Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Submerged Vortex Pair Influence on Ambient Free Surace Waves
Submerged Vortex Pair Influence on Ambient Free Surace Waves
Pages 491-502
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From page 491... ...
Although much research has concentrated on studying vortices near a still free surface, a theory for vertical influence on ambient free surface waves has not been addressed. Initial steps in uncovering the subtleties of the ambient wave modification by submerged vortices are taken utilizing first order free surface boundary conditions to demonstrate the importance of the vortex-induced surface current in the interaction of vortices with ambient waves.
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From page 492... ...
hi VORTICES Fig. 1 Ship Wake Vortex Model with Ambient Waves Prior studies of vortex-free surface interactions focused on the dynamics of an initially flat free surface under the influence of the vortex pair.
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From page 493... ...
. Note also that the O.S¢x term in tl~e dynamic boundary condition and the Foxed term in the kinematic boundary condition represent the influence of induced surface currents on the modification of ambient waves.
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From page 494... ...
4b Surface Profiles with Vortex Pair: First Order Theory with Induced Current Terms NONDIMENSIONAL PARAMETER IDENTIFICATION When ambient waves are included in the vortex/free surface problem, the characteristic length scale should correspond to the ambient wavelength. This wavelength is of primary concern since eventually it will be this scale which determines the character of radar return from the free surface.
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From page 495... ...
The most obvious effect of varying F in these cases is the change in time scale for the surface disturbance to develop. The occurrence of ambient wave modification at earlier times at higher F is due primarily to the increase in relative speed of the vortex pair moving towards the surface.
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From page 496... ...
An additional note on the variation of F is the transition occurring around values of 0.5 of the surface disturbance directly above the vortex pair. At values above 0.5, the creation of a center "humps appears similar to center humps calculated by Telste9 at higher Froude numbers without ambient waves.
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From page 497... ...
_ ~ TT1 -iT - ~-3 - 2 - 1 0 1 2 3 ~5 6 7 x/x Fig. 16 S/D Variation: S/D = 6.0 In these figures one can see the influence of the instantaneous vortex pair depth on the surface wave modification.
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From page 498... ...
The result of this process, is that ambient waves of higher speed may be halted by vortices of smaller magnitude than that predicted from v~/vg=1 . S/X Variation As mentioned in the S/D section above, initial vortex pair location is important in examining the influences on ambient surface waves.
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From page 499... ...
The ambient wavelength is set to 25 cm and corresponds to the Bragg scattering wavelength for an "L band" SAR operating at an incidence angle of 30 degrees. The initial vortex separation and depth are 5 m and 2 m respectively.
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From page 500... ...
This process has led to several discoveries in the nature of the interaction process between vortices and ambient waves. A perturbation analysis of the free surface boundary conditions about the zero Froude number base state shows that additional terms (not found in the classical free surface linearization for small amplitude waves)
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From page 501... ...
The ambient wave steepness and initial relative phase with respect to the vortices have only secondary influence in the surface modification. The simulation is then extended to represent the simple twin vortex wake model of a generic ship wake.
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