{"title":"在Navier-slip定温边界间的rayleigh - bsamadard对流的热通量边界","authors":"Theodore D. Drivas, H. Nguyen, Camilla Nobili","doi":"10.1098/rsta.2021.0025","DOIUrl":null,"url":null,"abstract":"We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead–Doering bound by Ra512 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering–Constantin Ra12 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957–5981). This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Bounds on heat flux for Rayleigh–Bénard convection between Navier-slip fixed-temperature boundaries\",\"authors\":\"Theodore D. Drivas, H. Nguyen, Camilla Nobili\",\"doi\":\"10.1098/rsta.2021.0025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead–Doering bound by Ra512 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering–Constantin Ra12 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957–5981). This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.\",\"PeriodicalId\":20020,\"journal\":{\"name\":\"Philosophical Transactions of the Royal Society A\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Philosophical Transactions of the Royal Society A\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rsta.2021.0025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophical Transactions of the Royal Society A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rsta.2021.0025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
摘要
本文研究了具有navier滑移、固定温度边界条件的二维rayleigh - bassanard对流，并建立了Nusselt数的边界。由于滑移长度随瑞利数Ra的变化而变化，该估计在自由滑移条件下由Ra512的Whitehead - Doering边界之间进行插值(Whitehead & Doering. 2011自由滑移固定温度边界之间二维Rayleigh - b nard对流的最终状态)。理论物理。经典的Doering - Constantin Ra12界(Doering & Constantin. 1996)和不可压缩流能量耗散的变分界。3对流。理论物理。Rev. E 53,5957 - 5981)。本文是主题问题“物理流体动力学中的数学问题(第一部分)”的一部分。
Bounds on heat flux for Rayleigh–Bénard convection between Navier-slip fixed-temperature boundaries
We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead–Doering bound by Ra512 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering–Constantin Ra12 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957–5981). This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.
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