Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction

Abstract

Abstract The nonlinear triad interaction of two opposing gravity waves with almost identical frequencies and one much longer acoustic-gravity wave is studied for non-resonance, as well as for exact resonance conditions. For non-resonance conditions the previously known results for a ‘bound’ acoustic-gravity wave are recovered. For resonance, or near-resonance conditions, where all three waves are ‘free waves’, the interaction is recurrent and the amplitude of the free acoustic-gravity wave turns out to be much larger than that known for the bound wave. The results for the recurrent evolution are given analytically, in terms of Jacobian elliptic functions and elliptic integrals .