Vol 54, No 2 (2019)

The theory of perturbations is constructed for a combination of Couette and Poiseuille flows. Asymptotic analysis of four types of neutral (or nearly neutral) linear eigen oscillations is presented.

An analysis of the linear stability of convective flow in a channel of rectangular cross-section inclined to the horizon is presented. The behavior of three-dimensional monotonic disturbances is considered for different values of the channel width and fluid properties. The main flow is obtained in an analytical form. Two angles of inclination, at which the convective roll changes, are determined. A strong dependence of the smaller inclination angle on the channel width and its weak dependence on the medium characteristics and a weak dependence of the greater inclination angle on the channel width are established.

The equations for three nonlinear approximations of flexural-gravity vibrations of a longitudinally compressed elastic plate which take into account the nonlinearity of acceleration of vertical plate displacements are obtained using the method of multiple scales. The ice plate unbounded in horizontal directions floats on the surface of a homogeneous ideal fluid. Asymptotic expansions up to the third order of smallness are constructed on the basis of the obtained equations for the plate-fluid surface elevation and the velocity potential of the liquid particles formed in the nonlinear interaction of two harmonics of progressive periodic surface waves. The amplitude-phase characteristics of the formed elevation of the fluid surface (bending of the plate) are analyzed as functions of the basin depth, the parameters of ice plate and interacting harmonics, and the nonlinearity of acceleration of vertical ice displacements.

Disturbance evolution in developed turbulent flows in a plane channel is numerically investigated at the Reynolds numbers up to Re_τ = 586. Steady turbulent flows calculated on the basis of the solution of the incompressible Navier—Stokes equations are then used as the baseline flows in studying the disturbance development process. The values of the highest Lyapunov exponent (HLE) λ₁ are found and the instantaneous and statistical properties of the corresponding leading Lyapunov vector (LLV) are determined. Under arbitrary initial conditions the regime of the exponential disturbance growth ~ exp(λ₁t) is reached for a time Δt⁺ < 50. It is found that the HLE value increases with the Reynolds number from λ₁⁺ ≈ 0.021 at Re_τ = 180 to λ₁⁺ ≈ 0.026 at Re_τ = 586. The LLV exhibits itself in the form of time- and space-localized spots of highly intense pulsations, concentrated in the buffer layer region. The distributions of the r.m.s. intensities of the velocity and vorticity pulsations in the LLV are qualitatively similar with the corresponding distributions in the main flow with near-wall streaks artificially extracted from it. The difference is a large disturbance concentration in the vicinity of the buffer layer, y⁺ = 10–30, and a relatively high (about 80% higher) vorticity pulsations amplitude. Basing upon the energy spectra of the velocity and vorticity pulsations we determined the integral spatial scales of the structures in the LLV field. It is found that the LLV structures are on average half as wide and long as the corresponding structures in the main flow. The contributions of all the terms included in the expression for the production of the kinetic energy of disturbances are determined. It is shown that the process of disturbance development is essentially controlled by the main flow inhomogeneity and the occurrence of transverse motion in it. Neglecting these factors leads to a considerable underestimation of the disturbance growth rate. Contrariwise, the presence of near-wall streaks in the main flow does not play a considerable role in the LLV disturbance development. The artificial extraction of the streaks from the main flow field does not change the nature of disturbance growth.

Asymptotic methods are applied to study a plane turbulent jet of a viscous incompressible fluid flowing out through a narrow slot into a space filled with a fluid. The complete Navier—Stokes equations are considered. The characteristic Reynolds number is assumed to be large, while the jet thickness is small. In analyzing the problem the method of many scales is used, which makes it possible to determine and investigate a steady secondary flow within the turbulent jet. The secondary steady solutions are analytically obtained for the normal and longitudinal velocity components and the pressure. It is shown that the self-induced fluid outflow of the jet core toward the jet periphery is the main secondary flow ensuring the supply of the kinetic energy from a maximum velocity zone into the turbulence production zone. The solutions obtained are in good agreement with the available experimental data.

The results of the experimental study of downward bubbly flow in a vertical pipe of 20 mm i.d. are given. Water-glycerin solution was used as the test liquid. The experiments were carried out over the Reynolds number range from 1000 to 1500. The local flow parameters (local void fraction, liquid velocity, velocity fluctuations) were measured using the electrodiffusional technique. The experiments demonstrated the strong effect of the gas phase on the flow structure. The effect is manifested in increase in the wall shear stress and flattening the liquid velocity profile in the central part of the pipe. A significant deviation from the single phase flow takes place even at low gas flow rate ratios.

—A new explicit form of the Navier—Stokes equations is obtained by means of the Reynoldsaveraging of these equations within the framework of the generally accepted model of spectrum-averaged fluctuations. The equations thus obtained contain some new terms caused by density fluctuations, while certain their terms included earlier on the intuitive level are now physically validated. The equations of the k—ω model are derived using the method of moments. A new equation for the vortex fluctuations, written earlier on the intuitive and analogue level, is obtained from the general momentum equation.