Equatorial water waves with underlying currents in the f-plane approximation

Abstract

We present an exact solution to the governing equations for equatorial geophysical water waves which admit a constant underlying zonal current and a variable meridional current in the f-plane approximation. The solution is three-dimensional, nonlinear and explicit in Lagrangian formulation. We provide an analysis of the mean flow velocities and the related mass transport.

Keywords:

• Geophysical water waves
• f-plane approximation
• exact solution
• mean velocity
• mass transport

AMS Subject Classifications:

• 76B15
• 86A05
• 74G05
• 70H03

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Science Foundation Ireland (SFI) [grant number 13/CDA/2117].