Variational Principles for Water Waves

TL;DR

This paper develops Hamiltonian structures and variational principles for water waves, including flows with vorticity, providing a unified framework for analyzing stationary gravity waves in incompressible fluids.

Contribution

It introduces Hamiltonian formulations and variational principles for water waves with vorticity, extending previous irrotational models.

Findings

Hamiltonian structures for water waves with vorticity derived

Variational principles for stationary gravity waves established

Framework applicable to both irrotational and rotational flows

Abstract

We describe the Hamiltonian structures, including the Poisson brackets and Hamiltonians, for free boundary problems for incompressible fluid flows with vorticity. The Hamiltonian structure is used to obtain variational principles for stationary gravity waves both for irrotational flows as well as flows with vorticity.