@article{Del Santo2023, 
author = {Daniele Del Santo and Francesco Fanelli and Gabriele Sbaiz and Aneta Wróblewska-Kamińska},
title = {On the influence of gravity in the dynamics of geophysical flows},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {1},
pages = {1-33},
keywords = {barotropic Navier-Stokes-Coriolis system, gravity, stratification effects, low Mach, Froude and Rossby numbers, multiscale limit},
url = {https://www.sciopen.com/article/10.3934/mine.2023008},
doi = {10.3934/mine.2023008},
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 ( Ma,  Ro and  Fr, respectively). The focus here is on the effects of gravity: albeit remaining in a low stratification regime  Ma/Fr→0, we consider scaling for the Froude number which go beyond the "critical" value  Fr=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.}
}