Extrema of the dynamic pressure in a solitary wave

TL;DR

This paper analyzes the behavior of dynamic pressure in large-amplitude solitary water waves, proving that the maximum dynamic pressure occurs at the wave crest and the minimum at infinity, regardless of wave size.

Contribution

It provides a rigorous proof of the extrema locations of dynamic pressure in nonlinear solitary waves, extending understanding beyond small-amplitude approximations.

Findings

Maximum dynamic pressure at wave crest

Minimum dynamic pressure at infinity

Results hold for waves of moderate to large amplitude

Abstract

We study the dynamic pressure in an irrotational solitary wave propagating at the surface of water over a flat bed, under the influence of gravity. We consider the nonlinear regime, that is, the case of waves of moderate to large amplitude. We prove that, independently of the wave amplitude, the maximum of the dynamic pressure is attained at the wave crest, while its minimum is attained at infinity.