Yu. D. Chashechkin

Hydrodynamics of a sphere in a stratified fluid

The flow pattern around a sphere moving at constant velocity in a fluid with an exponential density distribution is investigated by optical methods. The thin density boundary layer forming the high-gradient envelope of the wake is distinguished as one of the elements of the structure. The symmetry properties of the flow are investigated. The limits of applicability of the traditional approximation of weak stratification in the problem of excitation of attached internal waves are noted.

Evolution of the Diffusion-Induced Flow Over a Sphere Submerged in a Continuously Stratified Fluid

The problem of the stabilization of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid is solved using both asymptotic and numerical methods. The analytical solution describes the structure of the main convective cells, including thin meridional jets flowing along the surface and plumes spreading from the flow convergence regions above the upper and lower poles of the sphere which gradually return the fluid particles to the neutral buoyancy horizon. The total width of the flows adjacent to the surface exceeds the thickness of the salinity deficit layer or the density boundary layer. The numerical solution of the complete problem in the nonlinear formulation describes the main convective cells and two systems of unsteady integral waves formed in the vicinity of the sphere poles. At large times, out of the entire system of internal waves only those nearest to the neighborhood of their horizon of formation remain clearly defined. The calculated flow patterns are in agreement with each other and the data of shadow visualization of the stratified fluid structure near a submerged obstacle at rest.

Vortex systems in the stratified wake of a sphere

The fine structure of the flow and the characteristics of the principal types of vortex structures in the wake of a sphere moving uniformly and horizontally in an exponentially stratified fluid have been experimentally investigated.

Hydrodynamics of a drying multicomponent liquid droplet

Using microscopy methods on light and dark fields, the flow patterns developing in drying droplets of pure transparent liquids, solutions, and suspensions of micro- and nanoparticles are investigated. The flow patterns inside drying droplets of real, colloid, and mixed solutions containing nanoand microparticles-markers are studied by means of video and photo registration of microscopic images. The analysis of particle displacements indicates the existence of a global convective flow which forms a toroidal circulation with an ascending jet at the droplet center. The typical types of the structures depending on the droplet composition are distinguished. It is shown that the intensity of the flow inside the droplet affects the surface convection. The effect of the hydrodynamic flow on the transport of a substance, forming the dry-deposit texture, is studied.

Classification of three-dimensional periodic fluid flows

Each physical factor—rotation, stratification, and compressibility of a fluid—is associated with a characteristic type of waves, which are usually analyzed independently [1]. However, elementary waves (acoustic, internal, gyroscopic) do not completely present the properties of periodic flows in the bulk of a real fluid, where all factors act simultaneously and hybrid waves with a complicated dispersion law exist. When studying waves, dissipation effects are considered as corrections ensuring flow attenuation [2]. However, in continua, dissipation factors determine the order of equations and the total number of elements of periodic flows, including waves and sets of boundary layers on rigid boundaries and free surfaces. The consistent inclusion of dissipation effects enables one to find self-consistent solutions of linearized problems of the generation of internal waves [3] without additional empirical parameters (force and mass sources [2]).

Linear theory of the propagation of internal wave beams in an arbitrarily stratified liquid

Beams of harmonic internal waves in a liquid with smoothly changing stratification are calculated in the Boussinesq approximation taking into account the effects of diffusion and viscosity. A procedure of local reduction of the beam in a medium with an arbitrary smooth stratification to the case of an exponentially stratified liquid is constructed. The coefficient of energy losses in the case of beam reflection on the critical level is calculated. Parameters of internal boundary flows with split scales of velocity and density that are formed by a wave beam on discontinuities of the buoyancy frequency and its higher derivatives are determined.

Transport of oil in a compound vortex

The oil redistribution pattern in a compound vortex created by a uniformly rotating disk located on the bottom of a cylindrical tank is investigated. At the initial instant, a round spot of a lightweight oil is deposited on the free surface of the liquid at the center of the tank. In the course of the formation of the compound vortex, the oil is partially entrained into the interior of the liquid and forms a body of revolution. On the free surface, the spot loses the round shape, spiral branches stretch out from the appeared protrusions and cusps. The orientation of these branches is opposite to the direction of fluid rotation in the tank. Geometrical parameters of the structures for different flow regimes are studied.

Marker transport in a composite vortex

Using a coloring method, the pattern of the transport of a compact spot of markers in a composite vortex created by a uniformly rotating disk, which is located on the bottom of a cylindrical tank, is investigated. The markers were formed by droplets of an aqueous solution of uranyl or ink, which fell down on the free surface of the fluid. In a quiescent fluid, the spot of the markers was transformed into a slowly sinking cascade of vortices. The markers introduced at the center of the cavity on the composite-vortex surface formed a spiral branch. For a non-central introduction of the markers, two spiral branches were formed, one growing in the direction of the fluid rotation and the other growing in the direction, opposite to the rotation. The markers penetrate into the interior of the composite vortex along isolated cylindrical surfaces. The geometrical parameters of the flow are presented.

Dynamics of Separation of a Single Drop in Air

The processes of formation of alcohol and water drops, as well as formation of small fragments—satellites, are traced using the high-speed filming. The trajectory of a water drop satellite is nonmonotonic, at first the satellite moves upward against the gravity force, reaches the oscillating residual fluid at the nozzle exit, and then starts to move down. From the satellite, a microdroplet is ejected, which bounces off the residual fluid at the nozzle, returns back to the satellite and merges. In the case of an alcohol drop, no accompanying microdroplet is formed, and the satellite follows a nearballistic trajectory.

Sound Generation as a Drop Falls on a Water Surface

Impact of a drop on a water surface is accompanied by a series of sound pulses propagating in air and underwater. Depending on the falling mode (drop size and initial velocity), pulses substantially differ in amplitude, duration, and modulation frequency. We study falling modes in which in addition to conventional sound packets—the shock pulse and single resonance sound packets—several packets are observed. Experiments were conducted with simultaneous recording of sound in air and underwater and were accompanied by synchronous video depiction of currents in the drop impact region. Comparison of videograms and phonograms demonstrate that the sources of sound packets are gas cavities of arbitrary shape detached from the underwater cavern under the action of large accelerations (several km/s2) during a sharp change in its surface area, which gradually achieve equilibrial elliptical and spherical shapes.