Systematic Study of Rogue Wave Probability Distributions in a Fourth-Order Nonlinear Schr\"odinger Equation

TL;DR

This paper uses a fourth-order nonlinear Schr"odinger equation to quantitatively analyze how various environmental parameters influence the probability of freak wave formation in ocean surface waves.

Contribution

It systematically investigates the effects of input parameters on freak wave probability using numerical solutions of the CNLS4 model, including spatial dependence.

Findings

Wave height distribution varies with steepness, angular, and frequency spread.

Nonlinear effects significantly increase freak wave probability.

Spatial buildup of nonlinear development affects wave height distribution.

Abstract

Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of freak wave formation. The fourth-order current-modified nonlinear Schr\"odinger equation (CNLS4) is employed to describe the wave evolution. By solving CNLS4 numerically, we are able to obtain quantitative predictions for the wave height distribution as a function of key environmental conditions such as average steepness, angular spread, and frequency spread of the local sea state. Additionally, we explore the spatial dependence of the wave height distribution, associated with the buildup of nonlinear development.