Linear water waves with vorticity: rotational features and particle paths

TL;DR

This paper investigates steady linear gravity water waves with constant vorticity, revealing how vorticity influences internal waves, vortices, and particle trajectories, with distinct behaviors for positive and negative vorticity.

Contribution

It introduces analytical solutions for linear water waves with vorticity and characterizes how vorticity affects particle paths and wave features.

Findings

Negative vorticity leads to internal waves and vortices.

Particle trajectories are non-closed for negative vorticity.

Large vorticity significantly alters particle paths.

Abstract

Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed ellipses. For positive vorticity the situation resembles that of Stokes waves, but for large vorticity the trajectories are affected.