Shapes and Statistics of the Rogue Waves Generated by Chaotic Ocean Current

TL;DR

This paper investigates the shapes and statistics of rogue waves caused by chaotic ocean currents using an extended nonlinear Schrödinger equation, revealing how current perturbations influence rogue wave formation and their potential impact on offshore safety.

Contribution

It introduces an extended NLSE model accounting for current gradients, analyzes its instability under chaos, and links rogue wave formation to rational solutions influenced by current perturbations.

Findings

Chaotic current profiles induce rogue waves resembling rational solutions.

The extended NLSE remains energy-conserving despite phase shifts.

Current perturbation magnitude affects rogue wave statistics.

Abstract

In this study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrodinger equation (NLSE) extended by R. Smith (1976). This extended NLSE accounts for the effects of current gradient on the nonlinear dynamics of the ocean surface near blocking point. Using a split-step scheme we show that the extended NLSE of Smith is unstable against random chaotic perturbation in the current profile. Therefore the monochromatic wave field with unit amplitude turns into a chaotic sea state with many peaks. By comparing the numerical and analytical results, we show that rogue waves due to perturbations in the current profile are in the form of rational rogue wave solutions of the NLSE. We also discuss the effects of magnitude of the chaotic current profile perturbations on the statistics of the rogue wave generation at the ocean surface. The extension term in Smith's extended NLSE causes phase shifts and it does not change the total energy level of the wave field. Using the methodology adopted in this work, the dynamics of rogue wave occurrence on the ocean surface due to blocking effect of currents can be studied. This enhances the safety of the offshore operations and ocean travel.