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 ratioβ=0.06 and 0.18 respectively areconsidered for the Reynolds number range covering the first Hopfbifurcation point.With adequate initial conditions and temporaryimposition of small wave-type perturbation,multiple periodicflow states with three different pair numbers of spiralTaylor-Gortler(TG)vortices have been simulated successfullyforβ=0.06,of which the 1-pair and 2-pair of spiral Tgvortices are newly obtained.Three different periodic flow stateswith shear waves,Stuart vortices or wavy outflow boundary,have been obtained forβ=0.18.Analysis of the numerical resultsreveals these higher flow modes in terms of fundamental frequency,wave number and spatial structure.
