# On the influence of gravity in the dynamics of geophysical flows

2 EDPA - Équations aux dérivées partielles, analyse
ICJ - Institut Camille Jordan [Villeurbanne]
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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Journal articles
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https://hal.archives-ouvertes.fr/hal-03352242
Contributor : Gabriele Sbaiz Connect in order to contact the contributor
Submitted on : Thursday, September 23, 2021 - 9:19:55 AM
Last modification on : Monday, April 4, 2022 - 9:10:05 AM
Long-term archiving on: : Friday, December 24, 2021 - 6:15:34 PM

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DS-F-S-WK_gravity.pdf
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### Identifiers

• HAL Id : hal-03352242, version 1
• ARXIV : 2109.09841

### Citation

Daniele del Santo, Francesco Fanelli, Gabriele Sbaiz, Aneta Wróblewska-Kamińska. On the influence of gravity in the dynamics of geophysical flows. Mathematics in Engineering, AIMS, 2023. ⟨hal-03352242⟩

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