On the influence of gravity in the dynamics of geophysical flows

2021/09/20 by Del Santo, Daniele, Fanelli, Francesco, Sbaiz, Gabriele +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.09841

Abstract

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 → 0, we consider scaling for the Froude number which go beyond the "critical" value \rm Fr = √(\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.

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