Stability of spherical Couette flow in thick layers when the inner sphere revolves

A natural generalization of cylindrical Couette flow is the flow of a viscous incompressible liquid between two concentric spheres rotating about the same axis with different angular velocities. As has often been noted, spherical Couette flow is, despite the apparent similarity, considerably more complex than cylindrical flow. It consists of differential rotation about the axis and one- or two-eddy circulation (depending on the ratio between the angular velocities of the two spheres = ₂/₁) in the meridional plane and depends significantly on the Reynolds number Re = ₁r₁² and the relative thickness of the layer = (r₂-r₁)/r₁ (₁, ₂ and r₁, r₂ are the angular velocities and radii of the inner and outer spheres, respectively. The investigation of spherical Gouette flow and its stability has begun relatively recently (within the last 10 years) and has evidently been stimulated by applied problems associated with astro- and geophysics. Because of the great computational difficulties encountered in investigating such flow theoretically, experimental investigations have yielded more extensive and interesting results [1–8], although all the published results refer to the case of rotation of one inner sphere ( = 0).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–15, March–April, 1978.It remains to thank S. A. Shcherbakov for help in organizing automatic input of the signals to the BÉSM-6 computer.