{"title":"Taylor Nearly Columnar Vortices in the Couette–Taylor System: Transition to Turbulence","authors":"T. Akinaga, P. M. J. Trevelyan, S. C. Generalis","doi":"10.1134/s1995080224602388","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, <span>\\(\\beta\\)</span>, up to <span>\\(\\beta\\sim 3\\)</span> rather narrow Taylor vortices may be realized for Reynolds number <span>\\(R<80\\)</span>. These vortices will become unstable to states with columnar components with increasing <span>\\(R\\)</span>. We show that for low <span>\\(R\\)</span>, <span>\\((R,\\beta)\\sim(62.2,3.5)\\)</span>, a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers <span>\\(\\alpha\\sim 0.17\\)</span> with <span>\\(\\beta=3.5\\)</span>. We examine the bifurcation sequence of these states.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602388","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, \(\beta\), up to \(\beta\sim 3\) rather narrow Taylor vortices may be realized for Reynolds number \(R<80\). These vortices will become unstable to states with columnar components with increasing \(R\). We show that for low \(R\), \((R,\beta)\sim(62.2,3.5)\), a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers \(\alpha\sim 0.17\) with \(\beta=3.5\). We examine the bifurcation sequence of these states.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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