On nontraditional quasi-geostrophic equations

Lucas, Carine; McWilliams, James C.; Rousseau, Antoine

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 427-442

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 $\delta /\epsilon$, where $\delta$ (aspect ratio) and $\epsilon$ (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.

Classification : 35Q35, 76U05, 76M45, 35B40
Keywords: Ocean modeling, Coriolis force, traditional approximation, tilted quasi-geostrophic equations, slanted rotation

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