Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity

TL;DR

This paper demonstrates that the equations governing two-dimensional gravity water waves with constant vorticity possess a nearly-Hamiltonian structure, simplifying to a true Hamiltonian form for steady waves, which enhances understanding of wave dynamics.

Contribution

It reveals a nearly-Hamiltonian formulation for water waves with constant vorticity, extending Hamiltonian theory to non-steady wave scenarios.

Findings

Equations have a nearly-Hamiltonian structure.

Structure becomes Hamiltonian for steady waves.

Provides new insights into water wave dynamics.

Abstract

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.