Stability, non-uniqueness and transition to turbulence in the flow between two rotating spheres

Experimental and numerical stability analyses of the viscous incompressible fluid flow between two concentric coaxially rotating spheres are presented. The analyses cover a wide range of similarity parameters, and stability curves for different gap sizes are found. Several new types of basic flow instabilities are studied, which have nothing in common with those of the circular Couette flow (Fenstermacher et al., 1979; Walden and Donnelly, 1979) and the flow between disks. The non-uniqueness of the secondary flow regimes is shown for the same supercritical values of the parameters, both in the experiments and the numerical computation. The transition to turbulence in the wide gap case is investigated by spectral and correlation analyses of the radial velocity fluctuations. Results show that the onset of nonperiodicity in these spherical Couette flows differs significantly from the same process in circular Couette flows and Rayleigh-Benard convection (1979).