Experimental generation of axisymmetric internal wave super-harmonics

Abstract

In this paper, we present an experimental study of weakly nonlinear interaction of axisymmetric internal gravity waves in a resonant cavity, supported by theoretical considerations. Contrary to plane waves in Cartesian coordinates, for which self-interacting terms are null in a linear stratification, the nonlinear self-interaction of an internal wave mode in axisymmetric geometry is found to be efficient at producing super-harmonics, i.e., waves whose frequencies are integer multiples of the excitation frequency. Due to the range of frequencies tested in our experiments, the first harmonic frequency is below the cutoff imposed by the stratification so the lowest harmonic created can always propagate. The study shows that the super-harmonic wave field is a sum of standing waves satisfying both the dispersion relation for internal waves and the boundary conditions imposed by the cavity walls, while conserving the axisymmetry