Study on the Behavior of Weakly Nonlinear Water Waves in the Presence of Random Wind Forcing

TL;DR

This study derives a stochastic nonlinear Schrödinger equation to analyze weakly nonlinear deep water waves under random wind forcing, demonstrating that extreme wave solutions like the Peregrine breather can exist even in gusty wind conditions.

Contribution

It introduces a stochastic model for water waves with random wind forcing and shows that breather solutions persist under such conditions.

Findings

Breather solutions occur in strong gusty wind conditions.

The stochastic model captures the influence of random wind on wave behavior.

Extreme waves can form despite stochastic wind forcing.

Abstract

Specific solutions of the nonlinear Schr\"odinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the presence of gusty wind. Using the method of multiple scales, a nonlinear Schr\"odinger equation is obtained for the case of wind forced weakly nonlinear deep water waves. Thereby, the wind forcing is modeled as a stochastic process. This leads to a stochastic nonlinear Schr\"odinger equation, which is calculated for different wind regimes. For the case of wind forcing which is either random in time or random in space, it is shown that breather type solutions such as the Peregrine breather occur even in strong gusty wind conditions.