Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
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. REFERENCES 1. Cox, C. and Munk, W., "Measurement of the Roughness of the Sea Surface from Photographs of Sun's Glitter," J. Opt. Soc., Vol. 44, 1954, p. 838. 2. Chang, J.H. and Wagner, R., "Measurement of Capillary Waves," Conference on Atmospheric and Oceanic Waves and Stability, American Meteorological Society, 1976. 3. Kwoh, D.S.W. and Lake, B.M., "Laboratory Study of Microwave Backscattering from Water Waves, Part I: Short Gravity Waves without Wind," IEEE Journal of Oceanic Engineering, Vol. OK-9, No. 5, Dec. 1984, pp. 29 1 -307. 4. Wu, Z. and Meadows, G., "2-D Surface Reconstruction of Water Waves," OCEANS 90, IEEE Oceanic Engineering Society, in press. 358
OCR for page 359
5. Wright, J.W., "A New Model for Sea Clutter," IEEE Trans. Antennas Propogat, Vol. AP-16, 1968, pp. 217- 223. 6. Phillips, O.M., The Dynamics of the Upper Ocean, 2nd Ed., Cambridge University Press, 1980, 336 p. 359
OCR for page 360
Representative terms from entire chapter: