Influence of a magnetic field on the thermoacoustic stability of a high-temperature heat releasing gas

The conditions of thermoacoustic stability are found for a high-temperature electrically conducting gas with internal heat release in a constant magnetic field which transforms acoustic waves into fast and slow magnetoacoustic oscillations, and also introduces Joule dissipation. The investigation is by means of the energy balance method, and also by direct solution of the equations for small perturbations in the special case of wavelengths of the acoustic oscillations that are short compared with the inhomogeneity scales in the region of heat release. The limits of stability with respect to fast and slow magnetoacoustic oscillations are found.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 102–107, July–August, 1979.     

Simple waves in a plasma with anisotropic pressure

Fast and slow simple waves are studied in the framework of the anisotropic magnetohydrodynamics of Chew, Goldberger, and Low [1]. Baranov [2] has constructed fields of integral curves for fast and slow waves and in two special cases has shown that such waves break in the compression section. The possibility of breaking of a slow wave in a rarefaction section was noted by Akhiezer et al. [3]. However, their general relations in simple waves [3] have been shown to be incorrect [2, 4]. In the present paper the nature of the variation of the longitudinal and transverse plasma pressures is determined, and the problem of the breaking of fast and slow waves is completely solved. Conditions under which a slow wave breaks in a rarefaction section are found. A fast wave always breaks in a rarefaction section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 181–183, July–August, 1988.     

Nonlinear magnetoacoustic waves in a conducting liquid containing gas bubbles

The propagation of long waves in an incompressible conducting liquid saturated with nonconducting gas bubbles is considered on the basis of the equations of magnetohydrodynamics of a homogeneous gas-liquid medium. It is shown that the propagation of weakly nonlinear MHD waves in such a medium is described by the Burgers-Korteweg-de Vries (BKdV) equation. The influence of MHD interaction effects on the parameters of fast and slow weak magnetoacoustic shock waves is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 142–147, March–April, 1991.     

Propagation of modulated nonlinear waves in a relaxing gas-liquid mixture

The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980.     

Internal waves in a two-layer electrically conducting fluid in the presence of a magnetic field

The propagation of linear and nonlinear internal waves along the interface between two weakly conducting media differing in density and electrical conductivity is investigated and the influence of MHD interaction effects on their characteristics is analyzed. It is shown that in this system the waves propagate with dispersion and dissipation, and for harmonic waves of infinitesimal amplitude there exists a range of wave numbers on which propagating modes do not exist. For waves of finite amplitude a nonlinear Schrödinger equation with a dissipative perturbation is obtained and its asymptotic solution is found. It is established that the presence of electrical conductivity and an applied magnetic field leads to a decrease in the amplitude and the frequency of the envelope of the wave train.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–108, September–October, 1990.     

Structure and stability of quasiparallel small-amplitude magnetohydrodynamic shocks

The structure and stability of quasiparallel magnetohydrodynamic shock waves of small but finite amplitude are investigated. Only those waves whose propagation velocities are close to the Alfvén velocity are considered, i.e., fast shock waves in a medium in which the Alfvén velocity is greater than the speed of sound and slow shock waves in a medium in which the Alfvén velocity is less than the speed of sound and, moreover, intermediate (nonevolutionary) shock waves.In conclusion, the author wishes to thank A. A. Barmin for discussing his results and offering useful comments.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–160, July–August, 1989.     

Modeling the interaction of solitary waves in magnetic tubes

The Cauchy problems of the propagation of a single wave and the interaction of two solitary waves of different amplitude are solved numerically for the case of slow symmetric surface waves in a magnetic tube. It is found that the solitary waves interact in the same way as the solitons of the known soliton equations such as the Korteweg-de Vries and Benjamin-Ono equations, i.e., preserve their shape after interacting. The way in which the solitons decrease at infinity is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–186, March–April, 1989.The author wishes to thank M. S. Ruderman for formulating the problem and V. B. Baranov for his interest in the work.     

Reflection of magnetoacoustic waves

The problem of the reflection of magnetoacoustic waves at the boundary dividing an elastic medium from a fluid medium with infinite conductivity in the presence of an arbitrary constant magnetic field was treated in [1]. In writing down the boundary conditions the continuity of the tangential component of the magnetic field was used. This condition is valid when the conductivity of the medium is finite but not when the conductivity is infinite. In this connection a problem similar to that in [1] is solved, without employing this particular boundary condition. The amplitude conversion coefficients found for the limiting cases of weak and strong magnetic fields coincide with the respective coefficients given in [2,3] for media with a finite conductivity, if we allow the conductivity in the latter expressions to become infinite.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, January–February, pp. 56–61, 1970.     

Destabilisation of flows with free surface by high-frequency waves

When wave packets of small but finite amplitude propagate in liquids and gases average fields (average flows, average displacements of the interfaces between different liquids, etc.) arise because of the nonlinearity of the media [l, 2], their amplitude being proportional to the square of the wave amplitude. The present paper is an investigation of such fields that arise when a packet of surface waves propagates on a horizontally inhomogeneous flow. It is shown that the average flows induced by the waves can strongly destabilize or stabilize the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–163, May–June, 1983.     

Regular reflection of a magnetohydrodynamic shock wave from a conducting wall

In two-dimensional supersonic gasdynamics, one of the classical steady-state problems, which include shock waves and other discontinuities, is the problem concerning the oblique reflection of a shock wave from a plane wall. It is well known [1–3] that two types of reflection are possible: regular and Mach. The problem concerning the regular reflection of a magnetohydrodynamic shock wave from an infinitely conducting plane wall is considered here within the scope of ideal magnetohydrodynamics [4]. It is supposed that the magnetic field, normal to the wall, is not equal to zero. The solution of the problem is constructed for incident waves of different types (fast and slow). It is found that, depending on the initial data, the solution can have a qualitatively different nature. In contrast from gasdynamics, the incident wave is reflected in the form of two waves, which can be centered rarefaction waves. A similar problem for the special case of the magnetic field parallel to the flow was considered earlier in [5, 6]. The normal component of the magnetic field at the wall was equated to zero, the solution was constructed only for the case of incidence of a fast shock wave, and the flow pattern is similar in form to that of gasdynamics. The solution of the problem concerning the reflection of a shock wave constructed in this paper is necessary for the interpretation of experiments in shock tubes [7–10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 102–109, May–June, 1977.The author thanks A. A. Barmin, A. G. Kulikovskii, and G. A. Lyubimov for useful discussion of the results obtained.     

Three-dimensional Gouyon waves

Three-dimensional steady-state periodic waves in deep water with weak (of order of the wave amplitude) vorticity are considered. The solution describing the wave properties is constructed by the perturbation theory method in modified Lagrangian coordinates. The wave structure and dispersion properties are found correct to the square of the wave amplitude.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–130, July–August, 1996.     

Propagation of magnetohydrodynamic shock waves in a medium of decreasing density

It is explained under what condition instability develops in the wave front when a shock wave travels in a medium whose density is decreasing. It is shown that under laboratory conditions the buildup of such an instability may be suppressed by a diffusion of wave front segments into the walls of the system. Such an instability can occur, for example, in certain astrophysical bodies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 24–27, May–June, 1972.     

Structure of detonation waves,ionizing a gas,in the presence of an electromagnetic field. Cases of low magnetic viscosity

If behind a detonation wave, ionizing a gas, the magnetic Reynolds number is much greater than unity, then in order to describe such waves (just as for ionizing shock waves) complementary relations [1, 2] are necessary. These complementary relations are not the consequence of the basic integral laws, but can be found from a consideration of the wave structure. In [2], the structure of detonation waves, ionizing a gas, was investigated in an oblique magnetic field. It was supposed that the flow in a layer representing the structure is determined by the finite rate of the chemical reaction and the finite electrical conductivity. In the case when the characteristic length of the chemical reaction is much less than the characteristic dissipation length of the magnetic field, the complementary relations which ensure the existence of the structure are obtained in explicit form. The case is considered below when the characteristic length of the chemical reaction is much greater than the dissipation length of the magnetic field. In this case, the complementary relations are obtained in the explicit form.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 95–101, May–June, 1976.     

Shock wave intersection in magnetohydrodynamics

The flow formed in the neighborhood of the discontinuity intersection point when shock waves collide at a nonzero angle is studied. The investigation can be directly applied to problems of shock wave interaction in the interplanetary plasma [9–12]. In magnetohydrodynamics the nature of the flow and its investigation are much more complex than in gas dynamics because of the greater number of possible waves and governing parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 132–143, May–June, 1991.     

Modeling of long nonlinear waves on the interface in a horizontal two-layer viscous channel flow

The dynamics of two-dimensional waves of small but finite amplitude are theoretically studied for the case of a two-layer system bounded by a horizontal top and bottom. It is shown that for relatively large steady-state flow velocities and at certain fluid depth ratios the vertical velocity profile is nonlinear. An evolutionary equation governing the fluid interface disturbances and allowing for the long-wave contributions of the layer inertia and surface tension, the weak nonlinearity of the waves, and the unsteady friction on all the boundaries of the system is derived. Steady-state solutions of the cnoidal and solitary wave type for the disturbed flow are determined without regard for dissipation losses. It is found that the magnitude and the direction of the flow can alter not only the lengths of the waves but also their polarity.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 143–158. Original Russian Text Copyright © 2005 by Arkhipov and Khabakhpashev.     

Solitary wave trains in a cold plasma

The existence of traveling solitary waves, the products of modulation instability in a cold quasi-neutral plasma, is considered. Solitary waves of this type (solitary wave trains) are formed as a result of bifurcation from a nonzero wave number of the linear wave spectrum. It is shown that the complete system of equations describing the wave process in a cold plasma has solutions of the solitary wave train type, at least when the undisturbed magnetic field is perpendicular to the wave front. Sufficient conditions of existence of solitary wave trains in weakly dispersive media are also formulated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–161, September–October, 1996.     

Spatially polarized structure of detonation waves ionizing a gas

Additional relationships must be used [1–3], in addition to those following from the main integral laws, in describing ionizing detonation waves, exactly as for ionizing shocks. These additional relationships are obtained from the requirement for the existence of wave structure. The structure of detonation waves ionizing a gas in an oblique magnetic field was investigated in [1, 2]. The case of a plane-polarized structure was considered, when the velocity vector and the magnetic field lie in a plane passing through the normal to the front. The structure of ionizing detonation waves is studied in this paper for the case when the wave is spatially polarized and both transverse magnetic field components vary in the structure. It is considered that the magnetic viscosity and a quantity reciprocal to the chemical reaction rate are much greater than the remaining dissipative coefficients in the layer representing the structure. Conditions for the existence of such a spatial structure are clarified. Plane-polarized ionizing detonation waves whose structure is not planar are also considered. When the characteristic length of magnetic field dissipation is much greater or much less than the characteristic length of the chemical reaction, the additional relationships assuring the existence of structure are written down explicitly or are investigated qualitatively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 166–169, November–December, 1976.     

Phase and signal velocities of waves in dissipative media. Special relativistic theory

The signal and phase velocities (and their frequency dependence) for all possible plane waves in a relativistic gas (of molecules or photons) with dissipation have been determined from the linearized relativistic 13-moment theory. For each direction in 3-space, and for each frequency, one transverse and two longitudinal waves were found. (In addition, some waves are associated with the mass flow and have the mass flow speed.) Of the longitudinal waves, the fast one is a pressure (sound) wave. It is accompanied by a slow longitudinal thermal dissipation wave and a transverse viscous dissipation wave. The pressure wave has a velocity larger than the Laplace adiabatic speed of sound, while the two dissipation waves have a velocity less than the Laplace speed. All the speeds have been expressed explicitly in terms of quantities associated with the state of equilibrium which existed before passage of the wave. It has also been shown that in the ultrarelativistic limit (extremely high temperatures) all signal speeds remain less than the speed of light in vacuo.The major part of this article was presented at the Seminar on Natural Philosophy at The Johns Hopkins University, Baltimore, on November 24, 1971.     

Diffraction of acoustic waves on the leading edge of a flat plate in a supersonic flow

A scheme is proposed for calculating the intensity of the acoustic wave field generated by diffraction of a beam of acoustic waves on a sharp leading edge of a flat plate in a supersonic flow. This wave field is shown to be a functional of the mass-flow amplitude distribution in the acoustic field at the level of the plate surface upstream of the latter. This distribution can be found on the basis of measurements. The discontinuity of the normal-to-plate component of the velocity perturbation on the plate edge plays an important role in determining mass-flow fluctuations along the plate. At large distances from the leading edge of the plate, where the diffraction wave on the boundary-layer edge degenerates into longitudinal acoustic waves, the amplitude of mass-flow fluctuations decreases with increasing distance from the leading edge and depends on wave orientation.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 64–70, March–April, 2005.     

Fluid–structure interaction in water-filled thin pipes of anisotropic composite materials

The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small.