Abstract
Non-linear interactions among two surface waves and an internal wave which satisfy the resonance conditions such that k 1 = k 2 + k 3 and ω 1 =ω 2 +ω 3 , k and ω being wave-number vector and frequency, have been investigated using a two-layer fluid model in which each layer has different density and finite depth. Interaction equations for slowly varying amplitudes have been derived by the analysis to second order of amplitude, and solved. Total energy and momentum of an interacting triad are shown to be conserved to this order. The time scale which characterizes interactions has been calculated for a wide range of wave-number and various density differences.
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