Numerical simulations of modulated waves in a higher-order Dysthe equation

TL;DR

This paper performs numerical simulations of modulated water waves using a higher-order Dysthe equation, comparing results with full Euler solutions and lower-order models to explore wave stability and breaking conditions.

Contribution

It introduces and analyzes a higher-order Dysthe model for simulating steep and breaking water waves, extending previous lower-order models.

Findings

Higher-order Dysthe model shows re-stabilization tendencies for steep waves.

Simulations align well with full potential Euler solutions.

Lower-order models are less accurate for steep wave dynamics.

Abstract

The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves are concerned. The results are compared with the solution of the full potential Euler equations and with the lower order envelope models (the 3-order nonlinear Schrodinger equation and the standard 4-order Dysthe equations). The generalized Dysthe model is shown to exhibit the tendency to re-stabilization of steep waves with respect to long perturbations.