A variational principle for three-dimensional water waves over Beltrami flows

TL;DR

This paper establishes a variational principle for steady three-dimensional water waves with vorticity, specifically those with Beltrami vector fields, expanding theoretical understanding of complex wave behaviors.

Contribution

It introduces a novel variational framework for analyzing three-dimensional gravity-capillary water waves with Beltrami vorticity, under broad conditions.

Findings

Proves a variational principle for Beltrami water waves

Applicable to doubly periodic wave profiles

Enhances theoretical models of water wave dynamics

Abstract

We consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves with relative velocities given by Beltrami vector fields, under general assumptions on the wave profile.