Recovery of steady rotational wave profiles from pressure measurements at the bed

TL;DR

This paper develops a method to recover steady wave profiles and flow vorticity from pressure measurements at the seabed, applicable even with stagnation points, demonstrated through numerical examples.

Contribution

It introduces a novel set of nonlinear equations linking bottom pressure to free-surface profiles and vorticity, enabling recovery from pressure data in steady gravity waves.

Findings

Effective recovery of wave profiles from bottom pressure data

Flow vorticity can be determined solely from pressure measurements

Method works even with stagnation points

Abstract

We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure measurements at the bed. Furthermore, the flow vorticity is determined solely from the bottom pressure as part of the recovery method. This approach is applicable even in the presence of stagnation points and its efficiency is illustrated via numerical examples.