Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Marco Bravin, Francesco Fanelli
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引用次数: 0

Abstract

In this paper, we perform the fast rotation limit \(\varepsilon \rightarrow 0^+\) of the density-dependent incompressible Navier–Stokes–Coriolis system in a thin strip \(\Omega _\varepsilon :=\,{\mathbb {R}}^2\times \, \left. \right] -\ell _\varepsilon ,\ell _\varepsilon \left[ \right. \,\), where \(\varepsilon \in \,\left. \right] 0,1\left. \right] \) is the size of the Rossby number and \(\ell _\varepsilon >0\) for any \(\varepsilon >0\). By letting \(\ell _\varepsilon \longrightarrow 0^+\) for \(\varepsilon \rightarrow 0^+\) and considering Navier-slip boundary conditions at the boundary of \(\Omega _\varepsilon \), 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 \(\ell _\varepsilon \geqslant \ell >0\) for all \(\varepsilon >0\) remains largely open at present.

薄域中快速旋转非均匀流体与Ekman抽运效应
在本文中,我们执行了密度相关的不可压缩Navier-Stokes-Coriolis系统在一条细条\(\Omega _\varepsilon :=\,{\mathbb {R}}^2\times \, \left. \right] -\ell _\varepsilon ,\ell _\varepsilon \left[ \right. \,\)上的快速旋转极限\(\varepsilon \rightarrow 0^+\),其中\(\varepsilon \in \,\left. \right] 0,1\left. \right] \)是罗斯比数的大小,\(\ell _\varepsilon >0\)适用于任何\(\varepsilon >0\)。取\(\ell _\varepsilon \longrightarrow 0^+\)为\(\varepsilon \rightarrow 0^+\),并考虑\(\Omega _\varepsilon \)边界处的Navier-slip边界条件,给出了非均质流体中Ekman泵送现象的严格证明。与以前的研究(针对含密度流和可压缩流体进行的研究)相比,我们的方法的优点是避免了对边界层的复杂分析。据我们所知,这是第一个在三维环境下处理变密度快速旋转不可压缩流体渐近分析的研究。在这方面,我们注意到,对于所有人\(\ell _\varepsilon \geqslant \ell >0\)的情况\(\varepsilon >0\)目前在很大程度上仍然悬而未决。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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