Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Hydrodynamics of Ship Wake Surfactant Films
Hydrodynamics of Ship Wake Surfactant Films
Pages 533-552
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From page 533... ...
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.......
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From page 534... ...
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.
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From page 535... ...
Films can become concentrated enough to attenuate surface waves when they are compacted by horizontal convergences 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 generated by flow around the hull or currents associated with the breaking bow and stern waves.
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From page 536... ...
The viscous properties of the surfactant 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.
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From page 537... ...
Different batches of commercially available paraffin oil already contain traces of surface-active components, 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 Langmuir trough facility of the NRL Chemistry Division and can be more easily discussed in terms in terms of film pressures.
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From page 538... ...
44.55 TABLE 1. SPREADING OILS 3.2 Determination of Film Elasticity The important property of a surfactant film which governs the wave damping is its elasticity (Es)
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From page 539... ...
Presumably its spreading pressure is almost exactly the value of the surfactant film and the oscillation occurs because the ambient surface tension oscillates about a mean value due to alternate surface compactions and expansions induced by the passage of surface 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.
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From page 540... ...
It was unfortunate that oils 22 and 23 were not working or available during most of the Field Experiment because we could not establish the maximum value of the surface tension decrease in certain regions of both the ship generated and ambient surfactant 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 maximum 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.
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From page 541... ...
The resulting qualitative agreement between radar measurements and the calculated wave energy 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 formulations we have used for the source terms.
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From page 542... ...
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 equilibrium conditions is scanty, even less is known about it for the non-equilibrium condition of attenuated and regrowing short waves in a ship wake.
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From page 543... ...
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.
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From page 544... ...
Note also that a small change in surface elasticity can result in a significant change in capillary and small surface gravity wave damping for a given wavelength. We close this subsection by noting that in the presence of a turbulent free surface boundary layer, the actual surfactant-induced wave damping could be different than predicted by Dorrestein's laminar analysis.
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From page 545... ...
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 material is needed to relate the film elasticity Es to the measured surface tension.
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From page 546... ...
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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From page 547... ...
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 crosssections at 3735 m aft are also shown in the figures.
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From page 548... ...
Figure 17 shows the predicted L-band energy distribution 3735 meters aft when the wave energy decay rate due to turbulence in the ambient sea is reduced to seventy-five percent of the value used to produce Figure 14. This changes the decay rate in the wake because the ship-induced turbulent decay is taken as diminishing with distance aft (equations 10 and 14)
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From page 549... ...
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)
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From page 550... ...
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.
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From page 551... ...
Lyden, J.D., Hammond, R.R., Lyzenga, D.R. and Shuchman, R.A., "Synthetic Aperture Radar Imaging of Surface Ship Wakes," J
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From page 552... ...
and Stewart, R.H., 1982, "The Observation of Ocean Surface Phenomena Using Imagery From the SEASAT Synthetic Aperture Radar: An Assessment," J Geophys.
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