An exact solution for geophysical trapped waves in the presence of an underlying current

TL;DR

This paper presents an exact nonlinear solution for geophysical trapped waves influenced by Coriolis forces and underlying currents, highlighting their impact on wave behavior in different hemispheres.

Contribution

It provides a novel explicit solution to the governing equations including Coriolis effects, analyzing trapped waves with underlying currents in both hemispheres.

Findings

Coriolis force significantly affects admissible currents.

Exact solutions reveal differences in wave trapping between hemispheres.

Retention of Coriolis terms alters wave dynamics and current ranges.

Abstract

In this paper we propose an exact and explicit nonlinear solution to the governing equations which retains all the Coriolis terms. In the presence of an underlying current, we seek the trapped waves induced by these solutions in Northern and Southern hemisphere respectively, showing that the retention of the Coriolis force in the governing equations affects significantly the range of the admissible following and adverse currents.