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

Abstract

We describe a family of exact Gerstner-type solutions for the geophysical equatorial deep water wave problem in the f 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.