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 β=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-G{ortler (TG) vortices have been simulated successfullyfor β=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 for β=0.18. Analysis of the numerical resultsreveals these higher flow modes in terms of fundamental frequency,wave number and spatial structure.
