The pressure field beneath intense surface water wave groups

TL;DR

This paper develops a weakly-nonlinear potential theory to describe the complex pressure fields beneath intense surface water wave groups, highlighting differences between unidirectional and colliding wave trains.

Contribution

It introduces a second-order nonlinear model for pressure fields beneath deep water wave groups, including colliding groups, with application to sech-shaped soliton-like wave envelopes.

Findings

Dynamic pressure can be comparable to linear solutions during wave group collisions.

Pressure attenuation with depth depends on the group length, often exceeding individual wavelength.

Pressure field structures differ significantly between unidirectional and opposite wave trains.

Abstract

A weakly-nonlinear potential theory is developed for the description of deep penetrating pressure fields caused by single and colliding wave groups of collinear waves due to the second-order nonlinear interactions. The result is applied to the representative case of groups with the sech-shape of envelope solitons in deep water. When solitary groups experience a head-on collision, the induced due to nonlinearity dynamic pressure may have magnitude comparable with the magnitude of the linear solution. It attenuates with depth with characteristic length of the group, which may greatly exceed the individual wave length. In general the picture of the dynamic pressure beneath intense wave groups looks complicated. The qualitative difference in the structure of the induced pressure field for unidirectional and opposite wave trains is emphasized.