Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids

Autor: Edoardo Bocchi, Francesco Fanelli, Christophe Prange
Přispěvatelé: Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2022
Předmět:
Zdroj: Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 39:647-704
ISSN: 1873-1430
0294-1449
Popis: The primary goal of this paper is to develop robust methods to handle two ubiquitous features appearing in the modeling of geophysical flows: (i) the anisotropy of the viscous stress tensor, (ii) stratification effects. We focus on the barotropic Navier-Stokes equations with Coriolis and gravitational forces. Two results are the main contributions of the paper. Firstly, we establish a local well-posedness result for finite-energy solutions, via a maximal regularity approach. This method allows us to circumvent the use of the effective viscous flux, which plays a key role in the weak solutions theories of Lions-Feireisl and Hoff, but seems to be restricted to isotropic viscous stress tensors. Moreover, our approach is sturdy enough to take into account non constant reference density states; this is crucial when dealing with stratification effects. Secondly, we study the structure of the solutions to the previous model in the regime when the Rossby, Mach and Froude numbers are of the same order of magnitude. We prove an error estimate on the relative entropy between actual solutions and their approximation by a large-scale quasi-geostrophic flow supplemented with Ekman boundary layers. Our analysis holds for a large class of barotropic pressure laws.
Databáze: OpenAIRE
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