Simulations and experiments of short intense envelope solitons of surface water waves

TL;DR

This study combines laboratory experiments and numerical simulations to investigate the stability and properties of short, intense envelope solitons in deep water waves, revealing their structural features and nonlinear dynamics.

Contribution

It demonstrates the existence of stable, short intense envelope solitons in deep water, with detailed experimental and numerical validation, and compares them to classical envelope soliton solutions.

Findings

Stable intense wave groups remain unchanged over 60 wavelengths.

Laboratory results agree well with nonlinear numerical simulations.

Envelope solitons show vertical asymmetry similar to Stokes waves.

Abstract

The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g \approx 0.30$ are reproduced in laboratory experiments ($A_{cr}$ is the wave crest amplitude, $\omega_m$ is the mean angular frequency and $g$ is the gravity acceleration). We show that the groups remain stable and exhibit neither noticeable radiation nor structural transformation for more than 60 wave lengths or about 15-30 group lengths. These solitary wave patterns differ from the conventional envelope solitons, as only a few individual waves are contained in the group. Very good agreement is obtained between the laboratory results and strongly nonlinear numerical simulations of the potential Euler equations. The envelope soliton solution of the nonlinear Schr\"odinger equation is shown to be a reasonable first approximation for specifying the wavemaker driving signal. The short intense envelope solitons possess vertical asymmetry similar to regular Stokes waves with the same frequency and crest amplitude. Nonlinearity is found to have remarkably stronger effect on the speed of envelope solitons in comparison to the nonlinear correction to the Stokes wave velocity.