Experimental self-generation of axisymmetric internal wave super-harmonics

TL;DR

This study experimentally demonstrates that axisymmetric internal gravity waves can non-linearly generate super-harmonics within a resonant cavity, with these higher-frequency waves forming standing wave patterns that satisfy boundary and dispersion conditions.

Contribution

It provides the first experimental evidence of efficient non-linear self-interaction leading to super-harmonics in axisymmetric internal waves, contrasting with plane wave behavior.

Findings

Super-harmonics are generated through non-linear self-interaction in axisymmetric internal waves.

The super-harmonic waves form standing wave patterns satisfying boundary and dispersion relations.

The first harmonic frequency remains propagative due to stratification cut-off constraints.

Abstract

In this paper, we present an experimental study of weakly non-linear 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 stratifiation, the non-linear 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 cut-off 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.