On nontraditional quasi-geostrophic equations
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.
Received: 12 November 2015
Revised: 5 May 2015
Accepted: 30 May 2016
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.
Mathematics Subject Classification: 35Q35 / 76U05 / 76M45 / 35B40
Key words: Ocean modeling / Coriolis force / traditional approximation / tilted quasi-geostrophic equations / slanted rotation
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