Nonlinear interactions among standing surface and internal gravity waves

Abstract

A laboratory study has been undertaken to measure the momentum transfer from surface to internal gravity waves in a nonlinear, resonant interaction. The interacting waves form triads for which σ1s - σ2s ± σI = 0 and κ1s - κ2s ± κI = 0; σj and κj being the frequency and wavenumber of the jth wave. In particular, the experiment is designed to model a generating mechanism for high frequency, oceanic internal waves. Unlike previously published results involving single triplets of interacting waves, all waves here considered are standing waves. The growth to steady state of a resonant internal wave is observed while two deep water surface eigen modes are simultaneously forced by a paddle. Results are compared to theoretical predictions which assume, ab initio, all waves to be standing. Inclusion of viscous side wall dissipation and slight detuning permit predictions of steady state amplitudes and phases as well as initial growth rates. Good agreement is found between predieted and measured amplitudes and phases. The experiments also suggest that the internal wave in a resonant triad can act as a catalyst, permitting appreciable energy transfer among surface waves.