Abstract
<abstract><p>In the present paper, we study a multiscale limit for the barotropic Navier-Stokes system with Coriolis and gravitational forces, for vanishing values of the Mach, Rossby and Froude numbers ($ {\rm{Ma}} $, $ {\rm{Ro}} $ and $ {\rm{Fr}} $, respectively). The focus here is on the effects of gravity: albeit remaining in a low stratification regime $ {\rm{Ma}}/{\rm{Fr}}\, \rightarrow\, 0 $, we consider scaling for the Froude number which go beyond the "critical" value $ {\rm{Fr\, = \, \sqrt{\rm{Ma}}}} $. The rigorous derivation of suitable limiting systems for the various choices of the scaling is shown by means of a compensated compactness argument. Exploiting the precise structure of the gravitational force is the key to get the convergence.</p></abstract>
Highlights
In this paper we continue the investigation we began in [7], about multiscale analysis of mathematical models for geophysical flows
Our focus here is on the effect of gravity in regimes of low stratification, but which go beyond a choice of the scaling that, in light of previous results, we call “critical”
By definition, geophysical flows are flows whose dynamics is characterised by large time and space scales
Summary
In this paper we continue the investigation we began in [7], about multiscale analysis of mathematical models for geophysical flows. Our focus here is on the effect of gravity in regimes of low stratification, but which go beyond a choice of the scaling that, in light of previous results, we call “critical”. In order to explain better all this, let us introduce some physics about the problem we are interested in, and give an overview of related studies.
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