On the particle motion in geophysical deep water waves traveling over uniform currents

TL;DR

This paper presents exact Gerstner type solutions for equatorial deep water waves influenced by uniform currents, analyzing particle paths with and without Coriolis effects to enhance understanding of geophysical wave dynamics.

Contribution

It introduces a new family of exact solutions for geophysical deep water waves, accounting for uniform currents and Coriolis effects, which were not previously characterized.

Findings

Particle paths depend on current strength and Coriolis force presence.

Exact two-dimensional wave solutions are derived for the f-plane approximation.

Analysis reveals how currents influence particle trajectories in deep water waves.

Abstract

We describe a family of exact Gerstner type solutions for the geophysical equatorial deep water wave problem in the f-plane approximation. These Gerstner type waves are two-dimensional and travel with constant speed over a uniform horizontal current. The particle paths in the presence and absence of the Coriolis force are also analyzed in dependence of the current strength.