Geophysical flows and the effects of a strong surface tension

TL;DR

This paper reviews recent mathematical results on the asymptotic behavior of geophysical flows modeled by Navier-Stokes-Korteweg systems under strong surface tension, focusing on incompressible and rapid rotation limits.

Contribution

It provides a detailed mathematical derivation and physical interpretation of the asymptotic limits of geophysical flow models with surface tension effects.

Findings

Asymptotic behavior characterized under combined limits

Derivation of simplified governing equations

Insights into physical phenomena of surface tension effects

Abstract

In the present note we review some recent results for a class of singular perturbation problems for a Navier-Stokes-Korteweg system with Coriolis force. More precisely, we study the asymptotic behaviour of solutions when taking incompressible and fast rotation limits simultaneously, in a constant capillarity regime. Our main purpose here is to explain in detail the description of the phenomena we want to capture, and the mathematical derivation of the system of equations. Hence, a huge part of this work is devoted to physical considerations and mathematical modeling.