On the quasi-hydrostatic quasi-geostrophic model

Abstract : This paper introduces a rigorous derivation of the quasi-hydrostatic quasi-geostrophic (QHQG) equations of large scale ocean as the Rossby number goes to zero. We follow classical techniques for the derivation of the quasi-geostrophic (QG) equations (as in [BB94]), but the primitive equations that we consider account for the nontraditional rotating terms, as in [LPR10]. We end up with a slightly different QG model with a tilted vertical direction, which has been illustrated in previous works using the primitive equations (see [PMHA97, She04, WB06, GZMvH08, SKR02]), and for which we prove local and global existence results.
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Carine Lucas, James C. Mcwilliams, Antoine Rousseau. On the quasi-hydrostatic quasi-geostrophic model. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, 51 (2), pp.427-442. ⟨inria-00564819v4⟩

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