Vortical structures and velocity fluctuations of spiral and wavy vortices in the spherical Couette Flow

Abstract

Due to the spherical geometry and rotating effect in the spherical Couette flow(SCF) situation, understanding the dynamics of the fluid motion (vortices and waves) within such a spherical shell is relevant to both global astrophysical and geophysical processes and engineering applications. Most of previous experimental investigations on the spherical Couette flow were restricted to the cases of small and medium gap widths in which the first instability occurred as Taylor vortices at the equator (e.g., Munson & Menguturk [13]; Wimmer [22], [23]; Yavorskaya et al. [25]; Nakabayashi [14]; Bühler [4]; Bar-Yoseph et al. [2]; Egbers & Rath [6]). Some experimental and theoretical studies were also conducted recently on the case of wide gap widths in which the first instability appeared in a form of non-axisymmetric spiral waves (Egbers & Rath [6]; Araki et al. [1]; Wulf et al. [24]). When the outer sphere is held stationary, the spherical Couette flow between two spheres with the inner sphere rotating can be characterized by three control parameters. There are the Reynolds number, clearance ratio and rotative acceleration rate. Usually, the spherical Couette flow between two concentric rotating spheres shows dynamical behaviors analogous to the classical circular Couette flow between two concentric rotating cylinders in the equatorial regions, and the flow between two plane rotating disks in the polar regions, respectively. A series of our experimental work have been carried out on the spherical Couette flow between two concentric spheres for a range of the clearance ratio where the Taylor instability occurs in the equatorial region (Nakabayashi [14]; Nakabayashi & Tsuchida [15], [16]), and our previous experimental investigations on the spherical Couette flow showed a similar laminar-turbulent transition to that in the circular Couette flow(CCF).