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arXiv · 2109.09841

On the influence of gravity in the dynamics of geophysical flows

Daniele Del Santo·Francesco Fanelli·Gabriele Sbaiz·Aneta Wróblewska-Kamińska
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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 ${\rm Ma}/{\rm Fr}\,\rightarrow\,0$, 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.

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Daniele Del Santo, Francesco Fanelli, Gabriele Sbaiz, Aneta Wróblewska-Kamińska. 2021-09-20. On the influence of gravity in the dynamics of geophysical flows. https://arxiv.org/abs/2109.09841

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