Particle trajectories in linearized irrotational shallow water flows

TL;DR

This paper analyzes particle trajectories in linearized irrotational shallow water flows, revealing diverse path shapes and the absence of closed orbits, influenced by underlying currents.

Contribution

It demonstrates that in linear irrotational shallow water waves, particle paths are varied and no closed orbits exist, depending on current strength.

Findings

No closed orbits for particles beneath the waves

Particle paths include undulating, looping, and parabolic curves

Trajectory shape depends on the strength of the underlying current

Abstract

We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the water particles beneath the irrotational shallow water waves. Depending on the strength of underlying uniform current, we obtain that some particle trajectories are undulating path to the right or to the left, some are looping curves with a drift to the right and others are parabolic curves or curves which have only one loop.