Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio beta = 0.06 and 0.18 respectively are considered for the Reynolds number range covering the first Hopf bifurcation point. With adequate initial conditions and temporary imposition of small wave-type perturbation, multiple periodic flow states with three different pair numbers of spiral Taylor-Gortler (TG) vortices have been simulated successfully for beta = 0.06, of which the 1-pair and 2-pair of spiral TG vortices are newly obtained. Three different periodic flow states with shear waves, Stuart vortices or wavy outflow boundary, have been obtained for beta = 0.18. Analysis of the numerical results reveals these higher flow modes in terms of fundamental frequency, wave number and spatial structure.