The KP approximation under a weak Coriolis forcing

TL;DR

This paper rigorously justifies the KP approximation for weakly transverse water-waves influenced by Coriolis forces, deriving and validating asymptotic models in different forcing regimes.

Contribution

It provides the first mathematical justification of the KP approximation under Coriolis forcing and derives related asymptotic models in weak and very weak forcing regimes.

Findings

Justification of the rotation-modified KP equation under weak Coriolis forcing

Derivation of the classical KP equation under very weak Coriolis forcing

Rigorous asymptotic analysis of water-waves with Coriolis effects

Abstract

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.