Some problems of hydrodynamical stability in rotating spherical layers with application to dynamics of planetary atmospheres

A theoretical and experimental investigation of a shear viscous flow in a spherical layer due to coaxial rotation of boundary spheres is presented. It is found that all types of instabilities characteristic of incompressible viscous rotating fluid flows, such as the centrifugal instability, the Stewartson and Ekman layer instabilities, and nonviscous and viscous shear instabilities, are observed in the flow when different values of similarity parameters are considered. These different mechanisms result in a great variety of secondary flow regimes occurring in spherical layers. Since many of these mechanisms are characterized by hysteresis, nonuniqueness of the flow regimes occurs at the same stationary outer conditions. Thus, nonuniqueness is a result of different temporal developments in the flow as well as different instability mechanisms.