Secondary instabilities in rapidly rotating fluids: inertial wave breakdown

Abstract

Inertial waves are a ubiquitous feature of rapidly rotating fluids. Although much is known about their initial excitation, little is understood about their stability. Experiments indicate that they are generically unstable and in many cases catastrophically so, quickly causing the whole flow to collapse to small-scale disorder. The linear stability of two three-dimensional inertial waves observed to break down in the laboratory is considered here at experimentally small but finite Ekman numbers of [les ]10⁻⁴. Surprisingly small threshold amplitudes for instability are found. The results support the conjecture that triad resonances are the generic mechanism for secondary instability in rapidly rotating fluids but also highlight the ability of geostrophic flows to derive energy through a finite-amplitude inertial wave. This latter finding may go some way to explaining the significant mean circulations typically observed in inertial wave experiments.