Geodesic
On nontraditional quasi-geostrophic equations
Lucas, Carine1  ; McWilliams, James C.2 ; Rousseau, Antoine3 
1 MAPMO UMR CNRS 7349, Fédération Denis Poisson FR CNRS 2964, Université d’Orléans, 45067 Orléans cedex 2, France.
2 Dept. of Atmospheric and Oceanic Sciences, University of California, Los Angeles (UCLA), Mathematical Sciences Building, Room 7983, Los Angeles, CA 90095-1565. USA.
3 Inria and IMAG UMR CNRS 5159, Inria Chile, Av Apoquindo 2827, Las Condes, Santiago de Chile, Chile.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 427-442

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In this article, we work on nontraditional models where the so-called traditional approximation on the Coriolis force is removed. In the derivation of the quasi-geostrophic equations, we carefully consider terms in δ/ε, where δ (aspect ratio) and ε (Rossby number) are both small numbers. We provide here some rigorous crossed-asymptotics with regards to these parameters, prove some mathematical results and compare QHQG and QG models.

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Accepté le :
DOI : 10.1051/m2an/2016041
Classification : 35Q35, 76U05, 76M45, 35B40
Keywords: Ocean modeling, Coriolis force, traditional approximation, tilted quasi-geostrophic equations, slanted rotation

Lucas, Carine 1 ; McWilliams, James C. 2 ; Rousseau, Antoine 3

1 MAPMO UMR CNRS 7349, Fédération Denis Poisson FR CNRS 2964, Université d’Orléans, 45067 Orléans cedex 2, France.
2 Dept. of Atmospheric and Oceanic Sciences, University of California, Los Angeles (UCLA), Mathematical Sciences Building, Room 7983, Los Angeles, CA 90095-1565. USA.
3 Inria and IMAG UMR CNRS 5159, Inria Chile, Av Apoquindo 2827, Las Condes, Santiago de Chile, Chile. 
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     title = {On nontraditional quasi-geostrophic equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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     publisher = {EDP-Sciences},
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Lucas, Carine; McWilliams, James C.; Rousseau, Antoine. On nontraditional quasi-geostrophic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 427-442. doi: 10.1051/m2an/2016041

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