Vol 61, No 9 (2016)

The calculated dependences in elementary functions for determining the modular elliptic function λ(τ) =λ₁ + iλ₂ obtained on the basis of consecutive (six) conformal mappings of a curvilinear triangle to a complex half-plane are presented. Comparison of the values of λ(τ) from the proposed dependences with the results of the Hamel–Gunter exact analytical solution for the boundary contour of the curvilinear triangle, i.e., the real axis of the complex half-plane, gives a very close coincidence (with the largest error of ≤1%). The use of the complex values of the function λ(τ) for the entire internal region of the curvilinear triangle makes it possible to solve one of the most difficult problems of the theory of filtration (filtration through a rectangular dam) in the direct formulation and, for the first time, to construct the pattern of an equal filtration-rate field (the family of isotaches) over the entire internal region of the dam. In this case, the boundary values of filtration rates for special cases (along the sides and along the base of the dam) completely coincide with the results of the Masket exact analytical calculations.

This study is devoted to experimental investigation of hydrogen-combustion modes and the structure of a diffusion flame formed at a high-velocity efflux of hydrogen in air through round apertures of various diameters. The efflux-velocity range of the hydrogen jet and the diameters of nozzle apertures at which the flame is divided in two zones with laminar and turbulent flow are found. The zone with the laminar flow is a stabilizer of combustion of the flame as a whole, and in the zone with the turbulent flow the intense mixing of fuel with an oxidizer takes place. Combustion in these two zones can occur independently from each other, but the steadiest mode is observed only at the existence of the flame in the laminar-flow zone. The knowledge obtained makes it possible to understand more deeply the features of modes of microjet combustion of hydrogen promising for various combustion devices.

On the basis of Strutt’s approach, the problem of eigenoscillations of a gas in a cylindrical cavity with an internal membrane in the presence of a coaxial circular aperture in it (A.N. Fock’s problem) is analyzed. By an adequate numerical−analytical procedure, a high-precision solution is constructed to a boundary value problem for the eigenfrequencies and forms of lower order oscillation modes for various relative values of the aperture radius. A (qualitative and quantitative) correspondence is established to the results known in acoustics as applied to the concept of the “associated mass of an aperture.” New physical effects are obtained on the dependence of the frequencies and forms of long-wavelength oscillations of a gas on the geometric parameters of the system.

A nonconservative force field in the dynamics of a multidimensional solid is constructed according to the results from the dynamics of real solids occurring in the force field of the action of the medium. In this case, it becomes possible to generalize the equations of motion of a multidimensional solid in a similarly constructed field of forces and to obtain a complete list of, generally speaking, transcendental first integrals expressed through a finite combination of elementary functions. In the study, the integrability in elementary functions is shown for the simultaneous equations of motion of a dynamically symmetric fixed multidimensional solid under the action of a nonconservative pair of forces in the presence of the linear damping moment (the additional dependence of the force field on the tensor of angular velocity of the solid).

The nonlinear dynamics of multisoliton, differently polar fields is investigated within the framework of the modified Korteweg–de Vries equation. It is shown that the occurrence of abnormally large waves (freak waves) is possible in similar fields, which is associated with the modulation instability of cnoidal waves. The statistical moments of wave fields are investigated. It is shown that an increase in the coefficient of excess due to the interaction of solitons correlates with an increase in the probability of occurrence of freak waves. It is shown that the nonlinear interaction of differently polar solitons results in variation of the distribution functions of peak characteristics: the fraction of low-amplitude waves decreases, while that of the waves with large amplitudes increases. The dependence of the intensity of the density of the characteristics of the soliton gas is shown.

The flow of water mist in a narrow duct has been studied experimentally. The profile of the velocity of drops has been measured, and the viscosity of the mist has been calculated using the Navier–Stokes equation. It has been found that at low gradients of the rate of shear the viscosity of the mist can exceed that of clean air by tens and even hundreds of times. The electric charge of the drops has been measured. It has been found that the viscosity of the mist differs from that of clean air at gradients of the rate of shear that are less than the frequency of the establishment of electric equilibrium between the drops. A comparative analysis of the viscosities of the mist and a drop cluster has been carried out, and the dependence of the viscosity of the water aerosol on the radius and the charge of the drops has been predicted. The possible role of aerosols that contain submicron drops in the known “clear air turbulence” problem has been shown.

In this study, the method of molecular dynamics is used for investigation of the processes of energy losses of solitary protons and antiprotons in an electron gas in dependence on the kinetic energy of the charged particles and the value of the magnetic-field induction.

The processes of sorption on fibrous materials in the open elliptic cell filled with a two-layer oil−water liquid at rest are investigated experimentally. When the sorption efficiency dependent on the type of material proves to be reasonably high, large-scale flows are formed in the liquid. In this case, the uniformity of distribution of oil is violated and the free surface of the water is partially restored. The trajectories of motion of individual oil droplets on a released water surface are tracked, and the transfer rates are calculated in various phases of the process.