Theory of the vibrational hydrodynamic top

Dynamics of a viscous fluid is investigated theoretically in an annulus with the free inner cylinder under conditions of rotation in an external inertial or gravitational field. The two-dimensional formulation is used, corresponding to two long coaxial cylinders. The inner cylinder is free and occupies a steady position on the rotation axis under the action of the centrifugal force due to the fact that it is lighter than surrounding fluid. The action of external force, oriented perpendicular to the rotation axis, induces inertial circular, of the tidal-like type, oscillations of the inner cylinder (core). As a result of the oscillations, the core is brought into rotation relative to the cavity (the outer cylinder) on the background of a steady streaming in the annulus. The mechanism of this differential rotation consists in the generation of an average mass force, of the azimuthal direction, in the oscillating viscous boundary layers on the walls of the core and the cavity.