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Journal Articles Mathematics in Engineering Year : 2023

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

Daniele del Santo
• Function : Author
Francesco Fanelli
• Function : Author
• PersonId : 982878
Gabriele Sbaiz

#### 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.

### Dates and versions

hal-03352242 , version 1 (23-09-2021)

### Identifiers

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

### Cite

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

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