Propagation Of Small Perturbations Research Articles

Kinetic Models for a Gas Filled Porous Matrix. WAVE PROPAGATION

The propagation of small perturbation in a gas filled porous matrix is investigated. The skeleton is supposed rigid and governed by the energy balance equation, where the heat exchanged between the two phases is taken into account. The Boltzmann equation is written for the gas where the integrals of the collisions between gas and solid particles are evaluated as those for the particles of a mixture. Different choices of the time and space scales lead to models equations which hold for different rarefaction regimes. The wave propagation characteristics are then dealt with in various situations.

Numerical—Experimental Investigation of the Elastic Deformation of a Polymeric Pipeline under Impact

The paper reports results of numerical—experimental investigation of the hydroelastic process in a polyimide pipeline filled with a fluid. The propagation of small perturbations in the fluid is considered in an acoustic approximation based on wave equations. The equations are integrated using the method of characteristics and a two–layer difference scheme. The elastic problem is solved by the finite element method and the Newmark difference β–method. The stress—strain state of the pipeline is defined by a superposition of fast rod modes of motion and slow shell modes of motion. Satisfactory agreement between calculated and experimental data is obtained.

Acoustic Properties of Continuous and Discrete Models in Fluid Dynamics

The article investigates the propagation of small perturbations in fluids whose dynamics is described by Euler and Navier–Stokes equations or by a quasi-fluid-dynamic system derived from the difference approximation of the Boltzmann equation. The problem of wave reflection from the artificial boundaries of the numerical region is solved using various boundary conditions. The analysis is repeated for difference approximations of fluid-dynamic equations. The procedure is tested for viscous subsonic flow past a plate.

Critical conditions for the group speed of propagation of internal gravity waves

Four experimentally observed unstable and resonant regimes of generation of internal waves by a moving or oscillating cylinder are considered. Two of them can be treated as a manifestation of the critical-layer effect, but for the group rather than for the phase speed of propagation of small perturbations, one regime can be regarded as a manifestation of the effect of compaction of the energy of two waves, and one more regime admits both of the indicated treatments.

Investigation of the structure of a weak shock wave and the propagation of small perturbations in gaseous mixtures using burnett's equations

Two problems are investigated: the structure of a weak shock wave and the propagation of perturbations of small amplitude in a binary mixture of monatomic gases. In the first problem, the contributions to the hydrodynamic quantities are obtained in the second approximation with respect to the wave intensity. In the second problem, acoustic, thermal and diffusion mode are considered and it is shown that there is negative dispersion of the acoustic mode.

Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 1. Flow in ducts

Based on linear potential theory, the general three-dimensional problem of steady supersonic flow inside quasi-cylindrical ducts is formulated as an initial-boundary-value problem for the wave equation, whose general solution arises as an infinite double series of the Fourier–Bessel type. For a broad class of solutions including the general axisymmetric case, it is shown that the presence of a discontinuity in wall slope leads to a periodic singularity pattern associated with non-uniform convergence of the corresponding series solutions, which thus are unsuitable for direct numerical computation. This practical difficulty is overcome by extending a classical analytical method, viz. Kummer's series transformation. A variety of elementary flow fields is presented, whose complex cellular structure can be qualitatively explained by asymptotic laws governing the propagation of small perturbations on characteristic surfaces.

Magnetogravitational Instability of Anisotropic Plasma with Finite Ion Larmor and Generalized Polytrope Law

The effect of finite ion Larmor radius corrections on the propagation of small perturbations through self gravitating, anisotropic system with generalized polytrope law is investigated. The polytrope laws are considered for the pressure components in parallel and perpendicular directions to the magnetic field. The polytrope model proposed by Abraham-Shranuer can be reduced to CGL equations with double adiabatic equations of state and MHD set of equations with isothermal equation of state. The effects of FLR and polytrope indices are discussed on the gravitational, firehose and mirror instability. The critical Jeans wave numbers are found to depend on polytropic indices and derived for CGL and MHD cases. The FLR corrections are found effective in shorter wave length region and produce stabilizing influence. The condition of mirror instability is uninfluenced by FLR but dependent on polytropic indices.

Gas solubility effects associated with the propagation of small perturbations in bubbly mixtures

The effect of gas solubility on the oscillation characteristics of bubbles in an acoustic field, the propagation and damping of perturbations in bubbly mixtures and, moreover, the stability of such media is analyzed.

Determination of particle charge and size from the propagation of ultrasound in suspensions

The propagation of small perturbations in raulticomponent disperse media consisting of an uncharged dispersion fluid, positive and negative ions and charged particles or droplets of another fluid is investigated. When weak waves pass through emulsions and suspensions, because of the difference in the velocities of the ions and charged particles a non-uniform distribution of electric potential develops in the medium [1–3]. Expressions relating the amplitude of the electric potential and the amplitude of the fluid velocity in the wave, the particle charge and the parameters characterizing the medium are derived. Relations are obtained for the phase shift between the values of the electric potential and the fluid velocity. It is proposed to use the expressions obtained, which describe the propagation of ultrasound, for the experimental determination of the particle charge and other parameters of the disperse medium, in particular, the particle size.

Gradient-drift instability in the mid-latitude ionospheric sporadic E layer

Beginning with quasihydrodynamic equations for electrons and ions, expressions are derived for the tensor components of the complex permittivity for a weakly inhomogeneous collisional plasma with current. These equations are used for considering gradient-drift instability in the mid-latitude ionospheric sporadic E layer, which leads to small-scale inhomogeneities oriented along the geomagnetic field. The role of rotational corrections is discussed, which are insignificant for instability with the propagation of small perturbations in a direction transverse to the geomagnetic field.

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

AbstractThe effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly‐trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.

On the hyperbolicity, stability and correctness of the cauchy problem for the system of equations of two-speed motion of two-phase media

Unsteady one-dimensional two-speed flows of a disperse stream are investigated and properties of the respective system of differential equations are investigated. Propagation of small perturbations is studied on the example of a mixture of barotropic gas with incompressible particles. It is pointed out that the nonhyperbolicity and instability of small perturbations peculiar to the system of differential equations are due to incomplete definition of interaction between phases and inside the dispersed phase, and to transport effects, and unrelated to acoustic perturbation propagation. Estimates are obtained for the characteristic times of instability development in streams of the drop and bubble structure.

Propagation of small perturbations in coaxial cylindrical shells with a liquid filler

Propagation of small perturbations in coaxial cylindrical shells with a liquid filler

Allowance for nonstationary heat and mass transfer in the propagation of small perturbations in a liquid with bubbles

The propagation of small perturbations in a liquid with vapor-gas bubbles is studied. Heat and mass transfer between the phases is taken into account on the basis of the exact equations of heat conduction and diffusion. The aim of the present investigation is to make more precise the results of an earlier paper [1] of the author and verify the applicability of using fixed coefficients of heat and mass transfer for nonstationary heat and mass transfer between a pulsating bubble and the liquid.

Propagation of small perturbations and the slip line in a plastic medium

A study is made of surfaces, describing the propagation of perturbations in a plastic medium, described by equations proposed in [i]. A review of work in which these processes are investigated on the basis of other models can be found in [2], A partial case of the equations discussed here was proposed in [3]. The surfaces of the propagation of the waves are described using an acoustical matrix, which determines three waves: quasilongitudinal and two quasitransverse. The acoustical matrix issymmetrical and positively defined; these properties are determined by the required correctness (hyperbolicity) of the system of differential equations under consideration. The communication [4] is devoted to a description of a class of hyperbolic systems similar to that considered here, It is found that the acoustical matrix corresponding to the system of differential equations under consideration here, for an elasticoplastic medium, can degenerate at several surfaces. This kind of degeneration corresponds to the reversion to zero of the velocity of one of the quasitransverse waves. In the plane case of a system of equations linearized in some manner, these degenerate surfaces coincide with the slip surfaces of the classical theory of plasticity.

Propagation of small perturbations in a liquid with bubbles

Propagation of small perturbations in a liquid with bubbles

On the propagation of small perturbations in a sonic stream and in a quiescent gas: PMM vol. 40, n≗1, 1976, pp. 74–78

Approximate equations are derived for small unsteady perturbations of a constant sonic stream and of quiescent gas. These equations, unlike the equation used for defining unstable transonic flows of gas, provide a correct definition of perturbation propagation from a point source in all directions [1].

Sound waves in a magnetizable medium

This article considers the propagation of small perturbations in a medium which can be inhomogeneously and isotropically magnetized under the action of an electromagnetic field. It is shown that in such a medium there is the possibility of sound waves of the same kind as in a medium with a constant magnetic susceptibility. However, the phase velocities of fast and slow magnetosonic waves can take on imaginary values so that, in strong magnetic fields, there may arise the phenomenon of instability. Investigations were made of the diagrams of the phase velocities for para- and diamagnetic substances for a medium with magnetic saturation; the case of an incompressible medium is discussed.

Asymptotic behaviour of the solution of the wave equation with a piecewise-discontinuous coefficient

THE PROPAGATION of small perturbations in an infinite medium consisting of two different media is studied. The half-space z> O consists of a medium in which the speed of propagation of sound equals A, and in the half-space z< O sound propagates with speed a, where A> a. It is shown that in such a medium Huygens principle is violated, namely: at any point of space some time after an instantaneously acting point source a leading wave front arrives, but the trailing edge of the wave is absent. The perturbation at a spatial point decays with time as t −3.

Waves in a plasma with Hall dispersion

In a magnetohydrodynamic approximation, an investigation is made of the propagation of waves in a plasma, whose characteristic frequency Ω is much less than the collision frequency of the electrons Τe−1. It is assumed that the magnetic field is sufficiently strong so that the equality ΩeΤe≫1 will be satisfied, where Ωe is the cyclotron frequency of the rotation of the electrons. With large magnetic Reynolds numbers (Rm≫1), which are characteristic for many astrophysical problems, this latter condition leads to a need to take account of dispersion effects connected with Hall currents, in the absence of Joule dissipation. The dispersion equation for the propagation of small perturbations is analyzed in the limiting cases of weak dispersion and of a wave propagating along the magnetic field. In the case of weak dispersion, an equation is derived for nonlinear waves. The solutions are found in the form of stationary solitons. The region of such solutions is analyzed. A typical example of a medium with Hall dispersion is an interplanetary plasma, in which the parameter ΩeΤe is generally great.