Viktor G. Kozlov

The dynamics of a two-phase medium of water and glass beads in unevenly rotating horizontal cylindrical layer is studied experimentally. The rotation rate varies according to the law f=fr[1+ϵ cos(2πfosct)], where fr is the mean rotation rate, which is set so that the centrifugal force of inertia keeps the glass beads in a stable position near the outer boundary of the cylindrical layer. In an unevenly rotating cylindrical layer, the interaction of water with the layer's walls occurs exclusively in thin boundary layers. So, the core of the fluid rotates at a constant rate fr relative to the observer. From the perspective of glass beads, water oscillates azimuthally at a frequency fosc. It is observed that as the oscillation amplitude ϵ increases, a threshold redistribution of the glass beads occurs, resulting in the axisymmetric pattern formation. It is demonstrated that this phenomenon emerges when the viscous stress at the interface becomes large enough (the Shields number exceeds the critical value θcr), the glass beads become mobile and can move within the cylindrical layer. The present paper discusses the results of experiments on the axial segregation of glass beads. It is revealed that axial particle segregation is associated with the initiation of the vortical flows by standing inertial waves. The spatial period of the band formation is determined by the axial wavenumber of the inertial waves that satisfy the resonance condition.

Thermal convection in a relatively “thick” horizontal cylindrical layer with isothermal boundaries, uniformly rotating around a horizontal axis, is experimentally investigated. The inner boundary of the layer has a higher temperature—the liquid is stably stratified in a centrifugal force field. The subject of the study is the oscillations of a non-isothermal liquid in the cavity frame and the averaged convective flows excited by these oscillations—“vibrational” thermal convection. In the case under consideration, the oscillations of non-isothermal fluid in the cavity are excited by the gravity field and have a tidal nature. The excitation threshold of averaged convection is determined by the vibration parameter and the centrifugal Rayleigh number. The experimental findings align with the theoretical calculations, which are derived from the equations of vibrational thermal convection, obtained by the averaging method. A new mode of thermal convection, which consists of the excitation of intense parametric oscillations of a non-isothermal liquid in the cavity, has been discovered in the experiments. Under certain conditions, parametric instability manifests itself up to the excitation of vibrational thermal convection. Parametric instability has a threshold character and manifests itself in the form of an azimuthally periodic system of consistently rotating longitudinal two-dimensional rolls. The system oscillates at a frequency that is half of the rotation frequency, the frequency of the centrifugal force field modulation. To the best of the authors' knowledge, the excitation of parametric oscillations in a rotating non-isothermal fluid has been discovered for the first time. The conditions for parametric convective instability excitation have been thoroughly examined, and dimensionless control parameters have been delineated. Furthermore, a comprehensive map of stability and various convective regimes has been constructed. The study has demonstrated the significance of parametric oscillations in the context of averaged convective flows and heat transfer.

Recent studies of the oscillatory dynamics of the interface between fluids in Hele–Shaw cells have revealed a new type of instability termed the “oscillatory Saffman instability” in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.

The behavior of a viscous liquid film on the wall of a rapidly rotating cylinder subjected to angular vibrations is experimentally studied. The cavity is filled with an immiscible low-viscosity liquid of lower density. In the... | Find, read and cite all the research you need on Tech Science Press

The behavior of two immiscible low-viscosity liquids differing in density and viscosity in a vertical flat layer undergoing modulated rotation is experimentally studied. The layer has a circular axisymmetric boundary. In the absence of modulation of the rotation speed, the interphase boundary has the shape of a short axisymmetric cylinder. A new effect has been discovered, under the influence of rotation speed modulation, the interface takes on a new dynamic equilibrium state. A more viscous liquid covers the end boundaries of the layer in the form of thin films, which have the shape of round spots of almost constant radius; with increasing amplitude of the velocity modulation, the wetting boundary expands. It is found that upon reaching the critical amplitude of oscillations, the film of a viscous liquid loses stability, and the outer edge of the wetting spot collapses and takes on a feathery structure. It is shown that this threshold is caused by the development of the Kelvin–Helmholtz oscillatory instability of the film. The spreading radius of a spot of light viscous liquid and its stability are studied depending on the rotation rate, amplitude, and frequency of rotation speed modulation. The discovered averaged effects are determined by different oscillatory interaction of fluids with the end-walls of the cell, due to different viscosities. The effect of films forming can find application in technological processes to intensify mass transfer at interphase boundaries.

The stability of an oscillating interface between two immiscible liquids with a high viscosity contrast in an axisymmetric conical Hele–Shaw cell in dependence on the density ratio is studied experimentally. The symmetry axis of the cell is vertical, while the tangential component of the gravy acts on the axisymmetric interface. The contact line is almost motionless, while the low-viscosity liquid penetrates a high-viscosity one in the form of an axisymmetric “tongue” in the course of an oscillating cycle. The increase in the oscillation amplitude leads to the development of azimuthal patterns (fingers) at the interface. Fingers of a low-viscosity liquid appear when a viscous liquid is being squeezed out of the cell and reach their maximum length at the maximum displacement of the interface. Then, the fingers decrease and are replaced by small depressions penetrating into the low-viscosity liquid in the phase of maximum boundary displacement toward the low-viscosity liquid. The increase in the density ratio of liquids has a stabilizing effect on the interface: The instability threshold is shifted to the higher oscillation amplitudes. Also, the stability threshold is independent of whether the high-viscosity or low-viscosity liquid is denser than the other one. We propose a new dimensionless parameter that controls the stability of the interface—the multiplication of the square root of the capillary number and the dimensionless amplitude of interface oscillations. It is revealed that the critical value of the stability parameter increases linearly with an increase in the density ratio of liquids.

The oscillation of the liquid interface in axisymmetric Hele-Shaw cells (conical and flat) is experimentally studied. The cuvettes, which are thin conical layers of constant thickness and flat radial Hele-Shaw cells, are filled with two immiscible liquids of similar densities and a large contrast in viscosity. The axis of symmetry of the cell is oriented vertically; the interface without oscillations is axially symmetric. An oscillating pressure drop is set at the cell boundaries, due to which the interface performs radial oscillations in the form of an oscillating “tongue” of a low-viscosity liquid, periodically penetrating into a more viscous liquid. An increase in the oscillation amplitude leads to the development of a system of azimuthally periodic structures (fingers) at the interface. The fingers grow when the viscous liquid is forced out of the layer and reach their maximum in the phase of maximum displacement of the interface. In the reverse course, the structures decrease in size and, at a certain phase of oscillations, take the form of small pits directed toward the low-viscosity fluid. In a conical cell, a bifurcation of period doubling with an increase in amplitude is found; in a flat cell, it is absent. A slow azimuthal drift of finger structures is found. It is shown that the drift is associated with the inhomogeneity of the amplitude of fluid oscillations in different radial directions. The fingers move from the region of a larger to the region of a lower amplitude of the interface oscillations.

Fluid flow excited by inertial waves in a rotating annulus with a trapezoidal cross section is experimentally investigated. The forcing is introduced by the precession of a flat annular lid bounding the cavity. Such a setup allows to investigate interactions between inertial waves and zonal flows in the presence of equivalent topographic beta-effect, and its dynamic behavior under weak and strong forcing is experimentally studied for the first time. Due to the specific dispersion relation of inertial waves, a cavity shape supports wave attractors that appear only for retrograde lid precession. At a relatively low wave intensity, a zonal flow is generated in the vicinity of a “virtual” axial cylinder, the radius of which coincides with the radius of the focusing reflection from the conical bottom. A succession of non-linear regimes is observed as forcing increases, starting with a clearly identifiable case of triadic resonance. Further, the frequency spectrum is progressively enriched by emergence of additional discrete components, gradually reaching the state of “overheated” wave turbulence with a significant continuous background of the frequency spectrum. Finally, a strong low-frequency component develops in the frequency spectrum, and the continuous background of the spectrum decreases dramatically. The low-frequency component corresponds to azimuthally periodic structures identified as Rossby waves. In the case of strong forcing, a long-term variability of zonal-flow velocity at the timescale of tens of forcing periods is observed, which is likely a consequence of the interaction of azimuthal structures corresponding to a rich wave number set.