Instabilities and pattern formation in rotating spherical cavity with oscillating inner core

The flows in a rotating spherical cavity with liquid and a free solid core in the center are experimentally investigated. The core performs small amplitude circular oscillations in the cavity frame due to a static external field. It results in the excitation of a lagging differential rotation of the core and a two-dimensional axisymmetric azimuthal motion of the fluid with several points of inflection in the velocity profile. The flow has the form of nested columns, one of which is formed on the geometrical continuation of the inner core (Taylor column). With an increase in the differential rotation rate of the core the axisymmetric fluid flow becomes unstable and several modes of instability manifest themselves. First, two-dimensional vortices appear inside the Taylor column. After it, an azimuthal wave appears, which manifests itself in the deformation of the tangent cylinder and has a retrograde phase velocity. A new mode of instability manifests itself outside the Taylor column with an increase in steady flow intensity: a regular system of 2D rolls, parallel to the cavity axis, which propagate in the prograde direction. The discovered modes are characterized by different phase velocities, the dispersion relations are determined experimentally. It is shown that for small Ekman numbers the thresholds of instabilities are determined by the critical values of Reynolds number calculated on the differential rotation rate of the core.