Librations induced zonal flow and differential rotation of free inner core in rotating spherical cavity

Abstract

The paper is devoted to the experimental study of the dynamics of a free solid core and a liquid in a spherical cavity rotating about a horizontal axis. The cavity rotation rate consists of two components: constant and oscillating ones (librations). Under the action of centrifugal force the core with the density less than the density of liquid is located near the rotation axis. The gravity field causes a small stationary displacement of the core from the cavity center. In turn, this displacement induces mean retrograde differential rotation of the core and the fluid. It is found that the librations generate the mean effects (zonal flow and the retrograde differential rotation of the core), which manifest themselves in sum with the ones caused by gravity. The intensity of zonal flow and the core differential rotation is proportional to the square of the libration amplitude. The additivity of mean effects connected with librations and gravity is observed in a wide range of the libration frequency excluding the areas of very low-frequency librations and resonant (close to the rotation frequency and natural frequencies of the core translational oscillations) ones. At low-frequency librations, the core rotation rate changes periodically with the libration frequency and is accompanied by the periodic variation of the core position in the cavity. At some part of the libration period, the relaxation oscillations of the core with natural frequency are excited. Librations with the frequency equal to the cavity rotation exert the strongest resonant effect on the core, generating the core translational oscillations with large amplitude and substantial change of the structure of mean zonal flows. In this case and when the libration frequency coincides with the natural frequency of the core oscillations, the dependence of the differential rotational rate on the libration amplitude is different from the quadratic. This specific response of the system on the librations is caused by the shift of the core from the axis due to the gravity field.