Particle paths in small amplitude solitary waves with negative vorticity

TL;DR

This paper studies particle trajectories in small amplitude solitary waves with negative vorticity, revealing conditions under which particles move with or against wave propagation, including looping paths in certain flows.

Contribution

It provides new insights into particle motion in solitary waves with negative vorticity, especially regarding the influence of underlying flow conditions on particle paths.

Findings

Particles follow similar paths as in irrotational waves under favorable flow.

In non-favorable flows, some particles move opposite to wave direction.

Particles can trace paths with a single loop or hump in certain conditions.

Abstract

We investigate the particle trajectories in solitary waves with vorticity, where the vorticity is assumed to be negative and decrease with depth. We show that the individual particle moves in a similar way as that in the irrotational case if the underlying laminar flow is favorable, that is, the flow is moving in the same direction as the wave propagation throughout the fluid, and show that if the underlying current is not favorable, some particles in a sufficiently small solitary wave move to the opposite direction of wave propagation along a path with a single loop or hump .