论文标题
快速旋转的薄域中的非均匀流体和Ekman泵送效果
Fast rotating non-homogeneous fluids in thin domains and the Ekman pumping effect
论文作者
论文摘要
在本文中，我们执行快速旋转限制$ \ varepsilon \ rightarrow0^+$的密度依赖性不可压缩的navier-stokes-coriolis系统， $ω__\ VAREPSILON \，：= \，\ MATHBB {r}^2 \ times \，] - \ ell_ \ ell_ \ varepsilon，\ ell_ \ ell_ \ ell_ \ varepsilon [\，$，$ \ \ varepsilon \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in $ y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y＆$ y \ $ \ varepsilon> 0 $。通过让$ \ ell_ \ varepsilon \ longrightArrow0^+$ for $ \ varepsilon \ rightArrow0^+$，并考虑在$ω__\ varepsilon $的边界处的navier-slip边界条件，我们给出了严格的在泵送非homogene seposeen of-homogene sepone seponse of homogene sepons of-Homogsen seponseos of-oseen seponseos of-oseos的varrepsilon $。关于先前的研究（对碳密度和可压缩流体进行的流动进行），我们的方法具有规避边界层的复杂分析的优势。 据我们所知，这是第一个研究，涉及在$ 3 $ -D设置的情况下对快速旋转不可压缩流体的渐近分析。在这方面，我们指出的是，所有$ \ varepsilon> 0 $ $ \ geq \ ell> 0 $ 0 $目前仍在很大程度上开放。
In this paper, we perform the fast rotation limit $\varepsilon\rightarrow0^+$ of the density-dependent incompressible Navier-Stokes-Coriolis system in a thin strip $Ω_\varepsilon\,:=\,\mathbb{R}^2\times\,]-\ell_\varepsilon,\ell_\varepsilon[\,$, where $\varepsilon\in\,]0,1]$ is the size of the Rossby number and $\ell_\varepsilon>0$ for any $\varepsilon>0$. By letting $\ell_\varepsilon\longrightarrow0^+$ for $\varepsilon\rightarrow0^+$ and considering Navier-slip boundary conditions at the boundary of $Ω_\varepsilon$, we give a rigorous justification of the phenomenon of the Ekman pumping in the context of non-homogeneous fluids. With respect to previous studies (performed for flows of contant density and for compressible fluids), our approach has the advantage of circumventing the complicated analysis of boundary layers. To the best of our knowledge, this is the first study dealing with the asymptotic analysis of fast rotating incompressible fluids with variable density in a $3$-D setting. In this respect, we remark that the case $\ell_\varepsilon\geq\ell>0$ for all $\varepsilon>0$ remains largely open at present.
