{"title":"圆柱形域中的普朗特-巴歇尔流","authors":"Emmanuel Dormy, H. Keith Moffatt","doi":"10.1137/24m1637313","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. <br/> Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Prandtl–Batchelor Flow in a Cylindrical Domain\",\"authors\":\"Emmanuel Dormy, H. Keith Moffatt\",\"doi\":\"10.1137/24m1637313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. <br/> Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].\",\"PeriodicalId\":51149,\"journal\":{\"name\":\"SIAM Journal on Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/24m1637313\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/24m1637313","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
