The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration

CORC > 上海天文台 > 中国科学院上海天文台 > 空间导航与定位技术重点实验室

	The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration
	Zhang, Keke 1; Chan, Kit H.2; Liao, Xinhao3 ; Aurnou, Jonathan M.4
刊名	JOURNAL OF FLUID MECHANICS
	2013-04-01
卷号	720 页码:212-235
关键词	geophysical and geological flows rotating flows
英文摘要	We investigate the problem of oscillatory flow of a homogeneous fluid with viscosity nu in a fluid-filled sphere of radius a that rotates rapidly about a fixed axis with angular velocity Omega(0) and that undergoes weak longitudinal libration with amplitude epsilon Omega(0) and frequency (omega) over cap Omega(0), where epsilon is the Poincare number with epsilon << 1 and (omega) over cap is dimensionless frequency with 0 < <(omega)over cap> < 2. Three different methods are employed in this investigation: (i) asymptotic analysis at small Ekman numbers E defined as E = nu/(a(2)Omega(0)); (ii) linear numerical analysis using a spectral method; and (iii) nonlinear direct numerical simulation using a finite-element method. A satisfactory agreement among the three different sets of solutions is achieved when E <= 10(-4). It is shown that the flow amplitude vertical bar u vertical bar is nearly independent of both the Ekman number E and the libration frequency <(omega)over cap>, always obeying the asymptotic scaling vertical bar u vertical bar = O(epsilon) even though various spherical inertial modes are excited by longitudinal libration at different libration frequencies (omega) over cap. Consequently, resonances do not occur in this system even when (omega) over cap is at the characteristic value of an inertial mode. It is also shown that the pressure difference along the axis of rotation is anomalous: this quantity reaches a sharp peak when (omega) over cap approaches a characteristic value. In contrast, the pressure difference measured at other places in the sphere, such as in the equatorial plane, and the volume-integrated kinetic energy are nearly independent of both the Ekman number E and the libration frequency (omega) over cap. Absence of resonances in a fluid-filled sphere forced by longitudinal libration is explained through the special properties of the analytical solution that satisfies the no-slip boundary condition and is valid for E << 1 and epsilon << 1.
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 FLOWS ; INERTIAL OSCILLATIONS ; PRECESSING CYLINDER ; SPHEROIDAL CAVITY ; DRIVEN ; MOTION ; WAVES
收录类别	SCI
语种	英语
WOS记录号	WOS:000315456800009
公开日期	2014-09-22
内容类型	期刊论文
源URL	[http://119.78.226.72//handle/331011/15215]
专题	上海天文台_空间导航与定位技术重点实验室
作者单位	1.Univ Exeter, Dept Math Sci, Exeter EX4 4QF, Devon, England 2.Univ Hong Kong, Dept Math, Pokfulam, Hong Kong, Peoples R China 3.Chinese Acad Sci, Shanghai Astron Observ, Shanghai 200030, Peoples R China 4.Univ Calif Los Angeles, Dept Earth & Space Sci, Los Angeles, CA 90095 USA
推荐引用方式 GB/T 7714	Zhang, Keke,Chan, Kit H.,Liao, Xinhao,et al. The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration[J]. JOURNAL OF FLUID MECHANICS,2013,720:212-235.
APA	Zhang, Keke,Chan, Kit H.,Liao, Xinhao,&Aurnou, Jonathan M..(2013).The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration.JOURNAL OF FLUID MECHANICS,720,212-235.
MLA	Zhang, Keke,et al."The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration".JOURNAL OF FLUID MECHANICS 720(2013):212-235.