The pressure distribution in extreme Stokes waves

TL;DR

This paper proves that in extreme Stokes waves over finite depth, pressure increases with depth, decreases from crest to trough, and remains constant horizontally along these lines.

Contribution

It establishes new properties of pressure distribution in extreme Stokes waves, including monotonicity and stationarity aspects.

Findings

Pressure increases with depth beneath the wave.

Pressure decreases from crest to trough.

Pressure is stationary along crest and trough lines.

Abstract

In this paper we prove that the pressure beneath an extreme Stokes wave over finite depth is strictly increasing with depth. Additionally it is shown that the pressure decreases in moving between a crest-line and trough-line, while it is stationary with respect to the horizontal coordinate along these lines themselves.