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OCR for page 349
Non~ntrusive, Mullipl - Point Measurements
of Water Surface Slope, Elevation and Velocity
G. Meadows, D. L`yzenga2, R. Becki, I. Lyden2,
(iThe University of Michigan, USA)
(2Environmental Research Institute of Michigan, USA)
ABSTRACT
This paper describes the Hydrodynamic Monitoring
Facility (HMF), an instrument designed to measure slope,
elevation, and velocity simultaneously at an array of spatial
locations over an area of the water surface. The instrument
was designed to provide quantitative measurements used in
the study of ship wake phenomena. The HMF is
comprised of three separate systems: an optical wave
slope measurement system which uses a Helium-Neon
(HeNe) laser source and a wave height/surface velocity
measurement system which uses a CO2 laser. These
systems and the results of an initial experiment will be
discussed in detail.
The experiment utilized a subsurface air bubble source
and a surface wind wave source, in conjunction with the
HMF, to investigate the effects of short wave propagation
on a spatially variable current. A multi-frequency Doppler
radar system was employed to concurrently investigate the
interaction of active microwave energy with the surface
buoyant driven flow.
INTRODUCTION
Many of the hydrodynamic problems presently of
interest to the Navy have not traditionally been investigated
by ship hydrodynamicists. The purpose of the Program in
Ship Hydrodynamics (PSH) is to bring together an
interdisciplinary research team to investigate selected
aspects of these non-traditional problems. Because many
of the hydrodynamic aspects of the remote sensing (both
acoustic and non-acoustic) of ships are not well
understood, an increase in fundamental knowledge related
to this area has been chosen as the primary goal of the
PSH.
Much is still unknown and there is a lack of consensus
concerning the physics of the remote sensing of ship
wakes by Synthetic Aperture Radar (SAR). Therefore, a
major task of the PSH has been to obtain fundamental
experimental measurements in the controlled environment
of the towing tank. Calibrated radar scatterometers
contributed by the Environmental Research Institute of
Michigan (ERIM), have been mounted over the towing
tank and the return signals are correlated with high
resolution fluid surface measurements in order to
determine backscattering mechanisms of the moving
surface. This complete instrument suite, we believe, is
unique in the world.
349
The surface fluid flow in the wake of a self-propelled
body is a manifestation of the flow below the surface. The
flow in the wake is extremely complex, being a
combination of turbulent shear flows, coherent vortex
flows, free surface waves, internal waves and bubble
flows with complex interactions among the various
components.
The inaugural experimental use of the Hydrodynamic
Monitoring Facility (HMF) has been to provide a detailed
set of tow tank measurements of large coherent vertical
structures (with axes oriented parallel to the free surface)
(Figure 1~. These flows are modeled after the observed
diverging surface flow field in the wake of surface ships
producing a persistent, dark centerline wake in SAR
images (Figure 2~. The modeled flow fields are buoyancy
driven, with bubbles playing a significant role in the
observed persistence of the vertical structure. Surface
velocity, two-dimensional wave slope and height data were
obtained by the HMP along with calibrated Doppler radar
scatterometer data over the surface, wave/current
interaction region of these flows.
INSTRUMENT ATION
To make substantial progress in the understanding of
the hydrodynamic mechanisms which allow ship generated
disturbances to be remotely sensed, experimental
measurements which can correlate the hydrodynamic
properties of the flow field with the electromagnetic
properties of the sensing field are necessary. To make
these types of measurements, specialized facilities had to
be developed. To achieve this goal, the Hydrodynamic
Monitoring Facility was developed under Navy University
Research Initiative ~RI) sponsorship.
The experimental study of the surface perturbations
associated with the natural wind stressed ocean have led to
,
Figure 1. Depiction of diverging surface current flow field
generated by the passage of a high speed surface ship.
OCR for page 350
*
~ WIND (7 m/s )
X-Band ~ I
1 km
Figure 2. Simultaneously obtained L- and X-band optical SAR imagery of a dark centerline wake feature.
many novel observational techniques to determine the sea
state. The method of optical observation was quantified in
the classical work of Cox and Monk t1] in which they
related the distribution of brightness of the sun glitter to the
statistics of the sea surface slope distribution. This basic
analysis has been the underpinning of nearly all modern
work on optical and microwave scattering of larger scale
waves. However, the influence of the smaller waves,
particularly, in the study of microwave scattering has led to
the use of more complete scattering calculations. Recent
studies, which have relied on a deterministic approach
based on knowledge of the true surface morphology where
the microwave scattering occurred, have been very
successful in quantifying the scattering process.
The problem in the vicinity of a moving ship is more
complex than in the open ocean where only history and
350
wind create the sea, but the success of the deterministic
approach is compelling. To fully describe the "sea"
surface implies that the morphology of the fluid surface
and the associated velocity field are known in sufficient
detail to compute the scattering properties and other
signatures which are desired.
This constraint has led to the development of an
instrument system, the HMF, which provides a spatial
description of the surface wave height, slope and velocity
fields in two-dimensions. Furthermore, the HMF
provides this two-dimensional characterization in a
temporal period which is short compared to the wave
periods of interest. A detailed description of the surface
wave slope, height and velocity sensing systems will
follow.
OCR for page 351
Surface-Slope - Laser Refraction
The use of reflected and refracted laser light to profile
the instantaneous surface of a fluid medium has been
described by Chang and Wagner [2l, using methods
closely related to those described by Cox and Munk [11.
The reflection technique relies on the fact that when a
narrow beam of light crosses a dielectric boundary, such
as the water surface, a fraction of that light, about two
percent for vertical incidence, is reflected symmetrically
about the surface normal. Thus, if the reflected beam is
monitored by observing its intersection with a screen
during a scan of the laser beam across the water surface
one gains knowledge of the surface slope at all points
along the laser scan. This technique was employed by
Kwoh and Lake [31 to define a two-dimensional wave
distribution in water where microwave scattering
observations were being taken.
The reflected laser measurement of the wave surface is
extremely sensitive to the slope of the surface, being
reflected at twice the surface normal angle. In regions
where the surface slope is large, such as the near wake, the
reflection technique may in fact be too sensitive. The use
of a refracted ray from an underwater source reduces the
sensitivity to about 0.34 of the angle of the wave normal,
thus allowing much larger wave slopes to be monitored.
This technique was used by Kwoh and Lake but with the
origin of the laser located above the water rather than
below as we have employed here. The refraction method
was shown to be particularly suitable for determining the
structure of the wake where the surface is more structured
and varies rapidly in time and space and was adopted for
the HMF. A schematic representation of the fluid slope
sensor system is provided in Figure 3.
In this method, the laser beam is incident sequentially
in time and space with different angles of incidence from
below the water surface. The refracted beam is detected
instantaneously by a position detector on an imaging
screen above the water. The scanning range on the water
surface is approximately 1 meter by 1 meter. This area is
determined by the desired size of the imaging screen above
PoS fir ON DETECTOR
SCREEN
REFRACTED \ / /
BE - S - ~/ /,,
. . , · · , ~. .
the water surface, the laser intensity and the slope of the
wave surface. To reconstruct a wave surface, the water
surface area of interest is scanned in a user selected pattern
with M by N points. The number of scanning points on
the surface depends on the required accuracy of the
reconstructed surface. The scanning of the laser beam and
its detection are synchronous and fast enough to insure that
the positions of the laser beam at the initial time and
subsequent times are independent and unambiguous
events. A detailed description of the analysis procedure
and free surface reconstruction is provided in Wu and
Meadows (19901.
Surface Wave Height and Velocity Observations
Tracking of Laser Induced "Warm Spots"
The surface wave height and velocity of the water
behind a ship or in the laboratory behind a model are of
great importance in defining the wake characteristics. It is
imperative to observe the height and velocity fields with
spatial and temporal scales that match those of the waves
of interest. These high resolution requirements and the
desire to measure precisely on the free surface rule out
many of the conventional techniques of velocity
measurement. We have adopted a thermal tracer technique
as our method of choice for the HMF.
A pattern of distributed thermal perturbations or "warm
spots" are created using a modulated CO2, infrared laser,
Casing at 10.6 A) and a pointing system. These
perturbations are then tracked using stereo infrared thermal
scanners. The surface height and velocity fields are
determined from the displacement of these perturbations
between successive infrared image frames. The
distribution of spots are user selectable in linear patterns
providing velocity profiles, in structured patterns which
will yield two-dimensional vorticity and divergence, or in
other specific arrays which will depend upon the
information desired. At the present time warm spots of
5mm diameter are placed on the water surface at a
maximum rate of 40/see utilizing a 10 watt CO2 laser. The
water surface is warmed +0.75°C above ambient which
produces a 0.75 sec persistence time in the thermal
imagers. Data is recorded in standard video format at 30
full frames per second and is analyzed as Lagrangian
trajectories of tagged particles. A schematic representation
of this surface wave height and velocity sensing system is
provided in Figure 4.
_LOCIlV
THERMAL
I n*GERs r ~
30 FRAMES ~ \
PER SECOND / \
mu\
SWARM
SPOTS
Figure 3. Schematic representation of two-dimensional
fluid slope measurement system.
Figure 4. Schematic representation of two-dimensional
surface velocity and height system.
351
OCR for page 352
MAIN CARRIAGE VISIBLE LASER SCANNER SUB
- an\ CARRIAGE
C O2 LA SE R SCAN NER ~ \
SHIP MODEL \ THERMAL IMAGERY
\ :1 ~ J CAMERAS//
\ ~TOW TANK
/
Figure 5. Hydrodynamic Monitoring Facility configuration in the Ship Hydrodynamics Laboratory.
The entire HMF sensing system is mounted on a
subcarriage which is towed at selected distances behind the
main carnage which suspends the ship model. The HMF
field of view is also free to traverse in the cross tank
direction to provide spatial views of various sections of the
downstream wake. A schematic of the entire system
arrangement is provided in Figure 5. In addition, as a
result of the initial testing and inaugural experimentation,
the demonstrated and design capabilities of the HMF are
provided in Table 1.
ERIM Calibrated Doppler Scatterometer
The radar used in this experiment is a modification of a
previously constructed dual-polarized system operating at
C-band (4.8 GHz) and X-band (9.6 GHz). The original
device consisted of a transmit antenna fed by a frequency-
modulated r.f. source, and a pair of orthogonally-polarized
receive antennas whose outputs were mixed with a portion
of the transmitted signal and recorded on analog tape. This
device was modified by splitting the signal from one of the
receive antennas and adding a 90-degree phase shift in
order to sample the in-phase (I) and quadrature (Q)
components of the received signal. These I and Q
channels were simultaneously sampled, digitized, read into
memory, and subsequently recorded on floppy disks.
The Doppler spectrum of the radar return was obtained
by assigning the I and Q components of the received signal
to the real and imaginary parts of a complex number, and
352
Fourier transforming the resulting time series over a set of
256 samples. The data presented in this paper were
sampled at a rate of 100 complex samples per second and
thus cover the frequency range from -50 to +50 Hz. Each
spectrum shown represents an average 10 data segments of
2.56 seconds duration each. Data were collected at both
C-band and X-band, and with both vertical and horizontal
polarization; however, only the C-band vertically-polarized
measurements are discussed in this paper.
The range of parameters observed by this combined
instrumentation effort is summarized in Table 2. Wave
making and ancillary data collection capabilities of the Ship
Hydrodynamics Laboratory have been extensively
upgraded to accommodate the experimental opportunities
brought about by the development of the HMF.
INITIAL EXPERIMENT: BUOYANCY MAINTAINED
VORTICES IN To SllPlFACE SHIP WAKE
The inaugural experiments utilizing the HMF in the
Ship Hydrodynamics Laboratory at The University of
Michigan as part of the URI funded Program in Ship
Hydrodynamics, have sought to elucidate the effects of
bubbles in maintaining the flow patterns in surface ship
wakes.
Bubble clouds have been observed in the wakes of
ships at depths of several tens of meters. These bubbles
presumably originate from cavitation, entrainment at the
OCR for page 353
Proposed Demonstrated Capabilitles
Capabilities As ot May 1990
Slope Height,Velocity
(acceptable) (visible) (I.R. System)
Scan
TIme:.......................
Scan Area :..............
Heigh' Resolutlon:...........................
Maximum Height:
Slope Resol ution :........
Maximum Slope:..........
Velocitv Res olution :....
Maximum Velocity:.....
S pOt Sl2e: ..................
.. . .. . ..
100 x 100
(10 x 10)
0.1 ~
1 x 1 m
(.4 x .4 m)
1 mm
(2 mm)
15 cm
0.2
35
1 mmk
1 00 cm/s
1 mm
2 mm
Spot to Spot Cen1ers: 2 to 10 mm
(5 to 10 mm)
Table 1. Hydrodynamic Monitoring Facility design and
demons~ated capabilities
81 x 81 10 x 5
0.1 ~1.0 ~
0.5 m diem 25 x 18 cm
(-4 mm)
~?
0.5 ° typical ~.
-21°
5.4 cnilperalstence frames
300 cm/s
1.5 mm 10 mm
2 mm 10 mm
Frequency (~2) | 7 6 5 4 3 2 1 0 S
Perlod (see) 0.143 0.167 0.200 0.250 0.333 0.500 1.0 2 0
Wavelengtn (cm) 3.2 4 3 6.2 9.8 17 3 39.0 156 b42
Llm. Mgt. (cm) 0.46 0.61 0.89 1.40 2.47 5.57 22.3 91 7
i
tinf
~elgnt Q'solutlon
~r
Spot Slle Resolullon - ~ ~-
h' F
~loo'~ Resolut lon
ntmum of ont comPlet. _ |
~ w3ve cyc)e In a,oerture -|
^r nil. t I r
| Vert lc~ i
_ ~ ~ 1 ~,
wave meKer - ~otlon mach~n ~~ _
Wave maker
Scatterometer |
_ .
_ · . ~-
X - 8anC C -Band
~ cn, 5 Cm
~L - ~ ~ n a
Table 2. Summary of range of experimental conditions
achievable by the Hydrodynamics Monitonng Facility.
353
~ ~_ ~
E Qlh' Rada,
|Oregg wev' Rang'
OCR for page 354
surface, and possibly other sources. The buoyancy flux
associated with the bubble clouds may contribute
substantially to the maintenance of an upwelling region
which in turn leads to the persistence of the dark centerline
wake observed in radar images.
Hydrodynamic Measurements
A laboratory wave tank experiment was devised to
quantify the role of these buoyancy driven flows. A pair
of counter rotating vortices are generated near the free
surface, with vortex diameters on the order of two meters.
This vortex pair produces diverging surface currents to
simulate the centerline wake region of a large displacement
vessel traveling in the cross-tank direction. Measurements
of surface velocity, wave height, slope and radar cross-
section are made across the interaction region. This series
of measurements have been made both with, and without,
externally generated waves present on the surface. The
experimental configuration is depicted in Figure 6.
The objectives of this initial set of experiments was to
investigate the interaction of short waves with spatially
variable current similar to that produced by passage of a
large displacement ship. ~ addition, the role of buoyancy
driven flows in the maintenance and persistence of this
portion of the centerline wake is evaluated. The
measurements included a characterization of the free
surface (its two-dimensional slope, wave height, and
velocity distributions) as well as the radar cross-section
and Doppler spectrum variations across this region of
interaction.
The WAIF was configured to provide two-dimensional
surface wave slope information on a 50 x SO points grid at
1 cm spacing with a two-dimensional frame completed
every 0.06 seconds or 16.65 Hz. The infrared system for
surface wave height and velocity was configured for this
initial experiment in an array of 25 x 1 grid points at 2.5
cm spacing. The complete frame was sampled every 0.82
seconds or at a rate of 1.21 Hz. For this initial
experiment, the purpose was to consider variations in
surface roughness as a result of wave/current interactions
for direct comparison with radar measurements. The
selection of a 25 x 1 scan in the IR system precludes the
direct determination of wave height. However, since the
absolute elevation of the water surface is known within the
LB ~ 4 25 cm
,/~ ~ 6 5 HZ ~
/ ~
/ / / I wave I
~Ens IrrP I
Free Surrace ~U. U(X)
~ To ' ~
.~°
p00
I~W-W(Z)
\0.t
l~o°-l
Ott,
Bubb I e
Source
Figure 6. Experimental configuration for buoyancy driven
vortex flow.
Iniual Pressure = 10 psi; Vmax - 24.16 cams
O.h
E Q7
-
~, 0.6
>. 0.5
~ 0.4
_
O 0'3
0.2 .
0.1
QO ~
o
\
Figure 7. Mean surface velocity resulting from buoyancy
driven subsurface vortex.
frame, the two-dimensional wave height distribution can
be obtained from an integration of the two-dimensional
slope data.
The buoyancy flux required to initiate the large scale
vertical flow was provided by a linear bubble generator
located approximately 1 meter below the water surface.
The bubble volume in the rising column of fluid directly
above the linear bubble generator was approximately 6%
of the total water column. Averaging over the total
volume of the vertical flow (which has a width of
approximately 6 meters in the along-tank direction) results
in a void fraction of approximately 1x10-6. This void
fraction is consistent with open ocean measurements of
high near surface bubble densities.
The average surface flow resulting from this
experimental configuration is presented in Figure 7.
Maximum divergent surface velocities of approximately 24
cm/see were obtained near the bubble curtain which
spatially decays to approximately 40% of the initial value at
a distance of 3 meters from the bubble generator. Careful
selection and maintenance of air pressure at the bubble
generator produced extremely repeatable surface flow
conditions.
The rate of decay in the surface velocity field was
measured under two test conditions. In the first set of
experiments the initial bubble void fraction was
instantaneously reduced to zero at time t = 0 seconds. The
rate of decay of the coherent structures resulting from the
buoyancy flow was then measured with the HMF through
time. The time rate of decay of the maximum velocity is
presented in Figure 8 for these conditions.
Initial Pressure ~ lO psi; Vmax 5 24.16 ants
1 · DOc~gloOpa 1
· 1 · S~PDo~ m3ps,
0.0-1 · . . . . .
0 5 10 IS 20 2S 30
Time from Sbutot! (s)
Figure 8. Time rate of decay of the maximum surface
velocity for vortex decay with and without bubble
buoyancy flux.
354
OCR for page 355
Similarly a second set of experiments was conducted
with the same initial void fraction in buoyancy flux,
however, at time t = 0 the bubble density was reduced to
1% of the original volume (void fraction 1.7 x 10-7~. The
purpose of this second set of experiments was to simulate
role of a small buoyancy flux consistent with that observed
in the late wake of a surface ship in maintaining divergent
surface currents in the centerline wake region. The rate of
decay produced by the reduced buoyancy flux is presented
in the upper curve of Figure 8.
It is apparent that a substantial reduction in the rate of
decay of these large scale coherent structures is produced
by just a small buoyancy flux in the central region. The
implication of this set of observations is that bubbles
produced by the passage of surface ship wake appear to
play a substantial role in the maintenance of diverging
surface currents and the persistence of centerline wake,
very far downstream of high speed vessels.
To investigate the effect that these persistent and
sustained diverging surface currents have on the
anticipated radar return for the centerline portion of the
wake, wind generated waves produced by a near surface
fan were propagated across the spatially varying current
pattern. Presented in Figures 9 (a) through (c) are plots of
the along-tank wave slope spectra recorded by the HMF at
positions 1/2 meter upwind of the centerline of the
diverging current, 1 meter and 3 meters downstream,
respectively, plotted as a function of the along-tank wave
number. The corresponding radar backscattering
measurements are described in the following section.
Radar Measurements ° E
A series of calibrated Doppler scatterometer
measurements was made to investigate the variations in
radar backscatter caused by the wave/current interactions
across the diverging surface currents, both in the absence
of wind and in the presence of a wind-generated wave
field. Three sets of measurements were made using the
experimental setup shown in Figure 6. For this operating
configuration the radar footprint was approximately 50 cm
in diameter consistent with the chosen geometry of the
OFF.
The first set of measurements was conducted with the
bubble source in operation but without the fan. The
purpose of this set of measurements was to quantify the
surface roughness generated directly by the bubbles, or by
the bubble-induced turbulence. The second set of
measurements was made with the fan on but without the
bubble source. The purpose of this set of measurements
was to characterize the surface wave field generated by the
fan. Finally, a set of measurements was made with both
the fan and the bubbler in operation, in order to determine
the effect of the bubble-generated currents on the incident
wave field.
An example output from the first set of measurements
(with only the bubble source in operation) is shown in
Figure 10. During this set of measurements, the surface
wave height was much smaller than the radar wavelength
and thus, the backscatter is expected to be quite well
predicted by a simple Bragg scattering model (e.g.
Wright, [5~. The observed C-band Doppler spectra tend
to confirm this, being dominated in most cases by peaks
corresponding to approaching and receding Bragg waves.
The wavenumber of these Bragg waves is given by the
equation
E
o
w
E
R
A
E
C
T
R
U
M
S E-4~
C E-4 _
R
U ~
M E-i _
2
E-4 _
O
(a)
.
,...
\
~ I I. I
150 200 250 300
Ky ( red. /m)
(b)
~,W,
, ~ ,
__ 150 200 250 300
Ky ( red. /m)
(C)
_ ,
0 50 100 150 200 250 300
Ky ( red. Im)
Figure 9. Wave slope spectra across wave/current
interaction regions.
(a) 1/2 meter upwind of centerline
(b) 1 meter downstream
(c) 3 meters downstream
.
I I hL/l rv . ~
-50 HZ O
+SO Hz
Figure 10. Doppler spectrum measured 3 meters from
bubble source. Arrow "A" indicates primary Bragg peak
at -8.2 Hz and "B" indicates secondary Bragg peak at +4.9
Hz.
355
OCR for page 356
(9)
l
(f) I it
~ it.
1
(e)
(d)
(b)
(a)
· 111 ~
I ~
, i !
. 1,,,,,f,~i,...........
r
1l !
r
~a.! ' I
l
.
I 11 1 ~ i, ~I
'A I
; 1
1
!
I IJi 1 .
.~
,,
,' i
'TV
.t .:, .
'" ~ i
! !
. ·: 1
i
.
,. 1
my.,, _~ ' ~ ~
l
Figure 11. Measured C-band doppler spectra for bubble source only (left column), bubble source and fan-generated
waves (center column), and with fan only (right column). Rows correspond to down range positions in intervals of 1
meter, with row (d) centered on the bubble source.
356
OCR for page 357
kB=2koSin~
where kO=2~/~6.2cm) is the electromagnetic
wavenumber and ~ = 45° is the angle of incidence. This
yields a wavelength JAB = 4. 4cm for these waves. In still
water, the Doppler shift of the radar return equals the
intrinsic frequency of these waves, or fB = +6.5HZ. In a
current having a component u in the plane of incidence,
the Doppler shift equals the apparent frequency of the
waves, or
fD = fB + U/~B
The spectrum shown in Figure 10, which was collected 3
meters downrange from the bubble source is dominated by
a single peak corresponding to the receding Bragg wave,
as would be expected for waves generated near the bubble
source. A smaller peak corresponding to an approaching
set of Bragg waves is also shown. The average Doppler
shift for these two sets of waves is -1.6 Hz, which implies
a surface current of 7.2 cm/see away from the bubble
source.
The Doppler spectra observed at seven downrange
locations relative to the bubble source are shown in Figure
11. The spectrum shown in Figure 10 is reproduced in the
upper left corner of Figure 11, and the other spectra
observed during the first set of measurements are shown
below this one in the first column. The spectra observed
with both the fan and the bubble source in operation are
shown in the middle column, and the spectra obtained with
the fan in the same relative position but with the bubbler
off are shown in the right-hand column.
The Doppler spectra in the second and third rows of
the first column in Figure 11 show two peaks of
approximately equal amplitude, corresponding to the
receding and approaching Bragg waves. The mechanism
for the generation of the approaching Bragg waves is not
clear, but the amplitude of such waves would be expected
to increase due to their interaction with the surface currents
in his region. The average Doppler shifts for these data
sets are -3.4 Hz and -3.3 Hz, implying currents of 15
cm/see and 14.5 cmlsec, respectively.
C-BAND BACKSCATTER
o o
C)
~ o
a
Cat
at:
m
o.o 1.0
LEGEND
° fan only
2.0 3.0 4.0
DOWNRANGE DISTANCE (M)
5.0 6.0
Figure 12. Backscattered power due to fan generated
waves versus distance from fan.
The spectrum in Figure 1 lady, on the left, which was
collected with the radar footprint approximately centered
on the bubble source, is rather complicated but nearly
symmetric, indicating a zero mean surface current. The
peak on the left may be due to a set of receding Bragg
waves on the far side of the radar footprint which are
Doppler shifted by a current of approximately 19.6 cmIs
away from the center, while the peak on the right is due to
the corresponding set of approaching Bragg waves on the
near side of the footprint. The two central peaks may be
due to waves which are made nearly stationary by the
current near the bubble source.
Figures llfc), (b), and (a) show dominant peaks
corresponding to the approaching Bragg waves generated
near the bubble source and smaller peaks corresponding to
the receding Bragg waves. The average Doppler shifts are
3.2 Hz, 2.8 Hz, and 2.7 Hz, corresponding to currents of
14 cm/s, 12.3 cm/s and 11.9 cm/s, respectively, away
from the bubble source. Another peak appearing at about
11 Hz in each of these spectra is not accounted for, but a
set of peaks appears at the same frequency in the X-band
data collected during the same time interval, indicating the
possibility of external interference.
The second set of runs was made at a series of
distances away from the fan, with the bubble source turned
off. The resulting Doppler spectra are shown in the right-
hand column of Figure 11. These spectra are much
broader and are centered at roughly -8 Hz. The
broadening of the spectra is due to the presence of much
higher amplitude and longer wavelength waves. The
energy is mostly confined to negative Doppler frequencies,
corresponding to receding waves, as expected since the fan
was blowing away from the radar. The Doppler spectrum
appears to be centered at the Bragg peak with an additional
shift due to a surface drift current of about 6-8 cm/s. The
received power (i.e., the integral of the Doppler spectrum)
is plotted versus distance from the fan in Figure 12 and
shows an approximately linear falloff over this region.
The set of measurements shown in the middle column
of Figure 11 was made with both the fan and the bubble
source turned on. The fan was directed toward the bubble
source and was sufficiently far away so that waves were
C-BAND BACKSCATTER
o
~1
o
o
~ ;
o o
~ U,_
C)
Cal
LO
Do
m
-3.0 - 2.0
. , ,
-1.0 o.o 1.0
DOWNRANGE DISTANCE (M)
2.0 3.0
LEGEND
0 waves + bubbles
0 bubbles only
Figure 13. Backscattered power versus distance from
bubble source, with and without fan-generated waves
present.
357
OCR for page 358
generated only on the near side of the bubble source. The
spectra for the downwind side (at the top of Figure 11) are
almost identical to those collected with the fan off (left
column) indicating that most of the fan-generated waves
have been attenuated by the bubble-induced current.
Approaching the upwind side, the spectra become more
complicated but show a gradual transition toward the broad
spectra observed in the fan-only case (right column).
The total received power for the left and center
columns versus distance is plotted in Figure 13. The
received power with the fan off peaks at the position of the
bubble source, as expected. With the fan on, the received
power peaks slightly at the center and then falls off rapidly
on the downwind side.
The received power for the bubble-only case was
subtracted from the power for the combined measurement
to estimate the contribution from waves generated by the
fan which have propagated through the current, and the
results are shown in Figure 14. For the two points
furthest downwind, this contribution is on the order of a
few percent of the backscattered power in the absence of
the bubble-induced current.
DISCUSSION OF RESULTS
A comparison of the results of the radar and HMF
measurements with the predictions of wave-current
interaction theory can be made by applying the wave action
conservation principle and assuming that the backscatter is
proportional to the wave spectral density at the Bragg
wavenumber. Neglecting relaxation effects, the action
conservation principle (e.g., Phillips, [61) states that for a
continuous spectrum of waves, the action spectral density
for a given wave group remains constant, i.e.,
N(k~)=N(k2)
where kit and k2 are the wavenumbers for the wave group
at any two locations in the current pattern. These
wavenumbers are related through the kinematic
conservation equation, which can be written as
C-BAND BACKSCATTER
o
Cat
to
o
at:
o o
~ U.
C)
LLJ
L`J
o
6
m
to
US
O 0
O' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' ~1
-3.0 -2.0 -1.0 o.o 1.0 2.0 3.0
DOWNRANGE DISTANCE (M)
o
o
° o
LEGEND
0 = Pf-Pb
Figure 14. Backscattered power due to wind waves
interacting with bubble-generated current.
w1 + klu1 = o)2 + k2U2
where a) is the intrinsic frequency corresponding to the
wavenumber k. The currents at the positions
corresponding to Figures 9 (a) through (c), were
approximately -10 cm/s, respectively. Applying the
kinematic conservative equation, the wavenumber for the
left-hand peak in Figure 9(a) (i.e., 20 red/m, 32 cm
wavelength) is reduced by approximately a factor of two
(64 cm wavelength) at the location of Figure 9(b). This
wavenumber is not resolved by the chosen viewing
aperture of the HMF and, therefore does not appear in
Figure 9(b). The second peak in Figure 9(a), however,
appears to track through the other two measurements
specifically, a wavenumber of 80 red/m (8 cm wavelength)
in Figure 9(a) translated into 25 red/m (25 cm wavelength)
in Figure 9(b) and 32 red/m (20 cm wavelength) in Figure
9(c). For comparison with the radar measurements, we
have chosen u2 = 7 cm / s as the surface current at the
downwind endpoint and k2 = 1.4 red / cm as the Bragg
wavenumber, the apparent frequency of this wave is 50
rad/sec. The corresponding wavenumber at the location
where u1 = -7 cm / s would be k1 = 3.0 red / cm.
Assuming that the incident wave action spectrum falls off
as k , the Bragg wave spectral density at the end point
is then a factor of (1.4 / 3.0~ ~ =.03 smaller than that at
the wave source, which is in reasonable agreement with
the observed reduction in backscatter.
.
The significance of this apparent agreement is
encouraging in view of the simplifying assumptions made
In these calculations, notably the neglect of wave
dissipation effects and the use of a simple Bragg scattering
model. The calculations and the observations both
illustrate the large reduction in backscatter caused by the
injection of bubbles and indicate that the interaction of
waves with the mean surface current induced by the
bubbles is mainly responsible for this reduction. The
turbulent fluctuation of this current may increase the
damping effect, but does not appear to be necessary to
explain the observations.
ACKNOWI~DGEMENTS
This work was supported under the Program in Ship
Hydrodynamics at The University of Michigan, funded by
the University Research Initiative of the Office of Naval
Research, Contract No. N000184-86-K-0684.
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OCR for page 360
Representative terms from entire chapter:
water surface
