Vibrational Suspension of Light Sphere in a Tilted Rotating Cylinder with Liquid

The dynamics of a light sphere in a quickly rotating inclined cylinder filled with liquid under transversal vibrations is experimentally investigated. Due to inertial oscillations of the sphere relative to the cavity, its rotation velocity differs from the cavity one. The intensification of the lagging motion of a sphere and the excitation of the outstripping differential rotation are possible under vibrations. It occurs in the resonant areas where the frequency of vibrations coincides with the fundamental frequency of the system. The position of the sphere in the center of the cylinder could be unstable. Different velocities of the sphere are matched with its various quasistationary positions on the axis of rotating cavity. In tilted rotating cylinder, the axial component of the gravity force appears; however, the light sphere does not float to the upper end wall but gets the stable position at a definite distance from it. It makes possible to provide a vibrational suspension of the light sphere in filled with liquid cavity rotating around the vertical axis. It is found that in the wide range of the cavity inclination angles the sphere position is determined by the dimensionless velocity of body differential rotation. 1. Introduction Rotating hydrodynamic systems attract a great interest because of their wide distribution in nature. The density inhomogeneity of such systems ensures the nontrivial inertial properties and, therefore, possibility of controlling them using the vibrations [1]. For instance the action of transverse vibrations on the free boundary of the centrifuged liquid [2] leads to the excitation of an azimuthal wave and excitation of intensive averaged liquid flow. Similar resonance effects occur when the free flowing medium [3] or a light cylindrical body [4] are in rotating system instead of a gas phase. In the last case, the vibration leads to the oscillation of the body and the emergence of its intensive differential rotation relative to the cavity, called “vibrational hydrodynamic top.” Description of the differential rotation in the two-dimensional formulation is given in [4]. The presence of a rotating force field in a rotating frame leads to the circular oscillations of the body. The arising inertial azimuthal wave in the fluid causes the pulsating motion in the viscous boundary layer. This leads to the excitation of an averaged torque, spinning up the body. The direction of body rotation (outstripping or lagging) is determined by the direction of the azimuthal wave. The existence of the lagging and outstripping rotation is