Steady flows excited by circular oscillations of a free inner core in a rotating spherical cavity

This research involves experimental studies of the fluid flow excited by a light free spherical core in a spherical cavity rapidly rotating around the horizontal axis. The gravity force, directed perpendicular to the axis, causes a small radial displacement of the light core from the rotation axis; the displacement is steady in the laboratory reference frame. This corresponds to circular oscillations of the core in the rotating reference frame with the frequency equal to the rotation rate of the cavity. As a result, steady flows are generated in the fluid, which are accompanied by a lagging differential rotation of the core. Inertial waves created by the oscillating core also contribute to the generation of steady flows. The velocity field of fluid flow is studied using the PIV method. It is demonstrated that the mean azimuthal flow of the fluid has a two-dimensional structure, which means the azimuthal velocity magnitude is virtually constant with respect to the axial coordinate. The azimuthal flow consists of several coaxial cylindrical surfaces, nested into each other, rotating at different angular frequencies. The radial distribution of the azimuthal velocity is characterized by a series of inflexion points and is qualitatively different from the known case of a flow caused by a differential rotation of the core, mounted on the axis of the rotating cavity. The inflexion points, in their turn, form the basis for the development of various unstable modes. It is discovered that, before the instability threshold, the axisymmetric azimuthal flow of fluid is fully determined by the lagging differential rotation rate of the core. It is shown that the azimuthal fluid flow is accompanied by relatively weak flows of axial circulation in the form of toroidal vortices.