A new asymptotic method for the analysis of convection in a rapidly rotating sphere

	A new asymptotic method for the analysis of convection in a rapidly rotating sphere
	Zhang, KK ; Liao, XH
刊名	JOURNAL OF FLUID MECHANICS
	2004-11-10
卷号	518 期号:1 页码:319-346
英文摘要	Thermal convection in rapidly rotating, self-gravitating Boussinesq fluid spheres is characterized by three parameters: the Rayleigh number R, the Prandtl number Pr and the Ekman number E. Two different asymptotic limits were considered in the previous studies of the linear problem. In the double limit E much less than 1 and Pr/E much greater than 1, the local asymptotic theory showed that the convective motion is strongly non-axisymmetric, columnar, highly localized and described by the asymptotic scalings, (1/s)partial derivative/partial derivativephi = O (E-1/3), partial derivative/partial derivativez = O(1), R-c = O(E-1/3), where R-c denotes the critical Rayleigh number and (s, phi, z) are cylindrical polar coordinates with the axis of rotation at s = 0. A global asymptotic theory with novel features for the limit E much less than 1 and Pr/E much greater than 1, indicating the radial asymptotic scaling partial derivative/partial derivatives = O (E-1/3), was recently developed by Jones et al. (J. Fluid Mech. vol. 405, 2000, p. 157). In the different double limit E much less than 1 and Pr/E much less than 1, an asymptotic theory for the onset of convection building upon the theory of inertial waves was developed by Zhang (J. Fluid Mech. vol. 268, 1994 p. 211). It was shown that the convective motion at the leading-order approximation is represented by a single inertial-wave mode with a quadratic polynomial of s and z, obeying the asymptotic dependence partial derivative/partial derivatives similar to (1/s)partial derivative/partial derivativephi = O(1), partial derivative/partial derivativez = O(1) and R-c = O(E) for stress-free spheres.
WOS标题词	Science & Technology ; Technology ; Physical Sciences
类目[WOS]	Mechanics ; Physics, Fluids & Plasmas
研究领域[WOS]	Mechanics ; Physics
关键词[WOS]	ZONAL FLOW DRIVEN ; THERMAL-CONVECTION ; FLUID SHELLS ; INERTIAL WAVES ; ONSET ; DYNAMOS ; NUMBER
收录类别	SCI
语种	英语
WOS记录号	WOS:000225335600013
内容类型	期刊论文
源URL	[http://119.78.226.72/handle/331011/18322]
专题	上海天文台_天文地球动力学研究中心
作者单位	1.Univ Exeter, Dept Math Sci, Exeter EX4 4QE, Devon, England 2.Chinese Acad Sci, Shanghai Astron Observ, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Zhang, KK,Liao, XH. A new asymptotic method for the analysis of convection in a rapidly rotating sphere[J]. JOURNAL OF FLUID MECHANICS,2004,518(1):319-346.
APA	Zhang, KK,&Liao, XH.(2004).A new asymptotic method for the analysis of convection in a rapidly rotating sphere.JOURNAL OF FLUID MECHANICS,518(1),319-346.
MLA	Zhang, KK,et al."A new asymptotic method for the analysis of convection in a rapidly rotating sphere".JOURNAL OF FLUID MECHANICS 518.1(2004):319-346.