The dynamic pressure in deep-water extreme Stokes waves

TL;DR

This paper analyzes the dynamic pressure distribution in deep-water extreme Stokes waves, revealing that pressure peaks beneath the crest and trough, with a decrease along streamlines, despite mathematical challenges posed by stagnation points.

Contribution

It introduces a novel application of maximum principles and excision techniques to study dynamic pressure in complex wave flows with stagnation points.

Findings

Dynamic pressure peaks beneath the wave crest and trough.

Pressure decreases along streamlines away from the crest.

Mathematical complications from stagnation points are addressed.

Abstract

In this paper we consider the dynamic pressure in a deep-water extreme Stokes wave. While the presence of stagnation points introduces a number of mathematical complications, maximum principles are applied to analyse the dynamic pressure in the fluid body by means of an excision process. It is shown that the dynamic pressure attains its maximum value beneath the wave crest and its minimum beneath the wave trough, while it decreases in moving away from the crest line along any streamline.