Nonlinear Triad Interactions of Acoustic-Gravity Waves: Towards general evolution equations

In linear water wave theory, acoustic (compression) waves are virtually decoupled from free-surface (gravity) waves, since the speed of sound in water far exceeds the maximum phase speed of gravity waves. Nevertheless, we argue theoretically that these two types of wave motion could exchange energy via nonlinear resonant triad interactions. There are two cases of interest this talk focuses on: (I) two gravity waves interacting with an acoustic mode of a comparable timescale; and (II) two acoustic modes interacting with a gravity wave of a comparable lengthscale. Using multiscale analysis cubic nonlinear Schrödinger-type evolution equations are derived. For finely tuned monochromatic waves almost all energy initially stored in the gravity waves transfers into the acoustic mode, whereas for wavepackets a maximum of 40 percent energy transfer can be obtained

Implications of the result are presented for a wide range of applications: from oceanic scale microseisms (faint earth tremors), wave energy harnessing and tsunami generation and mitigation, to lab-size time reversals, standing Faraday waves in an oscillating bath, and pilot-wave quantum analogues. The talk is concluded with a discussion over pushing the boundaries towards the derivation of general evolution equations.