Lucas, Carine; McWilliams, James C.; Rousseau, Antoine On nontraditional quasi-geostrophic equations. (English) Zbl 1364.35280 ESAIM, Math. Model. Numer. Anal. 51, No. 2, 427-442 (2017). Summary: 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 quasi-hydrostatic quasi-geostrophic (QHQG) and QG models. Cited in 1 Document MSC: 35Q35 PDEs in connection with fluid mechanics 76U05 General theory of rotating fluids 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs 86A05 Hydrology, hydrography, oceanography 35Q86 PDEs in connection with geophysics 76B65 Rossby waves (MSC2010) Keywords:ocean modeling; Coriolis force; traditional approximation; tilted quasi-geostrophic equations; slanted rotation PDFBibTeX XMLCite \textit{C. Lucas} et al., ESAIM, Math. Model. Numer. Anal. 51, No. 2, 427--442 (2017; Zbl 1364.35280) Full Text: DOI