{"title":"Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect","authors":"Marco Bravin, Francesco Fanelli","doi":"10.1007/s00021-023-00826-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we perform the fast rotation limit <span>\\(\\varepsilon \\rightarrow 0^+\\)</span> of the density-dependent incompressible Navier–Stokes–Coriolis system in a thin strip <span>\\(\\Omega _\\varepsilon :=\\,{\\mathbb {R}}^2\\times \\, \\left. \\right] -\\ell _\\varepsilon ,\\ell _\\varepsilon \\left[ \\right. \\,\\)</span>, where <span>\\(\\varepsilon \\in \\,\\left. \\right] 0,1\\left. \\right] \\)</span> is the size of the Rossby number and <span>\\(\\ell _\\varepsilon >0\\)</span> for any <span>\\(\\varepsilon >0\\)</span>. By letting <span>\\(\\ell _\\varepsilon \\longrightarrow 0^+\\)</span> for <span>\\(\\varepsilon \\rightarrow 0^+\\)</span> and considering Navier-slip boundary conditions at the boundary of <span>\\(\\Omega _\\varepsilon \\)</span>, 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 <span>\\(\\ell _\\varepsilon \\geqslant \\ell >0\\)</span> for all <span>\\(\\varepsilon >0\\)</span> remains largely open at present.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00826-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-023-00826-3","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.