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Hydrodynamics of Ship Wake Surfactant Films R. Peltzerl, J.H. Milgram2, R. Skop3, J. Kaiserl, O. Griffinl, W. Barger ([Naval Research Laboratory, USA) Massachusetts Institute of Technology, USA) University of Miami, USA) ABSTRACT When compacted at the free-surface, surface-active ma terials have very strong wave damping properties. Careful measurements are required to characterize these physical ef fects. Prior to a Field Experiment in January 1989, we re hned the spreading oil technique, developed by Adam in 1937 to characterize the physical properties of a surfactant film, so as to provide the necessary spatial resolution to iden tify fine structure in the surface tension gradients on the surface generated by the passage of a ship. We present an in-depth look at the measurements of the cross-wake surface tension distributions that were obtained during the Field Ex periment for a Navy ship at 25 knots. These cross-wake sur face tension profiles, together with the film pressure-area and elasticity data also presented, allow us for the first time to re alistically calculate the changes in wave energy due to these surfactants for a given radar wavelength band. To accom plish these calculations we leave developed a computer model which uses the time series of surface tension together with the film pressure-area and elasticity data from the Langmuir trough and the wind velocity and direction as input to gen erate cross-wake profiles or two-dimensional maps of wave energy decay for a given radar wavelength. In this paper w describe the development of this model and present some results of wave energy decay for a given radar wavelength obtained with the model and compare these results to air craft SAR intensity measurements obtained during the run. v L, LWL Lt LU,P LWW n n SAW SAO Sow Sw Sal st Ss NOMENCLATURE free surface area of surfactant film surface wave height c wave phase speed cg, cg (vector) group velocity of a wave dw'/dz vertical derivative, RMS turbulent vertical velocity D ship draft E energy density spectrum Ea ambient spectral level outside the wake ES surface elasticity F force on Wilhelmy plate exerted by liquid gravitational acceleration depth below the free surface definition, h = E9k2k2 wavenumber H h k ship length, waterline length length of the zone of ship-affected turbulence length of Wilhelmy plate in contact with liquid length of the white water wake logarithmic slope of pressure-area curve propeller revolutions per second (Figure 1) surface tension force at the air-water interface surface tension force at the air-oil interface surface tension force at the oil-water interface wave energy growth due to wind energy input wave energy growth due to nonlinear interactions wave energy decay due to turbulence wave energy decay due to surfactant damping time friction velocity of the wind ten meter wind speed ship speed wake width downstream distance surface tension of clean water wind induced wave growth rate wind induced wave growth rate wave decay rate due to surfactant damping wind induced wave growth rate wave growth rate from nonlinear interactions definition, ~ = (gk + rip k3~/2 angle between wave and wind direction kinematic viscosity of seawater surface film pressure 3.14159....... density of seawater radian wave frequency measured surface tension definition, ' = ok t it* ulo V, VS W Xc' ~1 i02 As low p Tmeas 1.0 INTRODUCTION One prominent feature of the wake of a surface ship is a long narrow region of relatively calm water behind the ship that is characterized by the absence of short wavelength waves. This region is commonly referred to as the "dead" water or centerline wake region. It is usually several ship beans in width and persists for many ship lengths behind the ship. This region of relatively low radar backscatter is the most consistently seen wake manifestation in synthetic aperture radar (SAR) images of ship wakes on the ocean surface. Another feature in the SAR images of ship wakes is 533

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the appearance of dark lines aligned at some narrow angle to the ship's path that sometimes outline this centerline wake region far behind the ship. Surface tension changes caused by the presence of surface-active films that have been con- centrated at the edges of the centerline wake by the passage of the ship have been suggested as one of the physical mecha- nisms responsible for these SAR image features. Surfactant films strongly affect the propagation of short gravity and capillary waves which interact with electromagnetic waves at both radar and visible wavelengths. Surface tension and surface elasticity are the two major physical properties of surfactant films which contribute to short wave damping. To investigate the physical origin of these SAR im- age features, a small, towable, instrumented catamaran was built and deployed by NRL scientists to measure the cross- wake surface tension distribution after the ships passage. This instrument package was named the Surface TEnsion Measuring System (STEMS). The device measures surface tension by dropping a sequence of calibrated spreading oils along a straight line on the water surface and recording their behavior with a video camera. Each individual oil represents one surface tension value so that if one oil spreads and the next one does not, then the surface tension is bracketed be- tween the two values. Surface elasticity cannot be measured in situ by the spreading oil technique. Therefore, 1-liter water samples were collected for later measurements in a Langmuir trough. Surface elasticity is defined as the product of film area times the slope of the pressure-area curve at the corresponding value of the film area as measured in the trough. The sur- face elasticity distribution can then be calculated from the resulting pressure-area curve together with the ambient sur- face tension distribution measured using STEMS. Coupling the surface tension measurements made by STEMS to the determination of the pressure-area curves has for the first time allowed us to infer elasticity distributions for ocean VELOCITY BLOW W-AVE Rat //~ISR / , ~WAKED water and to realistically calculate the changes in wave am- plitude due to these surfactants. In this paper we describe the STEMS device and give examples of the results that were obtained during its deploy- ment in an extensive Field Experiment that was conducted in the vicinity of Santa Cruz Island, California in January, 1989 to study surfactant films. Previous to this experiment, in situ surface tension data have never been measured to the resolution in surface tension obtained or with such fine spatial resolution. The NRL data from the experiment show that these surface active films play a significant and some- times dominant role in the formation of the two SAR image features of ship wakes. We also present an overview of the chemical and physical properties of surface active materi- als and the techniques used to measure and determine their physical properties when they adsorb at the air-water inter- face. 2.0 BACKGROUND 2.1 Description of the Ship Wake Irk this section we will describe the wake of a surface ship from a perspective corresponding to the large-scale physical phenomena that are observed both visually and by means of remote sensing systems. A schematic of a surface ship wake is illustrated irt Figure 1. The wake is composed of white water, viscous wake, propeller wake, and Kelvin wake. The white water generally originates at the bow, is reinforced at the stern, and extends aft of the ship for a few ship lengths. The viscous wake extends many ship lengths aft from the stern of the ship and incorporates the flow moving in the direction of the ship's travel due to the viscous drag, as well as large-scale vertical flows and turbulence. Embedded within the viscous wake is the propeller outflow or propeller wake. Superimposed over Ellis is the classical Kelvin wave pattern or Kelvin wale. The Kelvin wake is also the source ^.eSY~ `~\ ~/ 3516' CUSP-CREST TANGENT LINES l 1 1 - L = 655 V 1 5 n-05 1 WW s it\ / \ SHIPS HULL ~ ~ SHIP'S \REGION \ ~~~ HULL ~ \ NEAR WAKE, PRODUCTION ~ REGION 1 ~t~vvv/LwL = 53.5 [Vs/(gL`A,L)o 5]1.4o - Figure 1. Schematic of a surface ship wake 534 -FAR WAKE, DECAY REGION - - - - -

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of many of the viscous wake manifestations. It is in fact the breaking bow and stern waves from the Kelvin wave system whirls contribute significantly to the white water regions at the bow and stern. These wake manifestations lie upon the ambient seaway made up of swell, wind waves, and short gravity and capillary waves; all of which confuses the picture even more. It is often useful to draw an imaginary ellipse, extend- ing several ship beans ahead of and off to each side of the ship and a ship length or so aft of the ship, around the ship. We call the region internal to the ellipse the near wake and the region external to the ellipse the far wake. The near wake can be thought of as the region where surface foam, subsurface bubbles, and strong turbulence is generated. It is also where the most rapid decay of these features occurs. In the near wake, the initial region of the viscous and propeller wakes is a region of high angular divergence (initial spread- ing region, ISR) of foamy, turbulent, white water directly aft of the ship's stern, generally outlined by what appears to be a spilling-type breaking wave. There are two addi- tional sources of highly energetic white water in the near wake. The bow wave that is generated by the ship's mo- tion breaks, producing white water and turbulence when the wave steepness ah (a = wave amplitude and ~ = wavenum- ber), is greater than ah _ 0.30 (Ramberg and Griffin 1987~. The region adjacent to the ship's hull produces foam, bub- bles and turbulence because of the frictional drag forces at the surface of the hull. The far wake is that region where the variations are relatively slow i.e., where the foam, viscous, propeller, tur- bulence and vertical features of the wake decay slowly and steadily and where the surface roughness and thermal char- acteristics gradually return to those of the surrounding am- bient surface. Measurements have shown that thermal and subsurface bubble wakes can persist for an hour or more after the passage of a ship (National Defense Research Committee 1969~. Under moderate to high wind conditions Auto > 3 m/s), the ambient surface is sufficiently rough so that, visually, the surface in the far wake appears smooth relative to the sur- rounding surface. Recent high altitude photographs released by NASA show that the centerline wake can be observed as far back as 100 km behind a ship. Centerline wakes are vis- ible in SAR imagery as a dark narrow line along the ships track when the surface is sufficiently rough to yield a mea- surable background return. Centerline wakes, in addition to various other wake features are also visible in SEASAT SAR imagery up to 15 km aft of flee ship (Lyden et al. 198S, Vesecky and Stewart 1982~. Observations of the dark cen- terline return irt many wake images show that this region is generally significantly greater than the ship's beam in ex- tent. The width of the dark centerline corresponds very well with the width of the region over which there are breaking bow and stern waves, waves from the Kelvin wave system. The Kelvin wave system's 192S' boundary lines (cusp lines) and 3516' cusp-crest tangent lines are illustrated in the figure. The apex of the boundary lines is always forward of the bow (Newman 1970~. The transverse and divergent wave crests are visible optically for many ship lengths astern and to either side of the ship's path. Tl~e shorter, steeper di- vergent waves tend to be emphasized in aerial photographs. Under moderate to high wind conditions the transverse and cusp waves appear in SAR images of the surface because these waves modulate the existing field of ambient Bragg waves (Lyden et al. 1988~. The persistence of surface foam in the far wake depends on the time it takes for the bubbles to break after they reach the surface. The major factors that increase the stability of a bubble at the surface are increasing salinity (Peltzer and Griffin 1988), decreasing water temperature (Miyake and Abe 1948), increased surface viscosity (Kitchener and Cooper 1957), and the presence of organic surface active ma- terials which modify the surface rheology (Adamson 1976~. A recent photographic analysis by Peltzer (1984) developed empirical relations for the length of the foamy white-water region. These empirical relations are shown in the figure and indicate that the length of the white water region is a function of the Froude number. 2.2 Surface-Active Materials The surface-active (surfactant) materials that are found in all natural water bodies are chemicals which are by- products of plant and animal life. The term surfactant means that the long-chain (10 to 1000's) carbon polar- organic chemicals which constitute these materials have a natural affinity for the free surface of the water in which they reside. Typically the molecules have an acid, alcohol, ketone or other water-soluble radical on one end, which makes that end of the molecule hydrophilic. The opposite end is very similiar to a pure hydrocarbon, which is insoluble in water and is hydrophobic. Because of the polar nature of these substances, when they reach the water surface they find a preferred state in which the hydrophobic end of the molecule removes itself (sticks out) from the water, and this reduces the Gibbs free energy of the water-surfactant system. The lower free energy of the system requires energy to be put back into the system to force the surfactants back into the bulk water. Wind stress is the primary mechanism to do this. As the surfactants adsorb on the surface, they reduce the surface tension and increase the two-dimensional elastic modulus of the surface. A small increase in the surface con- centration of the materials at the interface can lead to sig- niDcant capillary and small surface-gravity wave (< 20 cm) damping because the film viscously retards the very-small- scale velocity held just under the interface. When these areas become large enough they alter the appearance of the sea surface being observed by remote sensing instruments. In light to moderate winds Auto < 3 m/see) these surfactant films are highly persistent. The films can reduce the radar cross-section of the surface by as much as 15 dB depending on the concentration and elastic properties of the film and the radar wavelength. Films can become concentrated enough to attenuate surface waves when they are compacted by horizontal con- vergences due to current field variations at the ocean surface. The currents which are most likely to compact the surfactant films within a ship's wake are the transverse currents gen- erated by flow around the hull or currents associated with the breaking bow and stern waves. Surfactant material can also be rapidly transported to the water surface by adsorp- tion at the air/water interface of rising bubbles generated by air entrainment around the ship's hull, in the breaking bow and stern waves and, in the wake flow. As these bub- bles burst when they reach the air/water interface, the ma- terial is merged with that already adsorbed on the water 535

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surface (Skop, Brown and Lindsley, 1989~. These bubbles are also concentrated by the horizontal convergences in the wake flow behind the ship; this is an additional mechanism which should enhance surfactant concentrations in the sur- face convergence zones. Measurements and observations of the wakes of large ships (Kaiser et al., 1988) show the most persistent wake feature to be a pair of bands of compacted surfactant mate- rial aligned with the ship track along the edges of the tur- bulent wake. The bands are typically one to several meters wide and show a pronounced depression in surface tension. The surface tension in the core of the wake generally has the same value as the ambient water. Photographs suggest that the surfactant material is being organized into these bands by rising bubbles generated in the breaking bow wave which scour the surfactants from the water column. Bubbles are additionally important because they have been observed to persist for an hour or more in a ship's wake. Since these bub- bles presumably transport surfactants to the surface during this time, they may contribute substantially to the long per- sistence of the dark centerline wake signature. Remote sensing of these ship-generated surfactant bands with a SAR depends on the interaction of the electro- magnetic waves with the Bragg-resonant short waves in the region of the bands. The viscous properties of the surfac- tant films in these bands attenuate the short waves and also block their formation or reformation by wind. The damping of these short waves reduces the Bragg scattering in the films compared to that of the surrounding clean water and the film bands appear dark in SAR images. Laboratory experiments (Garrett 1967) have shown that surface-active materials at- tenuate capillary waves through viscous damping at the sur- face. Full-scale experiments (Huhnerfuss et al. 1981) have demonstrated that slicks of surface-active materials attenu- ate Bragg waves in the X- and L- SAR wavelength bands by 40 to GO percent. Since the magnitude of the backscattered radiation from the surface is proportional to the amplitude squared of the Bragg scatterers, this attenuation results in a significant reduction of the backscattered radiation. An example of the reduced return from these ship- generated slick bands is shown in Figure 2a (Ochadlick, et al. 1990~. The measurements were made near the Chesa- peake Light Tower by the NADC SAR during the SAXON 88 experiment. Note the remarkable similarity between the ship wakes and ambient features (mesoscale circulation pat- terns highlighted by surfactant film bands) in the SAR image and the similar features in the photographic image (Figure 2b) of the Mediterranean Sea taken from the Space Shuttle Challenger by Scully-Power in 1984 (Scully Power, 1986~. The photograph was taken into the sunglint pattern which is produced on the water surface by those wave facets which are oriented with respect to the surface to produce specular reflections of the SU1I. In this case, the long persistent ship wakes appear as bright, double bands with a darker area between the bands. Both of these images are approximately 10 km wide and 42 km long. These concentrated films af- fect the wake surface because they influence the transfer of energy and momentum from the wind to the wave field and inhibit wave formation (Barger et al. 19744. a) L-Band SAR Image by Pholographic Image . ~..S 40 km Figure 2. Airborne SAR and photographic images of ship-generated surfactant bands 536

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3.0 SURFACTANT MEASUREMENTS 3.1 Surface Tension Measurement by Spreading Oils Several techniques have been proposed to measure the mechanical properties of ocean surfactant films in situ (e.g., capillary wave damping, laser second-harmonic generation, and spreading oils), but only the use of spreading oils has been successful thus far. Adam (1937) was the first to use a series of buoyant calibrated oils to determine the surface tension of sea water in situ. More recently this technique has been described by Garrett and Duce (1980~. When sev- eral oils are dropped onto the surface of the sea where a film of surface-active material may or may not be present, some will spread while others will not, and therefore the surface tension of the sea at the test point can be bracketed between the calibrated values of any two oils in the set. Figure 3 il- lustrates (a) a spreading oil and (b) a non-spreading oil on the water surface. The straight white lines are toothpicks that were used to apply the oils to the surface. The reso- lution of the surface tension measurements depends on the differences in the calibrated values of the test oils. The oils must also be dispensed rapidly and close together to identify fine structure in the surface tension gradients. For the Field Experiment we refined this technique to provide the neces- sary spatial resolution and prepared a set of twenty three spreading oils to cover the surface tension range from 44 to 73 mN/m. The preparation and calibration of these oils and the principle by which these oils work is described below. a) Spreading Oil b) Non-SpreadIng Oil Figure 3. Video image of the spreading oil distribution The spreading oils were made from a pure non- spreading paraffin oil into which precisely controlled trace quantities of a pure surface-active compound, dodecanol, were dissolved. Different batches of commercially available paraffin oil already contain traces of surface-active compo- nents, so each set of spreading oils must be calibrated - they cannot be made reliably by following the recipe employed for an earlier set. Calibrations were carried out using the Lang- muir trough facility of the NRL Chemistry Division and can be more easily discussed in terms in terms of film pressures. Film pressure (II) is defined as the difference in surface ten- sion calculated by subtracting the surface tension of water covered by a film (Tmeas) from the surface tension of clean water Gil, or II = ct-TmeaS The surface tension (and therefore the film pressure) was varied in the Langmuir trough instrument by compress- ing or expanding a monolayer film of oleyl alcohol surround- ing the oil to be calibrated. The plateau film pressure (at which the oil drop had expanded to a thin disc that could be varied in diameter by expanding or compressing the mono- layer while still maintaining a constant film pressure) was the assigned equilibrium spreading pressure (ESP) of the oil. For oil drops of approximately 20 mg the diameter was approximately 3 cm at the ESP. The principle by which these oils work is illustrated in Figure 4. SAW is the surface tension at the air-water in- terface, SAO is tile surface tension at the air-oil interface, and Sow is the oil water interracial tension. Since SAO and Sow are reduced by adding a surface-active compound to the paraffin oil, a series of oils with varying spreading charac- teristics can be prepared. If SAW > (SAOCOSA + SOWCOSB) the oil will spread. Organic surface-active films on water will reduce SAW. AS the oil becomes thinner by spreading, both cosA and cosB approach the value of 1 and the force balance required for continued spreading becomes SAW > (SAO + SOW). When the colorless oil spreads to a thickness in the 500 to 700 nanometer range, interference colors can be observed visually from a distance. To make a measure- ment, oils with progressively higher concentrations of dode- canol are dropped onto the surface until one is observed to spread. SAW SAO Sow ~` AIR OIL ) - >/ WATER Figure 4. Balance of forces acting on an oil drop The resolution of the measurement in surface tension depends on the ambient surface tension. Table 1 gives the spreading pressures for tile twenty three oils used in the Field Experiment. The resolution is nominally the difference in pressure between adjacent oils, which is tabulated in Column Three of Table 1. Note that at high surface tensions (near s37

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the clean water values) the resolution is nearly 0.16 mN/m, but reduces to several mN/m at very low surface tensions. The spreading pressures were intentionally graduated this way to optimize the resolution of the measurement to the physical processes involved. Oil Number Surface Tension Difference 2 3 4 5 6 7 8 9 10 73.03 72.87 72.72 72.56 72.40 72.26 72.08 71.92 71.76 71.63 .16 .15 .16 .16 .14 .18 .16 .16 .13 .28 The measurement in the Langmuir trough consists of determining the pressure-area relationship for flee surfac- tant, from which its elastic properties are calculated. This procedure is described in detail by Barger and Means (1985) and outlined here. The surfactant material in the sample ad- sorbs to the surface in a few hours and forms a thin film. The free surface area (A) containing the film is decreased slowly by moving a barrier along the surface as the surface ten- sion (Tmeas) is measured with a Wilhelmy plate (Barger and Means 1985). The V\7ilhelmy plate technique uses a flame- cleaned thin platinum plate which is over the filmed water surface. It is carefully and slowly brought into contact with the film and a meniscus forms which then exerts a down- ward force F on the plate equal to 2TmeaSL1Vp, where Lop is the length of the plate in contact with the liquid (bonyancy and plate-effects are ignored here). The surface tension is Amens = F/2Lu,p. In the actual procedure the force is mea- sured with a strain gauge and the system carefully calibrated against known liquids. This procedure generates the func- tion VIA). The measured surface tension TmeaS is related to the underlying clean water surface tension (~) and the pressure (II) exerted by the surfactant film by the relation 11 71.35 .34 12 71.01 .17Tmeas = LY-II. (1) 13 70.84 .31The elasticity of the film is defined as 14 70.53 .53 ,5 70.00 .67E9 =-AdA. (2) 16 17 18 19 20 21 22 23 69.33 68.71 66.62 64.63 61.99 60.82 53.4() 44.55 TABLE 1. SPREADING OILS 3.2 Determination of Film Elasticity The important property of a surfactant film which gov- erns the wave damping is its elasticity (Es). However, we did not measure this in situ, but determined it indirectly as follows. We collected samples of water during the Field Experi- ment and then transported them back to NRL for measure- ment in the Chemistry Division's Langmnir trough. The bottles were chemically cleaned, one liter reagent bottles containing a residual amount of triple-distilled water. The bottles were drained, flushed several times with the sea wa- ter to be sampled from a depth of 0.25 to 0.5 meters, and then filled. This was done by lowering the bottles over the side of the host research vessel R/V Garnet Banks. The sam- ples were then treated with lo Al of a sodium azide solution to kill any life in the sample, thus "freezing" the chemical composition of the surfactants. The bottle was then sealed and stored in a cool, dark place until measurements were made in the Langmnir trough. .62 Theme hv t.~.kin~ t.h~ n~.tive. Of the logarithmic slope of the 2.09 1.99 2.64 1.17 _ ^^ ~ ~ _, ~ wade ~ -O O O ~ ~ Il(A) curve measured in the Langmnir trough we obtain the function Es(A). From the measured II(A) relation we then obtain ES = Es(~)' 7.42 8.85 hi, i, (3) cinch hate F7~tAN and 1[(AN are single valued over the range of values of II encountered in the Field Experiment (0 to 30 mN/m) In order to determine the elasticity Es by this method we make the assumption that the surfactant material ad- sorbing at the water sample in the laboratory has the same physical properties as that which had adsorbed on the sea surface. Treating the samples with sodium azide solution is intended to help insure this process. Very recent tests by W. Barger (private communication, 1990) suggest that sam- ples collected and measured within one hour give the same results as samples stored for months. Hundreds of film sam- ples collected by various techniques, including screens and rotating glass drums which sample a layer on the order of microns near the surface, have shown remarkably similar pressure-area relations (Barger and Means, 1985; Barger et al., 1988). In addition, surface chemists define the reciprocal of the elasticity as the coefficient of compressibility. Com- pressibility measurements for fifty two film samples from Atlantic surface, bulk and deep water and Chesapeake Bay water are reported in Barger and Means (1985) and also show remarkable similaries in behavior. However, there is the possibility that mechanical and chemical reactions occur on the ocean surface which may al- ter the mechanical properties of the surfactant film. The two most likely possibilities are photo-chemical reactions due to the ultraviolet component of the solar spectrum and working of the film due to the continual compaction and expansion 538

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caused by the passage of surface waves. Furthermore, in calm conditions the surface constituents may not have the same relative concentrations as those in the sampled water column. Presently there is little or no evidence to address these issues, so we are reasonably confident in the relation- ship given by equation (3) to determine the elasticity of films on the the ocean surface. 3.3 STEMS (Surface TEnsion Measuring Systems Description 3.3.1 Deployment and Operation STEMS is a catamaran which is towed from the host vessel (R/V Garnet Banks, an ex-Navy YTB class tug) from a boom (6 m long) off the forward port side of the vessel. A photograph of STEMS is shown in Figure 5. It is 2 m wide, 3 m long, and weighs 135 kg (300 lbs). Figure 6 shows the towing configuration employed in the Field Experiment. STEMS needs to be outside of any disturbance created by the host vessel, so it has a movable rudder to control its distance away from the towing vessel. In all cases it must sample an undisturbed water surface. Maximum tow speed depends on sea conditions and wind, but generally a tow speed of 0.5 m/see (1 kt) was found to give relaible perfor- mance of STEMS. During the operation we positioned the R/V Garnet Banks either north or south of the wake pro- duced by the passing target ship, about 100 to 200 meters off-track before the scheduled start of the individual test runs. As the target approached, we moved up on its track and towed STEMS across the wake, intending to follow the serpentine pattern shown in Figure 7. Our tow speed was about 0.5 m/see, so that in the time allocated for each run (approximately 50 minutes) we could only make three to four wake crossings. If the sea became too rough, turbu- lence and splashing within STEMS made observation of the spreading oil behavior difficult to impossible. The device measures the surface tension in situ by drop- ping any twenty two of the twenty three calibrated spreading oils on the water surface from twenty two individually regu- lated channels. The spreading behavior of the oils (whether they do or don't spread) is recorded with a video camera system. Each oil represents one surface tension value, so if one oil spreads and the next one does not, the in situ surface tension is bracketed between the values of the two spreading oils. In some cases a drop of oil will neither spread nor not spread, but it will oscillate instead. Presumably its spread- ing pressure is almost exactly the value of the surfactant film and the oscillation occurs because the ambient surface ten- sion oscillates about a mean value due to alternate surface compactions and expansions induced by the passage of sur- face waves. The dropping of each individual oil is controlled from the ship and a permanent video record of its spreading behavior is obtained for later analysis. In addition to being recorded on VHS video tapes, the STEMS data were mon- itored in real time with the operator annotating the videos with verbal comments on the audio track. A second video system was placed on a mast above the bridge to monitor STEMS and to record the general environmental conditions encountered. In addition, an audio cassette record was made from the bridge describing various facets of the operation, the environmental conditions, when STEMS entered a slick, and other pertinent test information. Surface TEnsion Illeasurement system (STEINS) Figure 5. Photograph of the STEMS ~30m ~ 0.5 m/se ~ R/V GARNET BANKS | = (1 at) ~ ~ \1 em BOOM \ TOWING/UMBIUCAL CABLE 15m \ \/\= SURFACE TENSION MEASUREMENT _13 m1- SYSTEM (STEMS) Figure 6. STEMS towing configuration ~ - -TTARR&aCEK - - - 1~ 1 /^ video,: t RN GARNET BANKS if 20C m _ __ ~WAKEN 100 m CENTERLINE I it)- SIIIOKE FLARE Figure 7. STEMS wake crossing pattern 3.3.2 Data Resolution and Quality One reading of surface tension was typically obtained every one to two seconds when the winds were under 5.5 m/see, and less frequently for higher wind speeds. This gave a cross-wake resolution of 0.5 to 1.0 m in the lighter- wind runs. The down-wake resolution was highly variable 539

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but averaged 50 m. The resolution in surface tension varied from 0.16 mN/m to a few mN/m based on the differences in spreading pressures of the oils (see Table 1~. Through the first nine days of the Field Experiment (Jan. 23rd to Jan. 30th), the oil number in the table corresponded di- rectly to the channel number on the STEMS. Channels 5 and ~ did not work throughout the entire test and channel 22 worked only on the final two days of the Field Experi- ment (Jan. 31st and Feb 1st). Oil 23 was used on the final day of the test (Feb. 1st) in place of oil 1. It was unfortu- nate that oils 22 and 23 were not working or available during most of the Field Experiment because we could not estab- lish the maximum value of the surface tension decrease in certain regions of both the ship generated and ambient sur- factant bands. If we assume that the physical properties of the compacted surfactant material in the bands were similar throughout the Field Experiment, we know that the maxi- mum surface tension decrease in the bands varied between our measured value of 11.3 mN/m and some value greater than 27.2 mN/m. There were regions where oils 21, 22 and 23 did not spread when they were used on the final day (Feb. 1st) of the Field Experiment and in addition, oils 21 and 22 did not spread during portions of the measurements on Jan. 31st. All of the film pressure - area curves we have exam- ined so far (1/26, 1/28, 1/29) have similar characteristics, which suggests that the physical properties of the surfactant films are indeed similar on a day to day basis. Furthermore, measurements of surface film pressures of surface-active or- ganic matter generated by marine phytoplankton typically range between 20 mN/m and 30 mN/m (Frew et al., 1990~. Considering all of the above, we can confidently assume that the maximum surface film pressure in the film bands varied somewhere between 11.3 ~nN/m and 30 mN/m. 3.4 Results of the Surface Tension Measure- ments The STEMS data processing consists of playing back the video tapes several times and recording the spreading behavior of each oil. In this manner the dividing line be- tween spread and non-spread is determined as a function of time on the video. Readings are made each second. The time series of surface tension is then input to a computer to- gether with the film pressure-area and elasticity data from the Langmuir trough. Also, wave damping coefficients (as a function of elasticity for a given surface wavelength) can be calculated. Finally cross-wake profiles or two-dimensional maps of surface tension, film pressure, elasticity and wave damping can be generated for a given surface wavelength. We include here for each of the wake crossings, the measured surface tension profiles across the wake. The corresponding film pressure profiles can be calculated using equation (1) with cat taken as the surface tension measured in the clean water well outside of the wake. The film pressure directly relates our field measurements to the laboratory-determined elasticity. The wake widths were determined by multiplying the speed of the towed STEMS platform by the total time it took the STEMS to cross the wake. Surface tension measurements were obtained during the 25 knot run along three wake crossings centered at 3735 m, 11978 m and 21316 meters aft of the ship. These surface tension distributions are shown in Figure 8. All crossings are plotted so that the water south of the wake (0.0 m) is at the left of the figure. The wake edges are defined as the lo . . cation of the edge of the outermost foam bands in the video record made by the STEMS as it crossed the wake and/or the region corresponding directly to the sudden decrease (or increase) in surface tension measured by the STEMS as it en- tered (or exited) these outermost surfactant bands. Regions of decreased surface tension relative to the ambient value are caused by increased film pressure of a compacted surfactant in those regions. Each of the three crossings has two edge bands of compacted film as well as one or more additional bands between the edge bands. From this data alone it is not clear whether these inner bands persist, but rather move around, or appear and disappear. The two outermost bands were visible to the eye as slicks, whereas this was not gen- erally true for the inner bands. Since the surface is already smooth in the centerline region of the turbulent wake, the visibility of these inner bands will be limited. In addition, the surfactant films will not allow the wind waves to regrow in these regions and will limit the regrowth throughout the entire centerline wake region. The outer bands are visible because of the contrast between the ambient surface where small waves are present and the smooth surface where the small waves have been damped by the compacted surfactant material. The surface tension in the core of the wake has the same value as the ambient (away from the wake). As was discussed in Section 3.3.2, we were not able to measure the minimum surface tension value in certain re- gions of the crossings. For the crossings shown in Figure 8 we have assigned an arbitrary value of 60.0 mN/m to those re- gions where oil 21 did not spread. This value is only slightly less than the measured value of 60.82 mN/m associated with oil 21 which did not spread. 4.0 MODEL DEVELOPMENT, CALCU- LATIONS AND COMPARISONS WITH MEASUREMENTS 4.1 The Energy Balance Equation To examine the short wave field in the wake of a sur- face ship, we have developed a model based on the spectral energy balance equation ) ot + cg( k ) - VE( k ) = SW( ~ ) + Snl( A' ) -St( k )-Ss( k ), (4) where E is the energy density spectrum, k is the circular wave number vector, t is time and cg( k ) is the group ve- locity vector for the spectral component and the S's are the energy source terms for the spectral component at the wave number k. SW and Snl represent the rates of energy input to the waves from, respectively, the wind and wave-wave nonlinear interactions. St is the rate of energy dissipation due to the interactions of the waves with turbulence. Ss is the direct rate of energy dissipation due to viscosity which can be in- fluenced by the effect of surface film elasticity on the free surface boundary layer. The energy balance in the form of equation (4) neglects wave scattering by turbulence and wave diffraction by mean flows. These effects are insignificant compared to the other 540

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_ 78 F 73 0 ._ 68- : ~ 63 In 58 78 E 73 ~ 63 In 58 78 ~ 73 ~ 0 In 68 In 58 a) Distance Aft, 3575 m (21.8L), Wake Width, 117 m (6.93B) I ~MAIMS \AI;~ _ I I Isaac ''IUtil -| Edge Band ~1 ~ Inner Band. is/ \* ~Edge Band b) Distance Aft, 11978 m (69.8L), Wake Width, 144 m (8.56B) ~ ~Wake Width .~ Edge Bandy ~Edge Band c) Distance Aft, 21316 m (124.2L), Wake Width, 165 m (9.83B) ,_ -Wake Width ~- 1 Edge Band Inner Bands ~ Edge Band | _ _! . . . . . . . . 15 65 115 165 215 265 Cross-Wake Distance, (m) Figure 8. Measured cross-wake surface tension distributions source terms except in the first few ship lengths of the wake (near field region), when estimated from the scattering the- ory of Phillips (1958) and the analysis of diffraction by ship wake flows by Skop et al. (1990~. At the present time little is known about relationships between the four source terms on the right hand side of equation (4) and oceanic conditions, either in or out of ship wakes, for the short waves associated with radar backscat- tering. For this reason, we cannot make a precise compar- ison between radar measurements and the predicted wave energy distribution. Instead, we shall compare radar mea- surements with predictions frown equation (4) using plausible formulations for the source terms based on what is currently known about them. The resulting qualitative agreement between radar measurements and the calculated wave en- ergy distribution, including its sensitivity to variations in the source term formulations, will indicate the important hydrodynamic effects leading to the short wave calming in ship wakes. Taking this approach, we now explain the for- mulations we have used for the source terms. -1 4.1.1 Wind Energy Input to Short Waves Wind induced growth of short waves was determined by Plant (1982) on the basis of available experimental data. He expressed the growth rate, ,Bw(a), of a spectral component with circular frequency ~ as: 1,, = (0.04 ~ 0.02)a(u*/c)2cos8. (5) Here it* is the friction velocity of the wind, c is the phase ve- locity of the wave component and ~ is the angle between the wind and the direction of wave propagation. Since the data used by Plant includes damping from viscosity, the growth due to wind alone should be slightly larger than his esti- mate. Therefore, we will use 0.05 for the numerical coeffi- cient which is slightly above the median, but still in Plant's range. Under typical conditions, u* is related to the ten meter wind speed ulo by: Ilm = Ulo/30. 541 (6)

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Useful information on wind energy input in addition to equation (5) is provided by the studies of Mitsuyasu and Honda (1982~. They found that when the water surface was calmed, interestingly achieved with a surfactant, the friction velocity was reduced to less than u~o/30. Changing from a naturally wind roughened surface to a nearly calm surface reduced the friction velocity by roughly 14 percent. If the formulation of equation (5) applies, this reduces the spectral growth by thirty percent. To account for the reduction in growth rate when the waves are calmed, rather than using Su, = 'dwE' we approx- imate Sw as: Sw = (41 + p2 E )E, (7) where Ea is the ambient spectral level outside the wake, and 31 + p2 = 0.05~(u*/c)2cos8. (8) For our subsequent "base case" calculations, we shall take p2 = pi/2. This corresponds to a 33 percent reduction in the energy growth rate from the wind if the waves were completely calmed. The short waves which are attenuated in the ship wakes have wavenumbers and frequencies several times that of the spectral peak. On the other hand, the available data used by Plant in developing equation (5) are based on wave fre- quencies close to the spectral peak. The validity of the for- mulation for frequencies much higher than the spectral peak is unknown. However, it is the best information presently available and that is why we have used it, modified by the reduction due to surface smoothness. We shall include the base case of p2 = 0 in our subsequent calculations to demon- strate the effect of neglecting the reduction in growth rate due to smoothness. 4.1.2 Nonlinear Energy Transfer to Short Waves The present state of the art in estimating nonlinear en- ergy transfer is the resonant interaction theory of Hassel- mann (1962~. This is a perturbation based theory that in- cludes Taylor series expansions about the mean free surface elevation. As a result, when short waves have lengths that are small in comparison to the long wave amplitudes, the range of use of the series covers many short wavelengths. The validity of the existing theory for this situation is un- certain and is an area of active fundamental research at this time. Nevertheless, with nothing more certain or bet- ter available at this time, we have applied a computer code based on the Hasselmann theory to the range of frequen- cies from very small to those responsible for L-band radar backscattering. Heretofore, application of the Hasselmann theory has not included these short, high-frequency waves. Figure 9 shows the computed nonlinear energy transfer rate to waves propagating in the wind direction as a func- tion of wave frequency for a Jonswap spectrum correspond- ing to a wind speed of 6.2 m/s (12 knots at a height of 10 meters). The figure also shows the wind energy input rate as a function of the theory according to Plant (1982~. For the frequency range corresponding to L-band scattering, the nonlinear energy transfer rate is roughly 20 percent of the wind energy input rate. 0.20 O. ~ ~ N E in 0 15 ' $ L`J o - 0.13 z 0.10 z 0.08 0.05 U. 0.03 . ~ ooooo FROM NONLINEAR INTERACTIONS ~ o 0 0 FROM WIND STRESS 1.00 1.50 2.00 2.50 FREQUENCY ( Hz ) Figure 9. Computed energy transfer to short waves from the wind and nonlinear interactions Although knowledge of nonlinear energy input to waves much shorter than the spectral peak wavelength in equilib- rium conditions is scanty, even less is known about it for the non-equilibrium condition of attenuated and regrowing short waves in a ship wake. To deal with this uncertainty here, we will take two steps: 1. Set the nonlinear energy input to 20 percent of the wind energy input for our "base case" calculations, Snot = HE (9a) = 0.20(,l], +,(12-). (9b) En 2. Perform calculations with other values of fly to deter- mine both the effect of the uncertainty and the order- of-magnitude of the influence of the nonlinear energy transfer on the short wave energy distribution through the wake. 4.1.3 Short Wave Energy Dissipation Due to Turbulence The primary mechanism for wave energy dissipation by turbulence in non-breaking wave conditions is thought to be downward convection of wave energy by the vertical velocity components of the turbulence. Kitaigorodskii and Lumley (1983) derived a mathematical relationship, based on this concept, between the dissipation rate and the correlation between the vertical turbulence velocity and the square of the fluid velocity due to the waves. However, as far as we know, this correlation has never been measured either in or out of a ship wake. Thus, we are directed to an alternative approach for estimating the downward convection of wave energy by turbulence. Olmez and Milgram (1989) measured the dissipation of short waves due to turbulence generated by a submerged oscillating grid in a laboratory tank. Using the concept of the downward convection of wave energy, they developed the following order-of-magnitude formula for St: 542

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St = ((2 WE = 0.4(dw'/dz)E, (10) where dw'/dz is the rate of increase of the RMS vertical turbulence velocity near the water surface. w' is presumed to be zero at the surface. To use equation lO, the RMS vertical turbulence ve- locity, flu', must be estimated. Kitaigorodskii et al., (1983) have estimated this velocity component from measurements made in Lake Oratorio. Their shallowest measurement loca- tion was 0.3 meters beneath the surface where both w' and the RMS horizontal velocity, u,, were roughly u~o/120. To is the wind speed at a height of ten meters. The turbulent velocity was estimated by subtracting the vertical wave ve- locity, inferred from the measured wave elevation, from the measured total velocity. We note nearly all errors in the estimate of wave velocity will lead to over estimates of w'. Brumley and Jirka (1987) studied the influence of a free surface on otherwise homogeneous turbulence. Parameters of the horizontal turbulence velocity were altered slightly whereas parameters of the vertical velocity were strongly altered in a layer having a depth about equal to the integral length scale of the horizontal turbulence. The vertical RMS velocity and integral length scale were nearly zero at the free surface and increased to values comparable to those of the horizontal turbulence at the bottom of the layer. The functional form of w' versus depth is uncertain. The Brumley and Jirka data show a linear dependence for the upper 2 percent changing to a (depth)~/3 dependence over the lower 95 percent. McDougal (1979) measured the effect of a rigid lid on otherwise homogeneous turbulence. His results were similar to those of Brumley and Jirka, ex- cept the increase of w' with depth was nearly linear over a depth equal to the integral length scale of the horizontal tur- bulence. Hunt and Graham (1978) have shown theoretically and numerically that the form of w' versus depth depends on details of the turbulence spectrum. For our purposes here, we will make the approximation that w, increases linearly from zero at the surface to u~o/120 at a depth ET (which we shall take to be 0.3 meters), dw,/dz _ u~o/~120H), (11) outside the wake. The only wake turbulence measurements available to us are those taken in model tests and provided to us by W. Lindenmuth (private communication, 1990~. Very strong turbulence just behind the ship model decayed such that at a distance of ten ship beams aft of the stern, u' was approxi- mately 0.02V in the near surface region, where V is the ship speed. The depth of the zone of influence of the free surface on the vertical turbulence velocity was about one-eighth of the ship draft (D/8~. Further aft, the turbulent velocities became too small to reliably measure with the laser doppler anemometer being used. We need to couple Lindenmuth's measurements with our measurements of wake widths and known features of turbulent wakes in general. Under the assumption of self-similar velocity profiles and eddy viscosities, a round drag wake grows asymptot- ically as W ~ x/3, where W is the width and x is the downstream distance. A wake with zero net axial momen- tum grows as W ~ X]/5 (Birkhoff and Zarantonello 1957~. Because of the low Froude numbers of wakes further aft than one ship length, they are expected to behave globally in the same fashion as round wakes. If all of the hull drag were due to skin friction, this drag would be exactly balanced by the propeller thrust and the wake as a whole would have zero axial momentum. Because of the energy radiated by the ship-generated waves, the wake has net momentum flux directed aft with a magnitude equal to the wave drag. How- ever, for the ship parameters and speeds of interest here, the skin friction drag is larger than the wave drag so we ex- pect the far wake behavior to be more like a zero-momentum wake than a drag wake or a jet. This expectation is justi- fied by the measured widths of the zone of wake-modified surface tensions. Figure JO shows these measured widths (corresponding to Figure 8) as well as the following equa- tion which fits the data well: W(~) = 22.9(x + 0.4B)~/5, (12) where W,x, and the ship beam B are measured in meters. For the ship that generated the data for Figures 8 and to the beam B = 16.75 meters. ~ 175 cY Al ~ ~ ~ 125 I _ C) _ 3 75 111 25-t ~ / _ - ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 '- ' 0 5000 10000 15000 20000 DISTANCE BEHIND SHIP (METERS) Figure to. Measured and theoretical wake widths For a self-similar zero-momentum wake, all velocities behave asymptotically as X-4/5, SO with u, = 0.02V ten ship beams aft of the ship, we model u' over the entire wake as: ( ) (a + 0 4B) (13) TheII, dw,/dz is approximated as dw, do = 0.02- 10.4B 4/5 / (D/8)(s+04B) , (14) inside the wake. Equation 14 neglects the variation in tur- bulence across the wake. Also, this equation is used in our model only when the turbulence gradient exceeds the ambi- ent level given by equation (ll). Setting the two expressions equal yields the length Lo of tl~e zone of ship-affected tur- bulence as: L 418B(H V )5/4 - 0 4B (15) 4.1.4 Dissipation of Energy Due to the Presence of a Surfactant Film The damping of surface waves in clean water is well known to have a l/e time of 1/(2uk2) where I' is the kine- matic viscosity and k is the wavenumber (Lamb 1945). The l/e times are about 4500 seconds for 30 cm waves responsi 543

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ble for L-band Bragg scattering, 32 seconds for 5 cm waves associated with C-band scattering and 5 seconds for 2 cm waves associated with X-band scattering. These decay rates are typically small in comparison to growth rates (equation 5) due to modest winds. What is less well known, is that elastic surface films can dramatically increase the viscous damping rates of short waves. In the absence of a surface film, the requirement of zero shear on the surface leads to a very weak surface bound- ary layer with similarly weak damping. In the presence of an elastic film, however, a much stronger boundary layer with increased damping can be necessary to provide a shear stress equal to the gradient of the surface tension. A thorough study of the wave damping due to a lami- nar boundary layer beneath an elastic surface film was con- ducted by Dorrestein (19513. His results can be written as: Ss = psE (16a) where with _ [ ~ I] [ ( ~ ) ( ~ ) ] (gk + ~k3)l/2 ~ = Ilk h = ash kit (16C) Here g = 980 cm/s2 is the gravitational acceleration, p = 1.02 gm/cm3 is the density of seawater, ~ = 0.01 cm2/s is the kinematic viscosity of seawater, cr = 73 mN/m is the nominal surface tension at the air/seawater interface, Es (in mN/m) is the film elasticity and ~ is the wavenumber of the wave. Figure 11 illustrates the rate of decay of capillary- gravity waves on the free surface due to the presence of a surfactant film based on the studies of Dorrestein. The wave- length range in the figure covers the Ka- to L-Band range in SAR operating frequencies. Plotted are a family of curves showing the ratio of the wave energy after one wavelength of propagation in the surfact ant film band to the energy at the beginning of the cycle for surfaces films with different physi- cal or elastic properties. In addition, the two limiting cases, a clean free surface where only the viscosity of the fluid is responsible for wave damping and a surface covered by an infinitely stiff, incompressible film are also included. The figure shows that the presence of a surfactant film greatly increases the rate of decay of capillary-gravity waves less than 20 cm in wavelength. Note also that a small change in surface elasticity can result in a significant change in cap- illary and small surface gravity wave damping for a given wavelength. We close this subsection by noting that in the pres- ence of a turbulent free surface boundary layer, the actual surfactant-induced wave damping could be different than predicted by Dorrestein's laminar analysis. However, it seems likely that the effect of turbulence would be small here, on the basis of the vanishing vertical turbulence veloc- ity at the free surface found by Brumley and Jirka (1987) and the very small depth, O(IJ/~), of the wave-induced lam- inar surface boundary layer. x J X 09 - o tr: 0.8 as 0.7 1.0 1 ;~ Clean Surface. Es = 0.0 -Elasticity, Es - 2 0 ~~( ~ Elasticity, Es - 50 ~= / f- o Elasticity, Es = 10.0 ,/ -~ Elasticity, Es = 25.0 ~ ~ Elasticity, Es=45.0 :~,~4 ~ Infinitely stin Surface 1 10 Wavelength, L (cm) Figure 11. Wave energy decay in a surfactant film 100 4.2 Data and Conditions Used for the Model Computations (16b) Calculations were carried out using data that were ob tained in the wake of a Navy ship at a speed of 12.9 m/s (25 kt) on January 28th, 1989. The Navy ship reported a wind speed of 5 knots whereas the R/V Sea Tech reported wind speeds varying between 7 and 9 knots while in the wake. These vessels reported disparate and varying wind directions with angles between 30 and 90 degrees with re spect to the cross-wake direction. We cannot fully resolve the disagreement over the wind speed. However, the direc tion of the short waves is clearly visible on a videotape made from the R/V Garnet Banks during the surface tension mea surements. This direction is about 50 degrees with respect to the cross-wake direction. The uncertainty of the actual wind speed is unfortu- nate for the modelling of L-band Bragg scattering waves. For these, the model growth rate terms from the wind and nonlinear interactions have the same order of magnitude as the dissipation terms from turbulence, viscosity and surfac- tants. Thus the L-band waves can be modelled as growing or decaying, depending on the chosen wind speed within the re- ported range. The same difficulty applies to C- and X-band waves in the first few ship lengths of the wake. However, it is not severe in the far field at C- and X-band because there, for all the reported wind speeds, these waves grow outside the surfactant bands and decay in the strong surfactant bands. We will use a wind speed of 7 knots at an angle of 50 degrees from the cross-wake direction in our model calcula- tions here. However, we must point out that if 9 knots were chosen very little wave attenuation would be predicted in the wake for L-band waves, and if 5 knots were chosen the waves would be predicted to decay, even outside the wake. The SAR image with which model calculations will be compared was made from an aircraft flying parallel to the wake. Thus the predominant Bragg scattering waves to which the SAR is most sensitive propagate directly across the wake. For our estimated wind direction, the value of to be used in Equation 5 is 50 degrees. Surface tension measurements were obtained along three wake crossings centered at 3735 m, 11978 m and 21316 meters aft of the ship. These surface tension distributions are shown in Figure 8. Regions of decreased surface tension 544

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- ~ ~ EN i* >.*s ~, sit ~ ~ ~ ~ ~ =,,~,~,~,,~,,,~.~s*i.:~.,,S,,.,,,..~,~:~^r~....5 ~ ~ ~--~ Figure 12. L-band SAR image of the Navy ship wake (courtesy of J. Lyden, ERIM) relative to the ambient value are caused by increased film pressure of a compacted surfactant in those regions. Each of the three crossings has two edge bands of compacted film as well as one or more additional bands between the edge bands. Figure 12 is an L-band SAR image of the Navy ship wake obtained from an aircraft during the same time that the surface tension measurements in the ship wake were be- ing made by STEMS as it was towed across the wake by the R/V Garnet Banks. C- and X-band data were also ob- tained simultaneously by the multi-band aircraft SAR. We will compare the multiband SAR backscatter intensity data with model calculations using the surface tension data from the 3735 m cut and film elasticity values calculated from the pressure-area curve of the water sample obtained prior to the 25 knot run as input to the model. The film pressure - area curve for the surfactant mate- rial is needed to relate the film elasticity Es to the measured surface tension. A subsurface water example was collected prior to the 25 knot run for later film pressure versus area measurements in the Chemistry Division at NRL. The re- sults of these measurements, plotted as the natural loga- rithm of the film pressure (in mN/m) versus the natural logarithm of the surface area (in cm2), are shown in Fig- ure 13. These data have been fitted with three straight line segments so that for each portion of the fitted curve we have II = CAn, (17) where n is the slope of the portion and C is a characteristic constant of that portion of the curve. Then, from equation (2), we find that Es =-nII (18) or, specifically from the three segment fit in Figure 13, ~ 0.0 II < 0.20, E _ J 5.21II 0.20 ~ II < 4.42, (19) s - ~ 2.90II 4.42 < II < 8.58, ~ 1.27H ~ ~ 8.58. As was noted in section 3.2, we make the assumption that the surfactant material adsorbing at the water surface in the laboratory sample has the same physical properties as that which had adsorbed on the sea surface during the test. It is quite possible that the film elasticity determined from 545 the subsurface water sample is not exactly representative of the film elasticity of the material in the surfactant bands. Nevertheless, the value of the film pressure at each location across the wake used in equation (19) to determine the cross- wake elasticity distribution used in the energy calculations is that measured by STEMS. _ ~ E ~ = -~.27 g X E h J ~58 mN/m - 6~ n = -2.90 - ~4.42 mN/m Awn = -5.21 . . . . . . , . , . ~ , . ~ 4.2 4.4 4.6 4.e 5.0 s.2 5.4 5.6 Ln Fllm Area, (cm.~2) Figure 13. Measured surfactant film pressure-area curve It is very difficult to nearly impossible to determine the exact composition of the material in the surfactant film bands measured during the January Field Experiment. There are literally hundreds of different materials present in these film bands. Surface chemists (Frew et al., 1990, Barger and Means, 1985) agree that the major constituents of these film bands are relatively soluble, highly oxygenated and condensed, but poorly defined polymeric materials of high molecular weight. However, it is not the composi- tion of the material in the bands that is important, but rather the effects of physical properties of the material on the ambient wave field. A small change in surface elastic- ity will lead to significant changes in capillary and small surface gravity wave damping. Given the relative similarity in the pressure-area curves of the water samples obtained during the Field Experiment with hundreds of samples ob- tained from varied locations throughout the major oceans (Frew, 1990, Barger and Means, 1985; Barger et al., 1988) we feel confident that the physical properties of the films present during the Field Experiment are representative of many films throughout the major oceans. To properly char

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acterize and measure the physical properties of surfactants that are important for wave damping studies, controlled nat- ural surfactant materials must be developed by extracting the material from natural seawater samples. Comparing the physical properties of these extracted films, which we now know the concentration of, with untreated seawater samples will provide some insight into the concentration of the ma- terials in the untreated samples. Surface tensions throughout the wake, for use in the model computations, are found by interpolating between measurements on the wake cuts. This requires an estimated surface distribution on a wake cut at the ship stern. For this, we have hypothesized two eight meter wide edge bands whose centers are spaced two ship beams apart. The surface tension used in the bands is 12 mN/m which is the lowest value we measured in the actual cuts. When integrating the energy balance equation, the re- sults at each time step must be restrained to prescribed up- per and lower limits. The upper limit is the ambient energy level outside the wake. For the lower limit we have used 20 percent of the ambient inasmuch as this is the typical re- duction in wave energy level we measured directly in wakes during the experiments. - m - ~ 30 c - , 25 .= a: - m 2 - ~O - ~ -2 Q -4 .= -6 -1 85 The initial condition we used for the model computa- tions has the energy reduced to 20 percent of the ambient level at the ship stern over a distance of one ship beam. The initial energy is taken as linearly rising from this depressed level back to the ambient level on each side of the ship over a distance of one-half a ship beam, thus making the entire depressed zone two ship beams wide. 4.3 Computations and Comparisons With Measurements Results of calculations for the spectral energy ratio (E/Ea) along the SAR look direction at a center distance of 3735 m aft of the Navy ship are shown in Figures 14, 15 and 16. This is the distance of our closest wake crossing mea- surements for which the surface tension distribution is also shown in the figures. The results are expressed in dB down from the ambient, [lOlog~O(E/Ea)~. For these calculations we have used 60.0 mN/m for the value of surface tension in the regions where oil 21 did not spread and we do not know the lower surface tension limit (see Section 3.3.2~. The re- sults are shown for three wavelengths: 15.9 cm, 3.6 cm and 2.0 cm which correspond to the L-, C- and X-band wave 78 E 73 c o ~ 68 i a) Cross-wake Surtace Tension 3735 m aft, Wake Width, 117 m (6.93B) Wake Width ~ I !r. . - ' , Id, lo,., Inner Bande /N ~Edge Band b) lUeasured Relative Intensity, (L-band SAR) ~4 k Wake Width >I Libel , W1 20 - ~ . . . . ~ . . . . . c) Calculated Spectral Energy Ratio of L-Band (15.9 cm) Waves `, 1'- Wake Width ~ - it, -135 -85 -35 1 5 65 1 1 5 165 Cross-Wake Distance, (m) Figure 14. Calculated spectral energy ratio of L-band waves together with the measured cross-wake surface tension and SAR intensity distributions 3735 m aft of the ship 546

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78 - a 73 o ,_ 68 63 :' 6 a) Cross-wake Surface Tension, 3735 m aft; Wake Width, 117 m (6.93B) | ~Wake Width: Edoe Band ~ Inner | Bande 1 ~1 ~Edge Band 11 - - m - ._ us - fir: m 4] - A~ b) Measured Relative Intensity (C-band SAR) |< Wake Width: - c) Calculated Spectral Energy Ratio of C-band (3.6 cm) Waves ~2 C O Al -2 Q -4 i.= -8 -195 -145 -95 -45 |< Wake Width:- Edge Band ~, It_ I Inner Bande ,/~1 ~Edge Band 5 55 105 155 Cross-Wake Distance, (m) Figure 15. Calculated spectral energy ratio of C-band waves together with the measured cross-wake surface tension and SAR intensity distributions 3735 m aft of the ship lengths at the incidence angle of 52 degrees used for SAR images of this experimental run. The measured SAR cross- sections at 3735 m aft are also shown in the figures. The SAR intensity data shown are averaged longitudinally over a length of 100 meters. The X-band signal to noise ratio was near unity for this run, so that any direct comparison with the data may be subject to some error. The mathematical model predicts L-band waves have not recovered to ambient levels and are attenuated across the entire wake. Conversely, the C- and X-band waves are predicted to have recovered to ambient levels except in and immediately downwind of zones of compressed surface films. These findings are consistent with the SAR measurements at the same location shown in the figures. The L-band SAR data shows the full width attenuation and several of its vari- ations in intensity across the wake can be visually "matched up" with spectral energy variations in the mathematical pre- dictions. Correlations between the regions of the largest backscatter intensity reduction in the SAR data and the re- gions of lowest surface tension are evident in the C- and X-band data as well. The reductions in image intensity in these regions are about 6 dB at L-band and 5 dB at C-band. Corresponding attenuations predicted by the mathematical model are about 5 dB at L-band and 7 dB at C- and X-band. The latter value is set by the arbitrary minimum energy level of 20 percent of the ambient level used for the computations. As is predicted by the mathematical model, the C- and X-band SAR data show backscatter intensity in the wake to be nearly at ambient levels except in isolated regions whose locations are in reasonable correspondence with zones of measured surfactant concentration. 4.4 Influence of Variations in Model Input Parameters Because of uncertainties about the accuracy of some of the formulations used for the source terms in the energy balance equation, a study of the influence of variations in the source terms should be done. Although a complete study of this type cannot be included in this paper, we will show the influences of a few variations. The effects of source term variations on the wake 3735 meters and further aft will be s47

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78 E 73 o ._ c 68 63 a) Cross-wake Surface Tension 3735 m aft; Wake Width, 117 m (6.93B) ~ Wake Width ~ ^- ~ ~- ~_-we_ --lo ~1 Edge Band ~ j Inner till 1 l Bands | ~ ~ 1~' *- Edge Band 25 ~ m ,~ 20 - ~ 15 .~ to to - m 4. As 2 o -2 Q on -4 .~; -6 a. -1 95 b) Measured Relative Intensity, (X-band SAR) |< Wake Width ~ c) Calculated Spectral Energy Ratio of X-band (2.0 cm) Waves |~----- Wake Width: | Inner | I Bands l I ~ ~Edge Band -145 -95 -45 Cross-Wake Distance, (m) 5 55 105 155 Figure 16. Calculated spectral energy ratio of X-band waves together with the measured cross-wake surface tension and SAR intensity distributions 3735 m aft of the ship most pronounced for L-band waves since the others have regrown to the ambient level except in the surfactant bands. We will compare results with source term variations with the base case L-band results shown in Figure 14. Figure 17 shows the predicted L-band energy distribu- tion 3735 meters aft when the wave energy decay rate due to turbulence in the ambient sea is reduced to seventy-five per- cent of the value used to produce Figure 14. This changes the decay rate in the wake because the ship-induced turbu- lent decay is taken as diminishing with distance aft (equa- tions 10 and 14) until it becomes equal to the ambient level. The effect of the modest reduction in decay from turbulence is strong with significant wave attenuation remaining only in the regions of strong surfactant concentration on the down- wind side of the wake instead of all across the wake as in the base case. Figure 18 shows the effect of raising the energy input due to nonlinear interactions by fifty percent. Compari- son with Figure 14 shows the significant change that can be caused by such an increase in the energy transfer from nonlinear interactions. As was discussed in Section 3.3.2, we were not able to determine the maximum value of the surface tension de- crease in the regions where oil 21 did not spread. For the original model calculations shown in Figure 14, we used 60.0 mN/m as the surface tension in these regions. It is entirely possible that that surface tension value could have been as low as 42.0 mN/m. Figure 19 shows the effect of decreas- ing the surface tension value in these regions to 42.0 mN/m. 42.0 mN/m is the lower limit on the surface tension value that can be associated with the compacted surfactant mate- rial at the surface during the Field Experiment. Decreasing the surface tension increases the surfactant damping in these regions. Comparing the two figures shows that the possible variation in surfactant damping is shown to have a marked effect on the L-band wave energy levels. Figure 20 shows the results of eliminating the effect of the reduction in wind growth rate due to surface smoothness. For this computation, The wind energy input rate was set to: Sw = 0.05a~u*/c)2Ecos8. (20) 548

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m 1 Calculated Spectral Energy Ratio of L-band (15.9 cm) Waves 1 _ 1 =2~-, ~ . 0 -3 Cal -185 -135 -85 -35 1 5 65 115 165 Cross-Wake Distances, (m) Figure 17. Calculated spectral energy ratio of L-band waves when the ambient turbulence level is reduced by seventy-five percent m 1 - ~ O c - -1 0 Q .2 a, - Calculated Spectral Energy Ratio of L-Band (15.9 cm) Waves -3 ...... -1 85 1~ Wake Width .1 ~ ,rv: ~ ,,,,,,,,,,V . -1 35 85 -35 15 65 Cross-Wake Distance, (m) 115 165 Figure 18. Calculated spectral energy ratio of L-band waves when the energy input due to nonlinear interactions is increased by fifty percent m 2 0 ~-2 Calculated Spectral Energy Ratio of L-band (15.9 cm) Waves O~ L Wake Width lo| L= :4L 74~1 ~ 0 -8 -1 85 -1 35 -85 -35 1 5 65 1 1 5 1 65 Cross-Wake Distance, (m) Figure 19. Calculated spectral energy ratio of L-band waves when the surfactant damping is increased 549

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al 1 - - c us -1 o - , -2 ~ Q V} ~3 .p _ . ~-. a -185 -135 Calculated Spectral Energy Ratio of L-band (15.9 cm) Waves k Wake Width >I I/ {N - 8 5 - 3 5 1 5 Cross-Wake Distance, (m) 65 115 165 Figure 20. Calculated spectral energy ratio of L-band waves when the reduction in wind growth rate due to surface smoothness is removed Comparing Figure 20 with Figure 14 shows that, at least at the 3735 meter location, the effect of this variation in wind energy input is clearly observable. Although a much more complete sensitivity study should be done in the future, the above examples clearly show that distributions of short waves in wakes are sensitive to all of the terms in the energy balance equation. However, it is because of the surfactant effects alone that attenuation can persist into the very far wake. The other attenuating effects and the energy input erects, at least to the extent that we presently understand them, would lead to wave re- growth to ambient levels in the very far wake if surface film concentration did not persist into Ellis region. This is prob- ably why SAR centerline images do not persist into the very far wake when the sea is rough. The mixing associated with wave breaking eliminates the bands of ship-induced surfac- tant concentration in that situation. 5.0 SUMMARY AND CONCLUSIONS Previous to this experiment in situ surface tension data have never been measured to the resolution in surface ten- sion obtained or with such a fine spatial resolution. Coupling these measurements to the determination of the pressure- area curves has for the first time allowed us to infer film elasticity distributions for ocean water and to realistically calculate the changes in wave amplitude due to the presence of these surfactants. The major process by which surfactants affect synthetic aperture radar (SAR) or other radar images of the ocean surface is through wave damping, and two important vari- ables in this process are the Bragg scattering wave number (if the incidence angle is not too large or small) and the sur- face film elasticity as determined above. It is apparent from our measurements, calculations, and comparisons with ob- servations that surfactant films play an important role in the formation and persistence of the centerline wake region. The role is probably dominant in the far wake. In the near and intermediate wake regions other influences on wave energy cannot be neglected. All of the ship wakes we have analyzed from the Field Experiment have exhibited a banded structure for many kilometers downstream. Even in one run in which the wind speed was 9 Parsec the bands were measured at distances nearly 20 km behind the target vessel. In lighter wind cases bands were easily detected more than one hour late (equiv- alent to 35 to 40 km behind the target). The width of the wake slowly grew in time as indicated in Figures ~ and 10. From our limited data analysis so far, we cannot reach any conclusions about the dependence of these ship-generated surfactant film bands on environmental parameters (wind speed and direction, ambient surfactant concentration) and ship operating characteristics (hull form, speed, number of propellers). However, we conclude that continued analysis of the remaining data will allow us to determine the effects of both environmental and ship operating parameters on the origin and downstream persistence of these ship wake sur- factant bands. As our sensitivity studies have shown, variations in each of the source terms in the model (within our present knowl- edge of what we can reasonably expect their variations to be) have a strong effect on the L-band calculations. This points out the need to learn more about these source terms. Within the present model, the approximations for wind wave regeneration and nonlinear energy transfer are both subject to limited data on which to base the approximations. Here again, both a careful analysis of available information and additional laboratory experiments are indicated in or- der to resolve the uncertainties which still remain after this "first look" analysis. In particular, existing theories and ex- periments apply to wave frequencies up to twice that of the spectral peak. On the other hand, radar scattering waves have frequencies about ten times that of the spectral peak. That is why new experiments are needed. Finally, wave damping by turbulence in ship wakes is the least understood of all the source terms. Our knowl- edge of wave damping by turbulence is very limited. Our knowledge of the amount of turbulence that actually exists in the wake more than a few ship lengths downstream is non-existent. Like all the other uncertainties, this one can only be fully resolved by careful experiments focused on the hydrodynamics in question. ACKNOWLEDGEMENT This work was sponsored by the Ship Wake Consortium and by the Surface Ship Wake Detection Program of the Applied Research and Technology Directorate (Code 12) of the Office of Naval Research. 550 - =~

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