Vol 51, No 3 (2016)

The paper is devoted to the mathematical modeling of naturally occurring downslope flows, such as snow avalanches, mudflows, and rapid landslides. The medium in motion is modeled as a non- Newtonian fluid, the non-Newtonian fluids of different types corresponding to different-in-nature flows. It is taken into account that the downslope flows capture the slope material and entrain it into the motion. The flow is assumed to be turbulent and the Lushchik–Pavel’ev–Yakubenko three-equation turbulence model is used. It is so generalized that it allows for flow unsteadiness, complicated rheological properties, the presence of a free boundary, and the mass transfer at the lower flow boundary. The effect of the bottom material capture and the nonlinear rheological properties of the medium in motion on the flow dynamics is numerically investigated.

It is shown that in the general case it is not possible to propose the Lagrangian viewpoint on the vorticity evolution, which would be unique for the entire flow, using the existing analogs of the Helmholtz theorems. This is related to the fact that, as distinct from the Helmholtz theorem oneself, these analogs are valid only for nonzero vorticity zones. New analogs of the Helmholtz theorems are proposed for the general case of flows (from incompressible fluid to viscous gas). They describe the vorticity evolution at all the points including the points of nonzero vorticity.

The influence of the channel diameter and length of the hydrodynamic oscillation generator on gas bubble dimensions in the case of wave dispersion of a gas in a liquid is experimentally investigated. The technique of measuring the bubble diameters based upon the computer analysis of the gas-liquid jet photos is presented. It is shown that on the gas flow rate range from 0.5 to 32 dm³/min the mean diameter of the gas bubbles produced by wave dispersers in water is estimated by an interval from 0.45 to 0.75 mm in optimum performance regimes.

The admitted region of five joint irreducible invariants of the strain and rotation rate tensors calculated as the traces of the products of these tensors is determined.

Estimates are presented for the effect of susceptibility of the inner surface of the blood vessel wall to shear stress on changes in diameter and volume blood flow rate. The model of thin-walled vessel with radius controlled by two parameters is used. The effect of rheological factors, hematocrit, and oxygen content in blood on the value of vessel response to a change in shear stress is considered. The estimates showed that the contribution of the vessel response in question to a change in blood volume flow rate amounts tens per cent. The influence of rheological (Fahraeus and Fahraeus-Lindqvist) effects on flow rate lies within several per cent. The role of the vessel response considered increases with anaemia: at low hematocrit its contribution to increase in flow rate exceeds 10%. Variation of oxygen concentration within the normal range has almost no effect on the hemodynamic parameters. With hypoxia, on the contrary, the participation of this response on changes in flow rate weakens: in severe hypoxia decrease in blood flow rate owing to a change in oxygen concentration equals approximately 9%.

The conditions of suppression of a combustion wave propagating along a homogeneous porous layer of organic combustible materials are investigated basing upon a physico-mathematical model. The dependence of free water effervescence intensity on the water volume fraction and the medium temperature is presented. A water supply source in motion is employed to suppress the combustion wave. It is shown that an increase in the mass water flow rate results in a considerable increase in the maximum velocity of the source motion, at which the combustion wave can be suppressed. This is due to a reduction in the loss of the water evaporating above the burning zone. The effect of the water supply point displacement on the efficiency of combustion wave suppression is analyzed.

The impact of the interplanetary magnetic field on transformation and disintegration of the Earth’s bow shock into a system of magnetohydrodynamic (MHD) shock waves, rotational discontinuities and rarefaction waves under the action of abrupt variations in the solar wind dynamic pressure is simulated in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model using the solution of the MHD Riemann problem of breakdown of an arbitrary discontinuity. This discontinuity arises when a contact discontinuity, on which the solar wind density increases or decreases suddenly and which travels together with the solar wind, impinges on the Earth’s bow shock and propagates along its surface. The interaction pattern is constructed in the quasisteady- state formulation as a mosaic of exact solutions obtained on computer using an original MHD Riemann solver. The wave flow patterns are found for all elements of the surface of the bow shock as functions of their latitude and longitude for various jumps in the density on the contact discontinuity and characteristics parameters of the solar wind and interplanetary magnetic field at the Earth’s orbit. It is found that when the solar wind dynamic pressure increases, a fast MHD shock wave, that first penetrates into the magnetosheath, is always formed. When the solar wind dynamic pressure decreases, the influence of the interplanetary magnetic field can lead to the development of the leading fast MHD shock wave in certain zones on the surface of the Earth’s bow shock. The solution obtained can be used to interpret measurements on spacecraft in the solar wind at the libration point and in the neighborhood of the Earth’s magnetosphere.

The dispersion relation is derived for a spheroidal charged drop oscillating in a uniform electrostatic field and radiating electromagnetic waves in the first and second orders with respect to the dimensionless oscillation amplitude and the steady-state deformation, respectively. For an individual drop and a model cloud the intensity of the electromagnetic radiation and the frequency bandwidth are estimated as functions of the drop dimensions and charge and the external electric field strength.