Measurement of Non-Linear Internal Waves and Their Interaction with Surface Waves Using Coherent Real Aperture Radars

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

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Non Linear Interactions Using Leaky Surface Waves

10.1109/ultsym.1972.196089 ◽

1972 ◽

Author(s):

M. Feldmann ◽

J. Henaff

Keyword(s):

Surface Waves ◽

Non Linear ◽

Linear Interactions

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Subharmonic resonance of short internal standing waves by progressive surface waves

Journal of Fluid Mechanics ◽

10.1017/s0022112096007707 ◽

1996 ◽

Vol 321 ◽

pp. 217-233 ◽

Cited By ~ 24

Author(s):

D. F. Hill ◽

M. A. Foda

Keyword(s):

Surface Wave ◽

Internal Wave ◽

Surface Waves ◽

Internal Waves ◽

Growth Rates ◽

Evolution Equations ◽

Standing Waves ◽

Second Order ◽

Inviscid Limit ◽

Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

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