Abstract

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are studied numerically by solving the unsteady three-dimensional Navier-Stokes equations. Narrow to medium gap widths are chosen with clearance ratio σ = 0.06, 0.14 and 0.18 respectively, and a wide range of Reynolds number is encompassed in the present study. The numerical method used is the artificial compressibility method with a dual-time stepping technique for obtaining time accuracy. A third-order upwind compact finite difference is used for the advective terms. The numerical results show that spiral and wavy Taylor-Gortler vortices are formed in supercritical high Reynolds number range, and multiple time-dependent solutions exist for the medium gap case σ = 0.18.

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