Precession resonance in water waves

TL;DR

This paper introduces a novel nonlinear resonance mechanism in deep water gravity waves, where energy exchange is enhanced through precession frequency matching, leading to significant energy transfer at finite amplitudes.

Contribution

It presents the first discovery of a new type of nonlinear resonance in surface gravity waves involving three-wave interactions and precession frequency matching.

Findings

Energy transfer efficiencies up to 40% observed.

Precession resonance occurs at finite amplitudes due to nonlinear effects.

First new nonlinear resonance identified since 1967.

Abstract

We describe the theory and present numerical evidence for a new type of nonlinear resonant interaction between gravity waves on the surface of deep water. The resonance constitutes a generalisation of the usual 'exact' resonance as we show that exchanges of energy between the waves can be enhanced when the interaction is three-wave rather than four and the linear frequency mismatch, or detuning, is non-zero i.e. $\omega_1\pm\omega_2\pm\omega_3 \neq0.$ This is possible because the resonance condition is now a match between the so-called 'precession frequency' of a given $\textit{triad interaction}$ and an existent nonlinear frequency in the system. In the limit of weak nonlinearity this precession frequency is simply due to the linear 'drift' of the triad phase; therefore, it tends toward the detuning. This means precession resonance of this type can occur at finite amplitudes, with nonlinear corrections contributing to the resonance. We report energy transfer efficiencies of up to 40%, depending on the model options. To the authors' knowledge this represents the first new type of nonlinear resonance in surface gravity waves since the seminal work of Benjamin & Feir (1967).