On the streamlines and particle paths of gravitational water waves

TL;DR

This paper studies the particle trajectories and streamlines of steady symmetric gravity water waves, revealing how particle drift varies with depth and providing detailed descriptions for both rotational and irrotational waves.

Contribution

It offers new insights into particle drift behavior and streamline structures in steady gravity water waves, especially regarding vorticity effects and depth-dependent drift magnitude.

Findings

Particles exhibit a mean forward drift in non-positive vorticity waves.

The drift magnitude increases from bottom to surface in certain wave classes.

Detailed descriptions of streamlines and particle paths, including irrotational cases.

Abstract

We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly increasing from bottom to surface. We also provide detailed information concerning the streamlines and the particle trajectories. This includes the case of particles within irrotational waves.