Deep water gravity wave triad resonances on uniform flow

TL;DR

This paper introduces a novel class of deep water gravity wave triad resonances caused by anisotropic dispersion in uniform currents, challenging previous assumptions that such resonances require inhomogeneity or capillarity.

Contribution

It demonstrates the existence of deep water triad resonances in uniform flows, providing analytical conditions and exploring their impact on wave interaction regimes.

Findings

Resonances occur even in deep water with uniform current.

Resonances significantly alter nonlinear wave interactions.

Dominant energy transfer directions vary with wavenumber scales.

Abstract

Triad resonances for gravity waves propagating in opposite direction with respect to uniform current are introduced. They are produced by multivalued and anisotropic dispersion and occur even in deep water. In contrast, existing literature suggests non-degenerate deep water triads require inhomogeneity or capillary effects. In this sense, the new resonances are a first of their kind. Analytical conditions for the existence of resonance may be reduced to universal constants. Solution of a three-wave interaction model, adapted to the wave-current problem, shows regimes wherein the dominant direction, speed and strength of resonant energy transfer differs between wavenumber scales. This suggests uniform current is a fundamental source of spatial inhomogeneity. The new resonances significantly modify the picture of nonlinear interactions in wave-current fields. Since the resonances are quadratic, they will also dominate well known quartet interactions.