ON THE INFLUENCE OF DIFFERENTIAL ROTATION OF A CORE, OSCILLATING IN A ROTATING SPHERICAL CAVITY, ON THE STABILITY OF STEADY FLOW
A comparative analysis of supercritical flows excited by an oscillating core in a rotating spherical cavity with a liquid is carried out. Two situations are considered, when the core is free and performs differential rotation, and when there is no differential rotation of the core. In both cases, the oscillations lead to the occurrence of steady azimuthal flow, in the profile of which there are several inflection points. An increase in the amplitude of oscillations leads to a loss of stability of an axisym- metric flow. In this case, a series of threshold transitions is observed in the supercritical region, associated with the shear instability of the averaged flow. The instability manifests itself in the development of an azimuthally periodic system of vortices elongated along the axis; various modes differ in azimuthal wavelength, location of vortexes (distance from the axis of rotation) and azimuthal drift velocity of the system relative to the cavity. It is shown that regardless of the presence of a differential rotation of the core, the scenarios for changing the supercritical flow regimes remain the same. At the same time, the critical values of the Reynolds numbers for instabilities of similar type are different.