{"title":"过渡平面库埃特流模型","authors":"Paul Manneville, Fabien Locher","doi":"10.1016/S1287-4620(00)00113-7","DOIUrl":null,"url":null,"abstract":"<div><p>A simplified model of plane Couette flow is derived by means of a cross-stream (<em>y</em>) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (<em>x</em>–<em>z</em>) space-dependence of a velocity field taken in the form: <em>u</em>=<em>U</em><sub>0</sub>(<em>x</em>,<em>z</em>,<em>t</em>)+[1+<em>U</em><sub>1</sub>(<em>x</em>,<em>z</em>,<em>t</em>)]sin(<em>πy</em>/2), <em>v</em>=<em>V</em><sub>1</sub>(<em>x</em>,<em>z</em>,<em>t</em>)cos(<em>πy</em>/2), <em>w</em>=<em>W</em><sub>0</sub>(<em>x</em>,<em>z</em>,<em>t</em>)+<em>W</em><sub>1</sub>(<em>x</em>,<em>z</em>,<em>t</em>)sin(<em>πy</em>/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).</p></div>","PeriodicalId":100303,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy","volume":"328 2","pages":"Pages 159-164"},"PeriodicalIF":0.0000,"publicationDate":"2000-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1287-4620(00)00113-7","citationCount":"13","resultStr":"{\"title\":\"A model for transitional plane Couette flow\",\"authors\":\"Paul Manneville, Fabien Locher\",\"doi\":\"10.1016/S1287-4620(00)00113-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A simplified model of plane Couette flow is derived by means of a cross-stream (<em>y</em>) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (<em>x</em>–<em>z</em>) space-dependence of a velocity field taken in the form: <em>u</em>=<em>U</em><sub>0</sub>(<em>x</em>,<em>z</em>,<em>t</em>)+[1+<em>U</em><sub>1</sub>(<em>x</em>,<em>z</em>,<em>t</em>)]sin(<em>πy</em>/2), <em>v</em>=<em>V</em><sub>1</sub>(<em>x</em>,<em>z</em>,<em>t</em>)cos(<em>πy</em>/2), <em>w</em>=<em>W</em><sub>0</sub>(<em>x</em>,<em>z</em>,<em>t</em>)+<em>W</em><sub>1</sub>(<em>x</em>,<em>z</em>,<em>t</em>)sin(<em>πy</em>/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).</p></div>\",\"PeriodicalId\":100303,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy\",\"volume\":\"328 2\",\"pages\":\"Pages 159-164\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1287-4620(00)00113-7\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1287462000001137\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1287462000001137","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A simplified model of plane Couette flow is derived by means of a cross-stream (y) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (x–z) space-dependence of a velocity field taken in the form: u=U0(x,z,t)+[1+U1(x,z,t)]sin(πy/2), v=V1(x,z,t)cos(πy/2), w=W0(x,z,t)+W1(x,z,t)sin(πy/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).
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