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Experimental study and direct numerical simulation of dynamics of an isothermal low-viscosity fluid are done in a coaxial gap of a cylindrical container making rotational vibrations relative to its axis. On the inner surface of the outer wall of the container, semicircular deflectors are placed regularly, playing the role of flow activators. As a result of vibrations, the activators oscillate tangentially. In the simulation a two-dimensional configuration is considered, excluding the end-wall effects. In the experiment a container with large aspect ratio is used. Steady streaming is generated in the viscous boundary layers on the activators. On each of the latter, beyond the viscous domain, a symmetric vortices pair is formed. The steady streaming in the annulus has an azimuthal periodicity. With an increase in the vibration intensity, a competition between the vortices occurs, as a result of which one of the vortices (let us call it even) approaches the activator and the other one (odd) rolls away and couples with the vortices from the neighbouring pairs. Streamlines of the odd vortices close on each other, forming a flow of a cogwheel shape that encircles the inner wall. Comparison of the experiment and the simulation reveals an agreement at moderate vibration intensity.

The dynamics of the interface between two immiscible liquids with a high viscosity contrast is studied experimentally when the liquids are pumped through a radial Hele-Shaw cell. Two cases are considered: a monotonous radial displacement of the viscous fluid, when the classical Saffman–Taylor instability develops, and an oscillatory interface motion due to harmonic flowrate modulation in the absence of the average displacement flow. At small amplitudes of flowrate modulation, the interface performs axisymmetric radial oscillations, maintaining the ring shape during the entire period, while with an increase in the amplitude, it loses stability in a threshold manner. In the phase of fluid displacement, finger instability develops at the interface in the form of an azimuthally periodic structure during a fraction of the period. Fingers reach the greatest length in the phase of maximum fluid displacement, while in the contraction phase (maximum displacement toward the cell center), the interface restores its concentric shape. The threshold for the occurrence of finger instability is determined by the relative amplitude of interface oscillations and under conditions of high contrast of viscosities (one liquid oscillates following the “viscous” law and the other obeys the “inviscid” law) coincides at different oscillation frequencies and different average radii of the interface. The discovered type of instability is new and is studied for the first time. A comparison of the wavelengths of the pulsating fingers with the well-known case of continuous displacement of a viscous fluid in a Hele-Shaw cell indicates that the Saffman–Taylor instability mechanism underlies the observed phenomenon.

Mean dynamics of light granular matter in liquid in the rotating horizontal cylinder subjected to transversal vibrations is experimentally investigated. The excitation of outstripping and lagging azimuth motion of the interface with respect to the cavity is revealed at definite ratios of rotation and vibration frequencies υ r . The motion is generated by the inertial oscillations arising in the system in a resonant way. The formation of regular spatial structures on the interface is revealed at intensive outstripping motion. These structures have azimuth and axial periodicity and their shape depends on the type of inertial waves arising in the cavity. Intensity and direction of azimuth flows as well as shape of patterns on the granular matterliquid interface are determined by the ratio υ r . It is shown, that the lagging motion exists at υ r < 1, and the outstripping one exists at υ r > 1. Combined action of vibrations and rotation provides an efficient mechanism of mass transfer control, the intensity of mean flows in the cavity frame can be of the same order of magnitude as the rotation velocity.

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The dynamics of an interface between two immiscible liquids of different density is studied experimentally in a horizontal cylinder at rotation in the gravity field. Two liquids entirely fill the cavity volume, and the container is rotated sufficiently fast so that the liquids are centrifuged. The light liquid forms a column extended along the rotation axis, and the heavy liquid forms an annular layer. Under the action of gravity, the light liquid column displaces steadily along the radius, downwards in the laboratory frame. As a result, fluid oscillations in the cavity frame are excited at the interface, which lead to the generation of a steady streaming, and the fluid comes into a slow lagging rotation with respect to the cylinder walls. The dynamics of the studied system is determined by the ratio of the gravity acceleration to the centrifugal one—the dimensionless acceleration. In experiments, the system is controlled by the means of variation of the rotation rate, i.e., of the centrifugal force. At a critical value of the dimensionless acceleration the circular interface looses stability, and an azimuthal wave is excited. This leads to a strong increase in the interface differential velocity. A theoretical analysis is done based on the theory of centrifugal waves and a frequency equation is obtained. Experimental results are in good agreement with the theory at the condition of small wave amplitudes. Mechanism of steady streaming generation is analyzed based on previously published theoretical results obtained for the limiting case when the light phase is a solid cylinder. A qualitative agreement is found.