Recovery of Stokes waves from velocity measurements on an axis of symmetry

TL;DR

This paper introduces a novel method to reconstruct the shape of Stokes waves and similar waves with smooth vorticity using horizontal velocity data measured along a vertical symmetry axis, applicable to periodic and solitary waves.

Contribution

A new technique for recovering wave profiles from velocity measurements on a symmetry axis, extending to waves with smooth vorticity and applicable to both periodic and solitary waves.

Findings

Effective reconstruction of Stokes wave profiles from velocity data.

Extension of the method to waves with smooth vorticity.

Applicability to both periodic and solitary waves.

Abstract

We provide a new method to recover the profile of Stokes waves, and more generally of waves with smooth vorticity, from measurements of the horizontal velocity component on a vertical axis of symmetry of the wave surface. Although we consider periodic waves only, the extension to solitary waves is straightforward.