Enhancement of the Benjamin-Feir instability with dissipation

TL;DR

This paper reveals a novel mechanism where certain types of dissipation unexpectedly amplify the Benjamin-Feir instability in water waves, due to the interaction of modes with opposite energy signs.

Contribution

It introduces a new understanding of how dissipation can enhance wave instability by focusing on mode interactions with opposite energy signs.

Findings

Dissipation can enhance the Benjamin-Feir instability under specific conditions.

Negative energy perturbations are amplified by dissipation.

The mechanism involves mode collision with opposite energy signs.

Abstract

It is shown that there is an overlooked mechanism whereby some kinds of dissipation can enhance the Benjamin-Feir instability of water waves. This observation is new, and although it is counterintuitive, it is due to the fact that the Benjamin-Feir instability involves the collision of modes with opposite energy sign (relative to the carrier wave), and it is the negative energy perturbations which are enhanced.