Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

TL;DR

This study compares rogue wave solutions from the nonlinear Schrödinger equation with numerical simulations of weakly and fully nonlinear hydrodynamic equations, demonstrating the solutions' relevance to real wave dynamics and improving modeling accuracy.

Contribution

It provides a comprehensive numerical validation of rogue wave solutions across different nonlinear models, including fully nonlinear simulations, enhancing understanding of wave evolution near breaking conditions.

Findings

NLS solutions reasonably describe steep wave dynamics.

Higher accuracy achieved with the modified NLS (MNLS) or Dysthe equation.

Fully nonlinear simulations reveal key characteristics of wave evolution.

Abstract

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation (MNLS) also known as the Dysthe equation. This numerical modelling allowed us to directly compare simulations with recent results of laboratory measurements in \cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.