Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Radar Backscatter of a V-like Ship Wake from a Sea Surface Covered by Surfactants
Radar Backscatter of a V-like Ship Wake from a Sea Surface Covered by Surfactants
Pages 235-248
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From page 235... ...
ship wake images frequently form of a bright V with a narrow half angle of 2-3 deg. These images persist for many kilometers behind the ship and can be explained as a result of the Bragg scattering from ship-generated divergent waves (Nlilgram 1988)
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From page 236... ...
The level of wave damping depends on many physical parameters of the water and the surfactants. The simplest mathematical model of the Marangoni phenomenon is based on the concept of a viscoelastic surface film and incorporates only three essential parameters: the water kinematic viscosity, a, the surface tension coefficient, a, and the elasticity of the surface film, c, ~ Levich 1962~.
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From page 237... ...
,m 16x16 Ground range resolution (at incident angle 50°) ,m 10x10 2 Wave elevations induced by a moving ship.
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From page 238... ...
A strong similarity between the wave elevation induced by a moving source and the wave elevation induced by a moving impulse of a normal stress applied to the free-surface is well known. For an inviscid fluid and irrotational fluid motion the wave elevation induced by a pressure impulse Pn moving over the free-surface is: (; _ jeer too p keik(xsin8+ycos8)
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From page 239... ...
(13) Liz fix In the presence of surface tension the linearized normal stress dynamics boundary condition on the free-surface can be written as: -p+2~( 00 + 05 ~ )
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From page 240... ...
, neglecting in Here and in the sequel it is understood that in all complex expressions for the wave elevation similar (24)
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From page 241... ...
For short divergent waves with the wave length Aw ~ 20-30cm the hull integral Ah is significant only over a small depth of order Aw . In this case Hh(x, y, z)
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From page 242... ...
k (37) It can be demonstrated that for short divergent waves the SHED ~ |Hh | which implies that the contribution of the line integral is dominant in the final expression for the wave elevation.
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From page 243... ...
Consider an orthogonal local coordinate system °~671 with an origin located at the center of the resolution cell. The coordinates ((, A)
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From page 244... ...
allows a clear physical interpretation: Al reflects the characteristics of the radar, A2 the parameters of the ship, As the direction of propagation of the divergent waves and the radar look of sight, A4 the interference between waves and their radiation decay and Bad
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From page 245... ...
18 16 ~9 10 dB 8 1 1 1 - I 1 ~ = 0 dyne/cm 6 _ 4 _ 2 _ O 1 1 .1 1 .. 1 1 1 1 1.5 2 2.5 3 3.5 4 4.5 5 X, km Figure 3: Rise of the radar cross-section above background versus distance aft of ship Bay Ridge.
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From page 246... ...
. Sea State 1 2 3 4....1.5 2 2.5 3 3.5 4 4.5 5 X, km Figure 4: Rise of radar cross-section above background versus distance aft of ship Bay Ridge for difference sea states.
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From page 247... ...
and Shuchman, R 1988 Synthetic aperture radar imaging of surface ship wakes.
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From page 248... ...
1990 Synthetic aperture radar imaging of ship wakes in the Gulf of Alaska.
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