Modulational instability in wind-forced waves

TL;DR

This paper analyzes how wind forcing influences the modulational instability of waves, revealing an enhanced instability regime with infinite gain bandwidth in the nonlinear Schrödinger equation framework.

Contribution

It introduces a modified NLS model incorporating wind forcing with Miles growth rate comparable to wave steepness, highlighting the resulting instability enhancement.

Findings

Wind forcing amplifies modulational instability.

A band of positive gain with infinite width emerges.

The wave momentum to norm ratio is not conserved.

Abstract

We consider the wind-forced nonlinear Schroedinger (NLS) equation obtained in the potential flow framework when the Miles growth rate is of the order of the wave steepness. In this case, the form of the wind-forcing terms gives rise to the enhancement of the modulational instability and to a band of positive gain with infinite width. This regime is characterised by the fact that the ratio between wave momentum and norm is not a constant of motion, in contrast to what happens in the standard case where the Miles growth rate is of the order of the steepness squared.