Coriolis effect on water waves

TL;DR

This paper rigorously analyzes water wave equations influenced by gravity and Coriolis force, proving local well-posedness and justifying shallow water models, including effects of non-constant surface pressure.

Contribution

It provides a rigorous mathematical proof of well-posedness for water waves with Coriolis force and vorticity, and justifies the shallow water approximation under various physical conditions.

Findings

Proved local well-posedness of water wave equations with Coriolis force.

Justified the shallow water model rigorously.

Analyzed effects of non-constant surface pressure on water waves.

Abstract

This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We prove a local wellposedness theorem for the water waves equations with vorticity and Coriolis force, taking into account the dependence on various physical parameters and we justify rigorously the shallow water model. We also consider a possible non constant pressure at the surface that can be used to describe meteorological disturbances such as storms or pressure jumps for instance.