Dominant Resonance in Parametric Subharmonic Instability of Internal Waves

TL;DR

This paper reveals that the dominant subharmonic waves in parametric subharmonic instability of internal waves have longer wavelengths than previously believed, challenging the traditional half-frequency assumption.

Contribution

The study provides a rigorous analysis showing that PSI's strongest interactions are not at half the primary wave's frequency, but at longer wavelengths.

Findings

Dominant subharmonic waves have longer wavelengths than previously thought.

Maximum amplification does not occur at half the primary wave's frequency.

The initial growth rate peaks at a different frequency than traditionally assumed.

Abstract

Parametric Subharmonic Instability (PSI) is one of the most important mechanisms that transfer energy from tidally-generated long internal waves to short steep waves. Breaking of these short waves results in diapycnal mixing through which oceanic abyssal stratification is maintained. It has long been believed that PSI is strongest between a primary internal wave and perturbative waves of half the frequency of the primary wave. Here, we rigorously show that this is not the case. Specifically, we show that neither the initial growth rate nor the maximum long-term amplification occur at the half frequency, and demonstrate that the dominant subharmonic waves have much longer wavelengths than previously thought.