the next four figures. Figure 2-3 and Figure 2-4 demonstrate the initial spectra

of pressure and velocity components on the left plots. The coherence functions between

pressure and velocity and between two velocity signals from different sensors are shown

on the right plots. The main difference between two figures is in elevation of ADVs

above the seabed. For Figure 2-3 the elevations were 9.5 cm for ADV2 and 15.8 cm for

ADV1. And for Figure 2-4 they were 35.0 cm and 41.3 cm for ADV2 and ADVI

correspondingly.
















100 UADV1 - ADV1 vs. Pres
SUADV2 UADV2
- Pressure - ADV1 ADV2

S10-4 ..

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

10-4 ..'. . :- .
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

10-4 0.5


0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz



Figure 2-3: Spectra and coherence functions. Elevations of sensors above the bed:
15.8 cm for ADVI and 9.5 cm for ADV2; 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 cross-shore, Vis a long-shore


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 10-4A

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

10-4 .
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


1-4 ~


0 0.5 1 1.5 2 0 0.5 1 1.5 2
Frequency, Hz Frequency, Hz



Figure 2-4: Spectra and coherence functions. Elevations above the bed: 41.3 cm for
ADVI and 35.0 cm for ADV2; H,,o 2.2 m, Tpeak 8.5 s, Opeak 64.6.




The coherence function between cross-shore velocity and pressure (PU

coherence) is very high on wave frequencies (0.05 0.5 Hz). The situation is very

different for long-shore components of velocity. The PV coherence is about half

compared with the VV coherence at the peak wave frequency and is ever less for the rest

of wave frequencies.
















0U
10 : ADV2
SWaves
- TKE



10-4

0 0.5 1 1.5 2


U)
C 0
o 10





- 10-4

10-




10-4
. 0 0.5

10)2





10- --


-v
ADV2
SWaves
TKE






1 1.5 2


100 ADV2
Waves
- TKE


10-4

4-4 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 2-5: Separation of wave and turbulent components in frequency domain by PV
method (left plots) and VV method (right plots). Elevations of sensors above the bed:
15.8 cm for ADVI and 9.5 cm for ADV2; 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 cross-shore velocity. That difference could be explained by small elevation of


sensors above the seabed: inside the turbulent boundary layer the intensity of turbulent


E


*4 *1 C


2









19



motion greater than the intensity of wave-induced 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 2-6: Separation of wave and turbulent components in frequency domain by PV
method (left plots) and VV method (right plots). Elevations above the bed: 41.3 cm for
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 2-3).


C,
E
U,
C 0
0 100






_ 10-




10-
0-
c

- 10-4

a,
CO,

10'





10"










ADV2 was closer to the bed and the TKE is greater at high frequencies. Figure 2-4

indicates that the velocity spectra are about the same, when the sensors were located 35.0

and 41.3 cm above the bed.

Figure 2-5 and Figure 2-6 show the spectra of wave and turbulent components of

velocity from ADV2. The spectra on the left plots were calculated using PV method and

on the right using VV method. There are several evident differences:

The slopes of the turbulent spectra at wave frequencies for the PV method

are different from the slope at high frequencies.

At a 9.5 cm elevation the turbulent spectrum of the long-shore component

of velocity has larger values at wave frequencies than the spectrum of the

wave component. At 35.0 cm elevation both turbulent and wave spectra

wave are nearly the same. This is a result of small values of PV coherence,

which was mentioned before.

For PV method the magnitude of turbulent spectra for horizontal

components differs from vertical by about a factor of 10.

The turbulent spectra from VV method of all components of velocity have

nearly the same shape and magnitude, which supports the hypothesis of

homogeneous turbulence.

The turbulent and total spectra of the vertical component of velocity are

about the same. Only a small part of the energy result from wave motions;

most of the vertical fluctuations are caused by near-bed turbulence.

The full turbulent kinetic energy, calculated by two methods, is shown on

Figure 2-7. The plots show the TKE at 9.5 and 35.0 cm elevations above the seabed











correspondingly. PV and VV methods provide the same results on high frequencies,

because coherence functions in both cases were very low at these frequencies. However,

in the wave frequency range the TKE estimated by PV method is much higher than the

TKE estimated using the VV method. Moreover, the slope of the PV spectrum changes,

then the curve goes through 'cut-off frequency. There is no such inflection on PP

spectrum.

Significant wave heights for both cases were almost the same and the bottom had

small ripples with 45 mm length and 5 mm height. PV method shows approximately the

same magnitudes of TKE at wave frequencies, but VV method reflects the difference in

elevation.


a) b)

PV -- PV

100 1 :0 . . ..100 ..... .

E IE

U) U)
C+J> 2 C+j> -2
) 10 -- U) 10





10-4 10-4 "
102 10 10-2 10
Frequency, Hz Frequency, Hz


Figure 2-7: Full turbulent kinetic energy from PV and VV methods.
a) Elevation of ADV2 is 9.5 cm; H,,o 2.1 m, Tpeak 11.6 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
Cut-off

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 10-3


1 2 3 4
Cut-off x 10-3


1 2 3 4
Cut-off 10-3


Cut-off x0-3
x 10


0 0.005 0.01 0.015 0 0.005
VV VV


0.015


Figure 2-8: Comparison of cut-off, 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 2-8. The estimated TKE is plotted in pairs by methods. The

functional dependencies between methods were approximated by linear regression. The

correlation coefficients (R) were calculated as well.

To summarize the results of the comparison several conclusions can be made:

All three methods of separation of turbulence from wave motion provide

qualitatively similar results, which follows from high correlation

coefficient between estimations of TKE by the methods described.

The 'cut-off method estimates the minimum amount of total TKE, which

is approximately 5 times smaller than from VV-method.

The PV method overestimates the total TKE in the long-shore direction

and overestimates the full TKE. The TKE is estimated 6 times larger than

by VV method and 30 times larger than by the 'cut-off method. This is

probably because a large amount of energy is the wave frequency band is

erroneously identified as turbulence.

The VV method provides the best estimation of turbulence in the wave

frequency band. The power spectrum of the turbulence has the same slope

over both wave and turbulent frequencies.











Separation in Time Domain

The methods described in previous section can be used for the separation of wave

and turbulent components of velocity in the time domain. Let x(t) be an initial signal and

X(f) its Fourier transformation, given by Equation 2-1. Then high or low frequency

components of the signal x(t) can be extracted as a convolution integral of signal with

some weighting functions h(r) and 1(z):


x, (t)= fh(r)x(t- T)dt
(2-18)
x, (t) = l(r)x(t r)dt


Fourier transform of convolution integral is a product of Fourier transforms of the

signal and weighting function:

F{x,(t)}= H(f)X(f), H(f)= F{h(t)}
(2-19)
F{x,(t)}= L(f)X(f), L(f)= F{l(t)}

The Fourier transforms H(f) and L(f) of the weighting functions will be

defined using step functions for 'cut-off method and coherence functions for PV and VV

methods.

Let f. be a 'cut-off frequency, then

L(f) =, 0.05< f< (2-20)
L(f) = 0, If > f,

H(f) = 1- L(f) (2-21)

For PV and VV methods the functions H(f) and L(f) are given by









L(f)=O, 0< Jf 0.05
(2-22)
L(f) = (f), If > 0.05

H(f) = 1- L(f) (2-23)

where y(f) is a coherence function, given by Equation 2-24 for PV method and

Equation 2-25 for VV method:


( (f)=) (2-24)
VfS ,, Sp (f)


v, v,2 (f) = VsIV2 (f) (2-25)
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 2-9 and Figure 2-10

versus cross-shore 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 cross-shore 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 2-9: 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 2-10: 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 2-9 shows that close to the bottom the difference in intensity of the

directional component of the turbulence significantly varies with elevation of sensor. The

ratio of vertical to horizontal amplitudes depends upon elevation above the seabed. The

distortion of the ellipse (ratio a/b) in the vertical plane is greater than in the horizontal


plane when the sensor is closer to the bottom. However, in the horizontal plane the


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 2-10) the ellipses are nearly circles for all projections. This means that

turbulent fluctuations have amplitudes that are approximately equal in the horizontal

directions.



Errors in Measurement of Turbulence due to Frame Vibration

The frame and the instruments mounted on it may vibrate under the wave forcing.

The amplitude and frequency of this vibration can affect velocity measurements and

therefore our estimations of turbulence. There are no measurements to estimate the

amplitude of longitudinal (cross-shore) and transversal (long-shore) vibration. However,

they can be evaluated indirectly from tilt measurements by the TTC sensor.

The TTC measures three angles: 0- in (x,z) -plane, 0- in (y,z) -plane, and 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 2-12. Both (0, 0) angles show the instability of the frame during the












experiment. The frame vibrated under waves and the amplitudes of all vibrations are


clearly related to the wave activity; and the largest values are reached during the storms.


/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 2-11: 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, =AO-r
aj = A(Z*r


(2-27)


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


The rates of vibration are given by Equations 2-28.


dax dO da d d
__A_ r; __ r--
dt dt dt dt


The spectrum of vibration rates can be calculated as follows:


(2-28)


(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) (2-29)

The results are shown on Figure 2-13. The errors generated by the frame vibration

at all frequencies are much smaller (1-2 order in magnitude), than the turbulent

fluctuations. Thus, the frame vibration did not affect turbulence estimations significantly.


0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

b)


E 100
0
C
_0
o







S -10
0. 10-
c 0

0

S100

0 0




_ 10
C 0
0
C





ca 10
(n 0


Figure 2-13: 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 one-dimensional measurements of bedforms. The

MTA is an acoustic instrument. It consists of a line of acoustic elements, situated with

fixed spacing. The entire array has three MTAs. The middle 32-element 50 cm length

MTA has 5MHz-transducers with 1.5 cm spacing between them. Each transducer has an

acoustic footprint on the seabed of approximately 2.5 cm if the array is 50 cm above the

seabed. Two other 100 cm length MTAs have 16 transducers with 6 cm intervals. The

frequency of transducers is 2MHz and the footprint is 4.5 cm for 50 cm elevation of

instrument above the seabed. The middle MTA has better spatial resolution, because of

higher operating frequency and overlapping of footprints of adjacent transducers.

Figure 3-1 shows dimensions and order of transducers of the MTA. The dots on the bed

profile, shown on the figure, correspond to the centers of the footprints of transducers

along the measured profile.

The minimum time resolution of the instrument is one profile every two seconds.

This limit results from using only one circuit to as a transceiver for all the transducers.

Therefore some time is needed for switching between two successive transducers.












MTA3 MTA1 MTA2

1 16 17 48 49 6 I4
6.0cm. 1.5cm. 4.0cm.









98.1cm. -- 50.0cm.- 98.1cm.

Figure 3-1: MTA structure and dimensions with an example of bedform profile.



The MTA has a flexible control system. Most of settings can be changed remotely

during the experiment. Each MTA has its own data logger, but the data can be collected

on a remote computer as well. The capacity of the internal loggers is large enough to

collect 2 hours of data with a sampling frequency of 0.5 Hz.

The MTA was designed to measure bedforms of two different scales. Ripples

with lengths from 12 cm up to 238.5 cm are measured by the entire array. Ripples with

lengths from 3 up 46.5 cm are discerned by the central MTA only.

Unfortunately, like any other measuring systems the MTA produces errors in

measurements. Understanding the possible sources of errors might help to develop better

data filtering algorithms and evaluate the precision of the instrument.

The errors in MTA measurements can be separated into three groups:

System errors related to the usage of acoustic elements, system design,

and methods of signal preprocessing by the MTA before recording the

data.










Environment related errors caused by influences specific to the

environment, such as the mobility of the bed, the presence of suspended

sediments, or the vibration of instruments.

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 3-2 shows an example of despiked data record from

Test #1 (see Alymov, 1999) for transducer #33. On the right plot the histogram is shown

with normal probability density function curve with mean of 316.9 mm and standard

deviation of 1.1 mm. This test was conducted in still water without suspended sediments,

and the elevation of the 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 I-In


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 3-2: Data from transducer #33, test #1. Despiked raw data points and their
histogram.




Two additional lines on the left plot of Figure 3-2 present two results of data

filtering. One of the filtering methods was used in previous works (see Jette, 1997;

Alymov, 1999). It is based on taking the histogram mode, calculated for each group of

successive data points. On the figure it is shown by a dashed line and called modal filter.

The lowpass filtering is a new method, which was developed to improve previous filter. It

will be described later.


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 'false-bed' response from higher elevations. But this kind of data points

usually looks like spikes, and can be successfully removed. The motion of sediments near

the bed causes the biggest problem. For some sets of data they do not show position of

the bed, which could be expected for particular flow conditions. For example, the

measured position of the seabed rises with increasing sediment concentration.



Run# 30: start = 258.3439 end = 258.3485; At = 2.0s xducer #33
518 I
+ MTA data points
519 - Modal filter
Lowpass filter
520- + + +

E521- + + + + +
522 + + 1++ 4+++ \-H+ + + +
I--
522 I-4 +4 + 4+H +- 44 ++ ++ 4+4-+ +-


E
8 524- H- /i-W4-i 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 3-3: Run #30 of Sandy Duck 97 data for transducer #33. Despiked raw data points
and data after applying filters.










Figure 3-3 contains the same information as Figure 3-2, except the data were

taken from Run #30 of the Sandy Duck'97 experiment, when the bed position was nearly

stable. Similar to the first case, the distribution of data points is approximately normal,

but now the standard deviation is larger.

The MTA measures 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 12-18 cm could be

estimated correctly by full MTA only if the same scales appear at the middle MTA (see

Alymov, 1999).



Filtering of Raw Data

The raw data consist of time series of distances between the MTA and seabed for

each transducer. The data from the three MTA's were collected separately, so

synchronization of records in time was made first.

Let's assume, that the total error, E8,,, is produced by several independent sources

of errors:

E,,, = Eo + + 2 + 3 +... (3-1)

where each of E, is an error of a specific type. In general case all these errors could

correlate with each other, making relations more complex due to non-linearity, but for

current analysis these types of errors will be neglected. The linearity of the error sources










means that each error could be removed by applying of certain filter successively. A set

of filters, used for current work, includes despiking and digital filter and is followed by

restoration of removed data points.


Table 3-1: Filter description.
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 N-element 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 3-1 describes all the filters that were applied to the raw MTA data and

particular settings for Sandy Duck'97 data. The column 'Routine' has a name of function

that reproduces the algorithm. All the functions were written in Matlab, and their listings

are included in Appendix A.

The first four filters remove prominent values from the data. The threshold for

instantaneous change in the bed elevation was chosen as 6 mm per sampling period (2, 3,

4, 7, 8, 9, 10, 12, 60 seconds). It was possible, because the mobility of the seabed was

small. Block processing is needed for bad data. If standard deviation for the block is

large, then the error is comparable with height of measured bedforms. It was found

experimentally, that the threshold value of 10 mm for standard deviation is acceptable for

this data set.

Figure 3-4 presents a histogram of percentage of removed data points from the

data. The mode of histogram is 10%. The histogram also shows, that about 63% of all

runs have 15% or less data points, removed by despiking. The runs, which have more

then 40% of removed data, are usually bad.



164 MTA data files; Mode = 10%


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 i-i F- r1


0 10 20 30 40 50 60 70 80 90
Percent of removed points

Figure 3-4: Histogram of percentage of removed data point.











For digital filtering the finite impulse response (FIR) lowpass filter with

Hamming window was used. The order of filter was 31 and normalized cutoff frequency

was 2/30. The main characteristics of this filter are shown on Figure 3-5.


FIR 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 3-5: Magnitude and impulse response functions of FIR lowpass filter of 31 order
with cutoff frequency 2/30.



The FIR filter was chosen because of linear phase response and larger transition

width in magnitude response. The phase shift was removed by applying the filter in both

directions. That resulted in squared magnitude response. The other filters with different

parameters were tested. The bottom plot on Figure 3-6 shows an example of applying of

elliptic infinite impulse response (IIR) filter of order 5 with cutoff normalized frequency

of 2/20. Taking into consideration the analysis of error sources and expected accuracy










from the previous section, it is hard to evaluate, which filter provides the better results.

As follows from Figure 3-6 the difference between two trends is about 1 mm, which is

comparable with the magnitude of system error. So both trends are close in terms of

expected error. On the other hand, the large cutoff frequencies lead to appearance of

higher fluctuations for one transducer, which are not correlated with the data from the

neighbor transducers. That results in random fluctuation of full MTA profile. The FIR

filter with parameters described above provides more reasonable results.


Run# 78: start = 270.5433 end = 270.5502; At = 3.0s xducer #63


0 100 200 300 400 500


0 100 200 300 400 500
Time, sec


Figure 3-6: Raw and despiked signal (top), and filtered of despiked data (bottom). (*) FIR
lowpass filter of 31st order; (**) elliptic IIR lowpass filter of 5th order.



Figure 3-6 shows an example of the filtering process. Raw and despiked data are

shown on the top plot. Raw data (thin line) has a number of large spikes. Those spikes










were successfully removed by despiking. The dots present the remaining data points.

Those points are shown on the bottom plot together with trends, calculated by applying

three different filters. The thick line presents a result of filtering, which will be used in

estimation of dimensions, mobility and migration of bedforms in the following sections.

The method of filtration, used in previous works (Jette, 1997; Alymov, 1999), was

based on the modal distance to the bed from the group of several data points, usually 10.

It was noted before, that the data from the MTA is recorded with 1 mm step, although the

true position of the bed could be inside the 1 mm interval. Such discreteness of data

allows this method to define the bed position well, but only on weakly noisy data.

Figure 3-2 shows the result of filtering by the modal filter (dash line) for a stable bed.

The jumps up to 2 mm of the trend show instability of this method in presence of noise.

To get better approximation more data points are required for mode calculation. For the

raw data with 2 seconds sampling filtered record will have at least 20 seconds time

resolution, which is not enough for study of migration and mobility of bedforms under

the waves.

The 'lowpass filter' method has several advantages:

Higher stability. The prominent points have less influence on a trend.

Higher accuracy. The system error is about normally distributed. The filter

removes noise more accurately (see Figure 3-2 as example).

Higher time resolution. The result of filtering has the same time step as

initial raw data.

Smoothly changing data. The bed changes gradually, but not stepwise.

The new method approximates a stable bed position ignoring short jumps.










The accuracy of filtered data could be evaluated only in comparison with other

data or from the expected behavior of the measured bedforms under flow effects. In the

section below 'Short Wave Ripples' it will be shown, that migrating ripples with height

of 2 mm are well distinguishable. So the accuracy of the measurements is less then 2 mm

in the vertical scale.



Short Wave Ripples

Dimensions

Short wave ripples (SWR) with lengths of 34-150 mm and heights of 2-24 mm

were observed during the SandyDuck'97 experiment (Hanes et al, 2001). Only 22% of

runs have SWR, during other runs flat bed conditions were established. Their analysis of

dimensions was based on data filtered by 'modal filter' method. Using new filtration

algorithm, these results can be improved and ripple dimensions can be established in

most cases.

Dimension analysis was made for data from middle MTA only. The interval

between transducers is 1.5 cm, number of points is 32 and full length of profile is

46.5 cm. From each profile a best-fit parabolic trend was removed first. To increase the

precision, the data for each profile was interpolated on a 0.3 cm grid. There is no direct

method to evaluate bedform scales less than 1.5 cm from the MTA measurements;

therefore these scales were ignored.

The ripple lengths and heights were approximated. These types of dimensions

imply periodicity of bedform shape, which roughly can be reproduced by some periodic

function with certain parameters, for example sine function:












h(x)= H-sin 2x+b (3-2)
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 one-dimensional 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 one-dimensional ripples will

be the same as original, but the length will depend on angle between normal to the crest

and direction of cross-section line. In case of three-dimensional ripples, there is no way to

approximate their length. In spite of this, attempts to estimate ripple dimension were

made for each recorded profile.



Approximation of Ripple Lengths

Three different techniques were used to estimate ripple lengths:

Autocorrelation.

Distances between crests or troughs for each profile.

Mode of distances between crests or troughs for blocks of several profiles.

The autocorrelation function is defined as



-x
-X

or for discrete series

N-k
Chh(k)- = N Z h,h,+k (3-4)
=-I


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












(3-5)


for grid interval S.

If the profile shape is defined by Equation 3-2 then the autocorrelation function is


H 2 28 o
C,,, = -cos -
8 L


(3-6)


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 3-4.


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


k = k8










Figure 3-7 shows an example of interpolated profile on top plot and normalized

by variance autocorrelation function for this profile on bottom plot. The dashed line

indicates offset position of local maximum. The profile shape is highly periodic. This

property could be described by a value of normalized autocorrelation function at

maximum, which is equal to correlation coefficient between initial and shifted profiles.

The correlation coefficients for each profile were calculated also.

Two other methods are commonly used in of estimation of wavelengths of

periodic signals, which are based on distances between extremes. The positions of crests

and troughs were found as local minimums and maximums. Threshold for smallest

vertical deviation between two successive extremums was used. It was taken to be equal

to 0.2 where o-is standard deviation of profile. After the crests and troughs were found,

the mean of distances between successive crests or troughs was calculated as ripple

length. The usage of crests or troughs is defined by the amount of each. Also the

distances between crests or troughs were collected for blocks of 30 profiles for

calculation of their mode.

Figure 3-8 show time series of estimated ripple lengths by each of three described

methods. The crest positions on the top plot allow evaluation of the accuracy of the

methods. At the beginning, seven crests are initially seen, which give a length of about

66 mm. For eight crests at the end the length of ripples is about 58 mm. No one method

provides smooth variations of estimated quantity; all of them have spikes and scatter in

values. In spite of this, the approximations are very close to each other, and show the

tendency in changing of ripples lengths toward the end.












The correlation coefficients, shown on bottom plot, are larger, than 95% level of

significance for 30 degrees of freedom. Consequently, the ripples have highly periodic

shape. It is also supported by visual analysis. On the top plot two zones of ripples

instability could be distinguished at 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 3-8.



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 3-8: 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 3-9 presents

the results of comparison of three methods. Good correlation is found. Note, as follows

from the plots, the 'mode' method slightly underestimates the ripple lengths, compared

with 'mean' and 'autocorrelation' methods. The estimation of ripple lengths by mean of

distances between crests or troughs was taken to be basic for further analysis.


140
E
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 3-9: 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 crest-trough pair the difference in elevations was calculated and stored for

evaluation of the next parameters:

Mean of ripple heights for each profile.

Maximum of ripple heights for each profile.

Modes of ripple heights for groups of several profiles.

Significant heights for groups of several profiles.


Run# 30: start = 258.3589 end = 258.3844
Mean 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 3-10: Approximation of ripples heights for run #30.










The significant height is defined here as a mean of 1/3 of largest excursions for

each group of 30 profiles. The maximum and significant heights describe characteristics

of the most prominent ripples.

Figure 3-10 shows an example of ripple height approximations for the same data

as on Figure 3-8. In spite of stable pattern of ripples, their heights can change rapidly in

time. For the data shown, measured ripple height fluctuations have about 2 mm

magnitudes. Not only true bed motion could cause them, but also suspended sediments. It

was noted before, that on 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 3-11 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 3-11: Comparison of methods of ripples heights approximation.



The accuracy of ripple length and height estimations is highly dependent on scales

of real bedforms, which were measured by the MTA. For small ripples, the error of

approximation is high and could be compared with accuracy of measurements. Therefore

presence of ripples with heights of 1.5-2 mm could be shown only from other

information, like ripple migration. Otherwise, flat bed conditions should be concluded.







52


The results of analysis of short ripple forms (Table B-1) and estimated ripple

scales (Table B-2) are included in Appendix B. The ripple forms during each run were

analyzed visually base on changing in time of bedform profiles, measured by MTA. The

bedforms were stated to be two dimensional only if the profiles have sinusoidal form.

Otherwise the bedforms were referred to three-dimensional. In cases of flat bed two

characteristics were used. If there were no short ripples the 'flat' bed conditions were

stated, but if some spikes were present the bedforms were referred to 'noise'. Those

spikes were usually resulted from instantaneous sediment suspension.















CHAPTER 4
RELATIONSHIPS BETWEEN TURBULENCE, SUSPENDED SEDIMENT
CONCENTRATIONS AND BEDFORMS


Analysis of Relations

The purpose of this chapter is to develop relationships between turbulent kinetic

energy other parameters. The relationships between turbulent kinetic energy (TKE),

bedform scales and suspended sediment concentrations have been analyzed. All relations

were found in form of linear regression and analyzed for different elevations of velocity

sensor.

The importance of study and development of empirical relationships is

determined by complexity of theoretical description of such relations. The number of

relationships can be estimated from 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 (4-1)
0

The TKE was calculated by VV method (see Chapter 2). The relationship is given

by Equation 4-2 and demonstrated on Figure 4-1 for both ADVs. The coefficients were

calculated from 1347 data records of 2 Hz data, with each record covering 34 or 68

minutes of observations. The correlation coefficient is calculated to be 0.85.

logo, = a (TKE)/2 +b, a =23.4, b = -3.9 (4-2)

The first moment of concentration profile relates to potential energy of suspended

sediments. Thus, Equation 4-2 provides the relationship between kinetic energy of

turbulent motion and potential energy of sediments. The relation is not linear, and cannot

be explained by a simple transfer of energy from one type to another. That demonstrates a

complexity of real mechanisms of sediment suspension, which cannot be described from

simple energy balance.


ADV1 ADV2
0.1 I 0.1



0.01 ." 0.01 .... .



0.001 ........ 0.001 . ... . .

.: y = 24.4x-3.9 y = 23.4x-3.9
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 4-1: 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 4-2 is shown in

Table 4-1 for these fits.




Table 4-1: Coefficients of relationship between TKE and first moment of concentration
for different ADV2 elevations.
Elevation of Correlation Number of data
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 4-1 shows that the correlation coefficients are high at all elevations and the

coefficients a and b of Equation 4-2 do not vary much with elevations of ADV2.



TKE and Bedforms

Scales of short wave ripples were compared with turbulent kinetic energy. The

length and height of ripples were estimated as described in Chapter 3. TKE was

calculated for each record from ADV2 by VV method. The relationships between

turbulent kinetic energy and bedform scales have been found in the following form:


TKE= 10h (Hs )" or log,,(TKE)=alog,o(Hs,)+b


(4-3)













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 = -0.7x-4.7
R = -0.74
SN=298




S:
'


-2.5 -2
h D=17.0..18.0 cm


y = -0.3x-3.6
R = -0.29
-2.5 ,- ..*N =177

-3

-3.5

-4
-3 -2.5 -2 -1
hADV2=20.0..23.0 cm
-1
y =-1.1x-5.6
R = -0.69
N = 270
-2 .



':.


-3 -2.5 -2
logl0(HSR)


-1.5


-2

-2.2

-2.4

-2.6
-3


hADV2=15.5..17.0 cm
y = -0.6x-4.5
; R= -0.50
N=282







-2.5
hADV2=18.0..20.0 cm
y = -0.4x-3.6
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 4-2: Relationship between short ripple height (HsR) and TKE for different
elevations of ADV2 (hADv2): R correlation coefficient, N- number of data points.


(4-4)



(4-5)


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

:





i












Table 4-2: 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*10-4
18.0...20.0 -0.27 245 -0.36 -3.57 2.70*10-4
20.0...23.0 -0.69 270 -1.08 -5.56 2.78*10-
>23.0 +0.29 75 0.10 -2.00 9.94*10'-


hADV2 <15.5 cm
2
y = -1.8x-5.1
.: : R = -0.72
5 |p ,* .... N=298




4 ----------------

4
-1.4 -1.2 -1 -C
hADV2=17.0..18.0 cm
2
y = -1.8x-5.1
R = -0.55
5 : .:" . N=177


-1.4 -1.2 -1 -0.8
hADV2=20.0..23.0 cm
-1
y = -3.1x-6.6
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 4-3: 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 = -1.8x-5.0
R= -0.56
^ .3. N=282

:r'


-0.


y =-1.8x-4.9
R = -0.49
N N=245



I s': a


8











8


-0.


y = -0.0x-2.3
R = -0.02
N =75


* I: -


-0.8


-2.2

-2.4










Table 4-3: Coefficients of relationship between TKE and short ripple length for different
ADV2 elevations.
Elevation of Correlation Number of
ADV2, cm coefficient data point a
<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*10-5
20.0...23.0 -0.74 270 -3.07 -6.61 2.43*10-'
>23.0 -0.02 75 -0.02 -2.25 5.56*10-


Figures 4-2 and 4-3 show the relationship between turbulent kinetic energy and

height and length of short wave ripples correspondingly. The coefficients of best-fitted

lines are included into Tables 4-2 and 4-3. Table 4-4 shows the coefficients and

correlations coefficients for the relation between TKE and steepness of short wave

ripples. The relationship is given by Equation 4-5 and has the same form as for ripple

length and height.


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


TKE and steepness of short ripples for


Elevation of Correlation Number of 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*10-4
17.0...18.0 -0.13 177 -0.17 -3.05 8.81*10-4
18.0...20.0 -0.11 245 -0.19 -2.89 1.29*10-3
20.0...23.0 -0.53 270 -1.10 -4.24 5.79*10-
>23.0 +0.20 75 0.08 -2.15 7.14*10-3


As it follows from figures and tables above, the TKE mainly decreases with an

increase of bedform scales. Only for elevations of ADV2 more then 23 cm the TKE

increases with increase of ripple height, but the TKE no longer depended on ripple length

(correlation coefficient is 0.02). The coefficients in relations 4-3 and 4-4 do not show











consistent dependence with ADV2 elevation. The highest correlation is found, when the

velocity sensor was closest to the bottom (<15.5 cm). Unfortunately, the ADV2 elevation

was less than 10 cm only for a few runs, for which bedform data are available.



Time Variations of TKE, Sediment Concentration, and Bedform Mobility


E
E
0<

0
CO


Crests positions



- __
00--,


7


x 10-3 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 4-4: Ripple crest positions, TKE, mean concentration and wave envelope for
run #30: start at 256.3589 in Julian days.










As example time series of ripple crest positions, turbulent kinetic energy,

vertically averaged concentration, and wave envelope are shown on Figure 4-4. The data

were recorded during run #30. The same bedform data were shown on Figures 3.8 and

3.10 with ripple length and ripple height parameters. Notice that at the 10th and 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 cut-off method defines a single frequency that

separates turbulence from waves. The 'cut-off frequency is found as a point of steepest

descent of the coherence function between pressure and velocity, or alternatively, where

the velocity spectrum changes its slope. This frequency was found for a large number of

observations to be 0.5 Hz with standard deviation of 0.1 Hz. Two other methods are

based on the coherence between velocity and pressure (PV method) and two velocity

signals from two sensors separated in space (VV 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 cut-off method estimates the minimum total TKE, which is approximately

5 times smaller than from VV method. The PV method overestimates turbulence due to

long-shore fluctuations and also overestimates the full TKE. The estimated TKE is 6

times larger than the VV method and 30 times larger than the cut-off method. The VV

method provides the best estimation of turbulence in the wave frequency band. The










power spectrum of the turbulence has the same slope over both wave and turbulent

frequencies.

The influence of frame vibrations on the measurement of turbulence was

investigated. The error of measurement of high frequency velocity fluctuations due to

frame vibration was estimated from measurements of frame tilt and was found to be small

(about 1%).

A new filtering technique based on the FIR filter was developed and applied to

the SandyDuck'97 dataset in order to improve the estimation of small wave ripples. Some

advantages of this technique are as follows:

Higher accuracy. Because the system errors are normally distributed, the

applied FIR filter removes noise more accurately.

Smoothly changing data. The seabed most likely changes gradually rather

than stepwise. The new method approximates a stable bed position

ignoring short jumps.

Study of short time effects becomes possible, such as the formation and

destruction of ripples during the passage of several large waves.

Flat bed conditions were found only during 71 out of 164 runs, and during 54 runs

the SWR were found and their dimension were estimated.

Several methods were used for estimation of ripple scales. Good agreement

between the methods was found. The precision of ripple height measurements was found

to be less than 2 mm, but for smaller ripples additional information, such as ripple

migration, could be used, to prove their existence.










The estimated turbulent kinetic energy was compared to other measured

parameters to find empirical relationships. Good correlation was found between TKE and

first spatial moment of suspended sediment concentration profiles. The first moment of

concentration profile relates to potential energy of suspended sediments. Thus, the high

correlation provides the relationship between kinetic energy of turbulent motion and

potential energy of sediments.

The correlations between TKE and ripple scales were analyzed for different

elevations of velocity sensor. A high negative correlation was found between TKE and

ripple heights and lengths when the velocity sensor was closer than 15.5 cm to the

seabed. At higher elevations the tendency remains, but correlation coefficients become

smaller.


























APPENDIX A

MATLAB PROGRAMS FOR FILTERING OF MTA DATA




Function MTA PROC.


function [mtal23] = mta_proc(FileName,DirIn, DirOut);

% Procedure 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
X-axis for MTA
X-asis for middle part of MTA in mm
time step for raw data and mtal23 profiles
list of parameters


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

% See also : MKMTA123, DUCKHIST, DESPIKE, MTA INTERP


%%%%%%%%%%%%%%%%%%%% Parameters %%%%%%%%%%%%%%%%%%%%%%

% Data
ExperimentYear = 1997; % set year of experiment

% Extreme values


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((i-l)*n+l:i*n,:);















tmp(:) = modetrend(tmp(:)',100,MaxDeviation);
mtal23e((i-l)*n+l:i*n,:) = tmp;
end;

% remove extreme values mean +/- 5*MaxDeviation mm
meanmta = nanmean(mtarl23(:));
mtal23e(find(abs(mtal23e-meanmta) > 5*MaxDeviation))=NaN;

% call despike function
mtal23d=despike(mtal23e(:,l:end-1),SpikeLevel,SpikeDuration,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*(i-l)+l:N*i));
% if stdev of block big -- bad data. Remove them.
if isnan(stdN) | (stdN > StDevLevel)
mtal23d(j,N*(i-l)+l:N*i)=NaN;
end;
end;
end;

% correct length of mtal23, mtal23d, mtarl23 and mtatime
mtarl23 = mtarl23(:,l:N*ly);
mtal23d = mtal23d(:,l:N*ly);
mtal23 = mtal23d;
% mtatime times of recording
mtatime = mtatime(:,l:N*ly)+jdst; % correct start in Julian date
else
mtal23 = mtal23d;
mtatime = mtatime + jdst; % correct start in Julian date
end;

% filtering of each transduser
if DoFiltering
% Elliptic IIR lowband filter 9 order (should be odd) with cutoff fr=2*deltat/T
% For T=N*deltat: fr = 2/N, N-number of points per 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(end-29:end));
else
mn b = mean(x);
mn e = mn b;
end;
x=[mnb x mne];

dx=x(2:end)-x(l:end-1);

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<= lx-1) & (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+j-1)=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 x-axis for MTA data. Use with mtal23 variable.
% Run
% profx = mkprofx;
%
% Oleg Mouraenko, 07/24/2001
%
% See also: MKMTA123

profx=[linspace(0,90,16),linspace(96,96+46.5,32),linspace(148.5,238.5,16) ;

return;

















APPENDIX B
SHORT RIPPLES DURING THE SANDYDUCK'97 EXPERIMENT


Table B-l: 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 B-l: 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 B-1: 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 B-l: 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 B-l: 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 B-2: 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 B-2: 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 B-2: 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 B-2: 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 B-2: 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
















LIST OF REFERENCES


Alymov, V.V, Wave-generated ripples measurement technique and dimensions, MS
thesis, Univ. of Florida, Gainesville, 1999

Bendat, J.S., A.G. Piersol, Engineering applications of correlation and spectral analysis,
John Wiley, New York, 1993

Hanes, D.M., V. Alymov, Y. Chang, C.D. Jette, Wave formed sand ripples at Duck,
North Carolina, Journal of Geophysical Research, in press, 2001

Jette, C.D., Wave-generated bedforms in the near-shore sand environment, Ph.D.
dissertation, Univ. of Florida, Gainesville, 1997

Jette, C.D., D.M. Hanes, High resolution sea-bed imaging: an acoustic multiple
transducer array, Meas. Sci. Technol., 8 (1997), 787-792

Kos'yan, R.D., S.Yu. Kuznetsov, H. Kunz, N.V. Pykhov, Sand suspension events and
intermittence of turbulence in the surf zone, 1996, XXV Coast. Eng. Conf.,
Orlando, ASCE, 4111-4119

Mouraenko, O.A., D. M. Hanes, Field measurements of turbulence near the seabed,
Transactions, American Geophysical Union, 2000

Thosteson, E.D., Development and field application of a littoral processes monitoring
system for examination of the relevant time scales for sediment suspension
processes, Ph.D. dissertation, Univ. of Florida, Gainesville, 1997

Trowbridge, J.H., On a technique for measurement of turbulent shear stress in the
presence of surface waves, Journal of Atmospheric and Oceanic Technology, 15
(1998), 290-298

Voulgaris, G., J.H. Trowbridge, Evaluation of the Acoustic Doppler Velocimeter (ADV)
for Turbulence Measurements, Journal of Atmospheric and Oceanic Technology,
15 (1998), 272-289

Wolf, J., The estimation of shear stresses from near-bed turbulent velocities for combined
wave-current flows, Coastal Engineering, 37 (1999), 529-543
















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.




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs