Influence of an external force field on the dynamics of a free core and fluid in a rotating spherical cavity

This research involves experimental studies of the dynamics of a free spherical core and fluid motion in a spherical cavity rotating around the horizontal axis. The gravity field causes circular oscillations of the core in the reference frame of the cavity creating an averaged force in the Stokes boundary layer which makes the core rotate relative to the cavity (vibrational hydrodynamic top). The core rotates in the direction opposite to that of the cavity (lagging differential rotation). The research shows that the differential rotation intensity is determined by the ratio between the gravitational and centrifugal acceleration, as well as the ratio of the core size to the thickness of the Stokes layer. Various regimes of the fluid flow have been studied. The shape of subcritical flow is a circular-section column extended along the geometric continuation of the sphere. Increasing the differential rotation rate of the core results in various independent modes of instability of the column. One of such modes involves development of an azimuthal wave on the column boundary. The second mode is a system of two-dimensional vortices extended along the axis and rotating inside the column. It has been discovered that the development of supercritical structures causes changes in the differential rotation rate of the core.