General procedure for free-surface recovery from bottom pressure measurements: Application to rotational overhanging waves

TL;DR

This paper introduces a boundary integral method using Cauchy formulas and Eulerian-Lagrangian formalism to accurately recover free-surface water waves, including overturning ones, from bottom pressure data.

Contribution

It presents a general, basis-free boundary integral approach for reconstructing complex free-surface water waves from pressure measurements.

Findings

Method accurately recovers free surfaces in numerical tests.

Approach handles overturning and rotational waves effectively.

Eliminates need for predefined basis functions.

Abstract

A novel boundary integral approach for the recovery of overhanging (or not) rotational (or not) water waves from pressure measurements at the bottom is presented. The method is based on the Cauchy integral formula and on an Eulerian--Lagrangian formalism to accommodate overturning free surfaces. This approach eliminates the need to introduce {\em a priori} a special basis of functions, providing thus a general means of fitting the pressure data and, consequently, recovering the free surface. The effectiveness and accuracy of the method are demonstrated through numerical examples.