Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulations

TL;DR

This paper develops a Gaussian variational ansatz model for oceanic rogue waves and compares its semi-quantitative predictions with direct numerical simulations of nonlinear water waves.

Contribution

It introduces a Gaussian variational approach to model rogue wave formation and validates it against detailed numerical simulations.

Findings

The Gaussian model captures key features of wave focusing.

Qualitative differences between linear and nonlinear focusing are identified.

The model provides a semi-quantitative understanding of rogue wave mechanisms.

Abstract

The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schr\"odinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-crested water waves is carried out.