The long view of triadic resonance instability in finite-width internal gravity wave beams

TL;DR

This study investigates the complex development of triadic resonance instability in finite-width internal gravity wave beams through experiments and weakly non-linear modeling, revealing non-monotonic amplitude modulations and sensitivity to spatio-temporal configurations.

Contribution

It introduces a weakly non-linear model capturing the spatio-temporal evolution of the instability, highlighting the non-steady behavior of triadic interactions in finite-width beams.

Findings

Instability amplitudes do not reach steady equilibrium but modulate continuously.

The evolution is highly sensitive to the triadic configuration and system parameters.

Competition between growth rates and residence time influences modulation patterns.

Abstract

This paper presents our investigation into the modification of a finite-width internal gravity wave beam arising from triadic resonance instability. We present both experimental and weakly non-linear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability develops over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly non-linear theory, we find that the approach to a saturated equilibrium state for the triadic interactions is not monotonic; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour we develop a weakly non-linear approach to account for the spatio-temporal evolution of the amplitudes and structures of the beams over slow time-scales and long distances, and explore the consequences using a numerical scheme. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatio-temporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.