Journal of Applied Mechanics and Technical Physics最新文献

This paper describes the propagation of vertically polarized surface acoustic waves at a boundary between porous media saturated with methane hydrate and ice (water), as well as horizontally polarized waves at an interface between a hydrate-saturated porous medium and a water-saturated porous medium. A mathematical model is developed for flat harmonic waves. The porous medium saturated with gas hydrate or ice (water) is assumed to be an elastic isotropic body. The mathematical model includes wave equations for scalar and vector potentials of wave velocities with account for displacement and stress vector components of the medium particles. Conditions for the continuity of displacements and stresses in porous media at the interface are given. The obtained dispersion equations are analyzed, and the results are compared with experimental data. It is revealed that the penetration depth of a transverse wave into hydrate-saturated sand is greater than the penetration depth of a longitudinal wave. It is proposed to determine the presence of hydrate-saturated sand at positive temperatures of bottom sediments by the penetration depth and the variation of the zero mode velocity of the horizontally polarized wave.

This paper presents the study of a viscous fluid flow between two wavy horizontal surfaces unbounded longitudinally and transversely. Full Navier–Stokes equations are applied to describe the linear stability of such a flow with respect to various three-dimensional perturbations. Two types of wall waviness are studied: longitudinal and transverse periodic corrugation. The first stage is comprised of obtaining the main solution and linearizing initial equations in the vicinity of this solution. The second stage is comprised of solving the generalized problem of determining eigenvalues and analysing the entire possible spectrum of perturbations. The varied parameters are the Reynolds number, as well as corrugation amplitude, period, and shape. Velocity and pressure field perturbations are generally characterized by two wave numbers, which are additional parameters. The influence of the parameters and shape of the wall waviness on the region where the laminar-turbulent transition begins is investigated.

This paper presents a mathematical model of a medium consisting of active particles capable of adjusting their movement depending on so-called signals or stimuli. Such models are used, e.g., to study the growth of living tissues, colonies of microorganisms and more highly organized populations. The interaction between particles of two species, one of which (predator) pursues the other (prey) is investigated. Predator movement is described by the Cattaneo heat equation, and the prey is only capable of diffusing. Due to the hyperbolicity of the Cattaneo model, the presence of long-lived short-wave patterns can be expected in the case of sufficiently low diffusion of preys. However, the mechanism of instability and failure of such patterns is found. Explicit relations for the predator transport coefficients are derived that block this mechanism.

The existence of a classical solution was established for a one-phase radial viscous fingering problem in a Hele-Shaw cell under surface tension (original problem) by means of parabolic regularization for a certain subsequence ({varepsilon_n}_{n in mathbb{N}}), (varepsilon_n>0). In this paper, we prove the uniqueness of the classical solution to the original problem with the use of parabolic regularization for the full sequence of the parameter ({varepsilon}), (varepsilon>0).

The role of the hidden integral of motion in the correct description of the far field of velocities and pressures for non-self-similar submerged jets of an incompressible viscous fluid with a source of motion of non-zero characteristic size is discussed based on the full Navier–Stokes equations. It is shown that the emergence of the hidden conservation integral is due to the fact that for real spatially extended sources of jet flow, the coordinates of the effective point source of momentum may not coincide with the coordinates of the effective point source of mass. Using special functions, an exact analytical solution is obtained for all terms of the asymptotic expansion of the far field of a non-self-similar submerged jet which is described by all integrals of motion: conservation of total momentum flux, conservation of total angular momentum flux, conservation of total mass flux, and the additional hidden conservation integral associated with the conservation of total angular momentum flux. It is shown that the hidden integral was actually first obtained by Loitsyanskii in studying a non-self-similar solution for a submerged jets using the boundary layer approximation, but it was mistakenly interpreted as the integral of conservation of mass flux from the jet source. Based on the obtained exact solution, the velocity and pressure fields at different Reynolds numbers and different values of the hidden integral are calculated for a model of jet flow issuing from a circular tube of finite size. The influence of the hidden integral of motion on the flow pattern is analyzed.

Linear model equations in partial derivatives with two independent variables are considered. The highest operator symmetries and general solutions for a series of hyperbolic equations are found. Equivalence transformations are constructed for some equations.

This paper presents the study of asymptotic behavior of solutions of initial-boundary-value problems arising in simulation of motion of incompressible viscoelastic fluids in the case of various combinations of small relaxation parameters (constant-strain stress relaxation time and constant-stress strain relaxation time), one of which can be equal to zero.

The characteristics of joint flows of evaporating liquid and a laminar gas stream in a plane horizontal channel are studied based on an exact partially invariant solution of thermosolutal convection equations. The influence of the liquid layer thickness and the conditions for the temperature function on the upper wall of the channel on the rate of evaporation caused by gas pumping is investigated. The exact solution is verified by comparison with experimental data. The linear stability of the exact solutions is studied. It is established that regardless of the type of boundary thermal regime, oscillatory instability in the form of cellular convection always appears in the system. Thermal insulation of the upper wall does not lead to a change in the structure of the most dangerous perturbations, slightly destabilizes the flow in the case of long-wave perturbations, and has a stabilizing effect in the case of short-wave perturbations.

Rotational sedimentation of neutrally buoyant particles in suspensions in the case of two-dimensional circular flows between two cylinders is studied by mathematical simulation. Particle separation in the absence of gravity is caused by rotation of the inner cylinder. It is revealed that sedimentation depends on particle rotation. Within the framework of the Cosserat continuum, the suspension is considered as a micropolar fluid. The effect of the eccentricity of noncoaxial cylinders on the sedimentation front is investigated.

Unsteady one-dimensional shear flows of a viscoelastic fluid are considered. A general approach is formulated for fluids with several relaxation times, which allows the known models of viscoelastic flows to be presented as evolutionary systems of first-order equations. Conditions of hyperbolicity of flow classes considered are found for the Johnson–Segalman, Giesekus, and Rolie-Poly models. The equations of motion of the viscoelastic fluid are presented in the form of a full nonlinear system of conservation laws. A method of calculating unsteady discontinuous flows within the framework of the models under consideration is proposed. The class of unsteady Couette flows in the gap between the cylinders used in rheological tests is studied numerically. The process of shear banding and its influence on the structure of steady flows are investigated. The numerical results obtained are compared with experimental data.