Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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A Model for the Generation and Evolution of an Inner-Angle Soliton in a Kelvin Wake
A Model for the Generation and Evolution of an Inner-Angle Soliton in a Kelvin Wake
Pages 453-464
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From page 453... ...
If the wave amplitude in the ray is small, or if the Kelvin wake model uses a linearized form of the free surface 453 boundary condition, then each ray inside the cusp line diverges linearly as it propagates aft: the width increases linearly with distance aft and the amplitude decreases as the inverse of the square root of the distance aft (the cusp line, of course, diverges slower)
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From page 454... ...
The ship speed is 15 knots. The lower photo shows the port side cusp line and soliton.
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From page 455... ...
4 o o ~ o Cal Cal · _( 4_ o Cal o 4 .0 o en Cal o Ct Cal 4 o o AD o Cal U
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From page 456... ...
~ is the velocity potential for the perturbation to the uniform oncoming flow, ~ is the free surface elevation relative to the mean ambient level z=0, and P is the surface pressure divided by the density. The source at the bow, SB, and the sink at the stern, Ss, are given by point singularities: SB = UA §(X - a)
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From page 457... ...
3. NONLINEAR THEORY We model the evolution of the ray into an oblique nonlinear solitary wave packet by using a time-dependent, twodimensional nonlinear Schrodinger equation for the complex packet envelope.
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From page 458... ...
fir OSI SZI OOI SL (YV)
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From page 459... ...
for PDB and bandpass the result so that it only contains the narrow band of spectral components PDB that generate the ray. The rigorous procedure for bandpassing PDB involves finding the wavevectors of the two nodes in the Kelvin wake that bound the ray, then using a top hat filter to pass all of the spectral components along the Kelvin wake dispersion curve in between these nodes.
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From page 460... ...
, is shown in Figure Sb. The nonlinear term arrests the dispersion of the ray yielding an oblique nonlinear solitary wave packet.
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From page 461... ...
r~ ~ C ·_ , ._, C~ ao Ct a~ ~: _} Ct 4_ O ~ '4·_ Ct ~ ~ Ct
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From page 462... ...
The generation is modeled as an interference maximum due to a source-sink pair and the evolution is modelled using the nonlinear Schrodinger equation. Although some of the parameters in the model are fit to experimental data, the values of the parameters are physically reasonable, thus we conclude that the model captures the essential physics.
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From page 463... ...
, the spatial width of the feature was 8.9m (measured at 1/e of the peak) and the peak wave amplitude was 15.1 cm (this was 1.1 times the theoretical soliton value calculated from the other parameters)
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