Triadic resonant instability in confined and unconfined axisymmetric geometries

TL;DR

This paper investigates the resonance conditions of axisymmetric internal wave sub-harmonics in confined and unconfined domains, revealing how boundary conditions influence spatial structures and resonance behaviors, supported by experiments and analytical models.

Contribution

It provides a comparative analysis of resonance conditions in confined versus unconfined geometries, highlighting the dominance of boundary conditions in confined domains.

Findings

Sub-harmonics can be generated if resonance conditions are met.

In unconfined domains, sub-harmonics follow 3D spatial resonance similar to TRI.

In confined domains, boundary conditions determine sub-harmonic structures.

Abstract

We present an investigation of the resonance conditions of axisymmetric internal wave sub-harmonics in confined and unconfined domains. In both cases, sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies, of the form $\omega_0 = \pm \omega_1 \pm \omega_2$. We demonstrate that, in an unconfined domain, the sub-harmonics follow three dimensional spatial resonance conditions similar to the ones of Triadic Resonance Instability (TRI) for Cartesian plane waves. In a confined domain, however, the spatial structure of the sub-harmonics is fully determined by the boundary conditions and we observed that these conditions prevail upon the resonance conditions. In both configurations, these findings are supported by experimental data showing good agreement with analytical and numerical derivations.