Electrical breakdown in air in a transverse magnetic field

The electrical breakdown of gases in a transverse magnetic field is discussed in references [1–16]. Attention has mainly been concentrated on the case of coaxial electrode geometry [1–10]. The existing experimental data on breakdown between plane-parallel electrodes [11–14] relate to a narrow range of variation of the parameters characterizing breakdown (P, d, H, U). The author has made an experimental study of the process of electrical breakdown in air in a transverse magnetic field between plane-parallel electrodes of finite size in the pressure interval from 650 to 5·10^–3 mm Hg at gap lengths of from 1 to 140 mm and magnetic inductions from 0 to 10 600 G.     

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.     

Magnetohydrodynamic flow past a drop at low Reynolds and Hartmann numbers

The flow of an electrically conductive liquid past a solid spherical particle at low Reynolds and Hartmann numbers in longitudinal and transverse magnetic fields was first investigated in [1,2]. The effect of a weak magnetic field on the strength of the resistance of a conductive drop in a dielectric medium was considered in [3]. In the present paper we consider the motion of a conductive liquid drop in an electrically conductive medium and calculate the strength of the resistance in the Stokes approximation for an arbitrary orientation of the uniform magnetic field and in the Oseen approximation for the case in which the direction of the magnetic field coincides with the direction of the oncoming stream. As in the previous studies, we do not consider the possibility of the formation of a double layer on the interface between the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 19–25, November–December, 1978.The authors are grateful to G. I. Petrov and the participants in the seminar they conducted for their comments on the work.     

Investigation of the properties of a shock wave arising in a supersonic flow of plasma,passing through a transverse magnetic field

In a flow of plasma, set up by an ionizing shock wave and moving through a transverse magnetic field, under definite conditions there arises a gasdynamic shock wave. The appearance of such shock waves has been observed in experimental [1–4] and theoretical [5–7] work, where an investigation was made of the interaction between a plasma and electrical and magnetic fields. The aim of the present work was a determination of the effect of the intensity of the interaction between the plasma and the magnetic field on the velocity of the motion of this shock wave. The investigation was carried out in a magnetohydrogasdynamic unit, described in [8]. The process was recorded by the Töpler method (IAB-451 instrument) through a slit along the axis of the channel, on a film moving in a direction perpendicular to the slit. The calculation of the flow is based on the one-dimensional unsteady-state equations of magnetic gasdynamics. Using a model of the process described in [9], calculations were made for conditions close to those realized experimentally. In addition, a simplified calculation is made of the velocity of the motion of the above shock wave, under the assumption that its front moves at a constant velocity ahead of the region of interaction, while in the region of interaction itself the flow is steady-state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–91, January–February, 1975.     

Convection in an oscillating force field and microgravity

Convective flows in a plane layer of viscous fluid in the presence of an oscillating external force are investigated numerically [1 – 8]. The layer is assumed to be placed in a gravitational field. The cases in which the external field oscillations are generated by rotation about the horizontal axis or by vibration in the longitudinal direction are considered. The Navier-Stokes equations and the Boussinesq approximation are used for describing the fluid motion. The flows developing in the layer in the presence of a transverse temperature gradient are determined, the stability boundaries of these flows are found, and the supercritical motion regimes are studied. These investigations are carried out using the averaging method (in order to find the stability limits for high rotation velocities and vibration frequencies) and the Galerkin method.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–106, September–October, 1994.     

Some exact solutions of the ferrohydrodynamics equations

The theoretical study of nonisothermal flows of magnetizable liquids presents serious matheical difficulties, which are intensified as compared to to the study of normal liquids by the necessity of simultaneous solution of both the hydrodynamics and Maxwell's equations, with corresponding boundary conditions for the magnetic field. Thus, in most cases problems of this type are solved by neglecting the effect of the liquid's nonisothermal state on the field distribution within the liquid, and also, as a rule, with use of an approximate solution for Maxwell's equations and fulfillment of the boundary conditions for the field [1–3]. The present study will present easily realizable practical formulations of the problem which permit exact one-dimensional solutions of the complete system of the equations of thermomechanic s of electrically nonconductive incompressible Newtonian magnetizable liquids with constant transfer coefficients. A common feature of the formulations is the presence of a longitudinal temperature gradient along the boundaries along which liquid motion is accomplished. Plane-parallel convective flows of this type in a conventional liquid and their stability were considered in [4–6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 126–133, May–June, 1979.     

Convective instability of a fluid in a vibration field under conditions of weightlessness

The problem of the convection and convective instability of a fluid in a high-frequency vibration field under conditions of weightlessness was formulated in an earlier paper of the authors [1]. In the present paper, the conditions of equilibrium are discussed and the boundaries of vibration instability are determined for some equilibrium states: a plane layer of fluid with transverse temperature gradient and arbitrary direction of the vibration, a cylindrical layer with radial gradient and longitudinal direction of the vibration, and an infinite circular cylinder with transverse and mutually perpendicular directions of the temperature gradient and the vibration axis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–19, July–August, 1981.We thank G. I. Petrov for helpful discussions.     

Flow of a conductive gas in a circular tube in a strong axiosymmetric magnetic field

The flow of a conductive gas along a channel in an external axiosymmetric magnetic field with a finite value of the magnetogasodynamic parameter N is examined. Numerical flow calculations are performed for a circular tube in such a field. Gas dynamic parameter fields, total pressure losses, and electric current intensities with the presence of transsonic zones and highly compressed regions are determined. Through comparison of the results obtained with linear theory data, the range of applicability of the latter is determined. Of the works dedicated to study of flow in external magnetic fields with N1, we should take note of [1], in which the process of entry of the gas into a transverse magnetic field was examined; [2], which studied one-dimensional transient motion with shock waves; and [3], where mixed flow in a Laval nozzle with an axiosymmetric homogeneous magnetic field was studied. Flow in a circular tube was examined in [4]; but the analysis performed by the characteristic method permitted calculation of only the initial supersonic flow zone. Motion in circular tubes in the presence of an axiosymmetric, magnetic field was studied in the linear formulation in [4, 5].Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–155, September–October, 1972.     

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.     

Conservation of the resultant force vector in the plane of the angle of attack for slender star-shaped bodies in supersonic flows

At high supersonic flight speeds bodies with a star-shaped transverse and power-law longitudinal contour are optimal from the standpoint of wave drag [1–3]. In most of the subsequent experimental [4–6] and theoretical [6–9] studies only conical star-shaped bodies have been considered. For these bodies in certain flow regimes ascent of the Ferri point has been noted [10]. In [11] the boundary-value problem for elongated star-shaped bodies with a power-law longitudinal contour was solved for the case of supersonic flow. The present paper deals with the flow past these bodies at an angle of attack. It is found that for arbitrary star-shaped bodies with any longitudinal (in particular, conical) profile the aerodynamic forces can be reduced to a wave drag and a lift force, the lateral force on these bodies being equal to zero for any position of the transverse contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–141, November–December, 1989.     

Instability of combined convective flow in a vertical layer

In the present paper, a study is made of the stability of plane-parallel flow induced by a transverse temperature difference between the boundaries of a layer and a longitudinal pressure gradient. This problem was solved earlier by the author [3] in a purely hydrodynamic formulation without allowance for thermal factors; the results then obtained correspond to the limiting case of small Prandtl numbers. In the paper, a numerical solution to the problem with the complete formulation is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1982.I thank G. Z. Gershuni for supervising the work, and also M. A. Gol'dshtik and V. N. Shtern for a helpful discussion.     

On the influence of a transverse magnetic field on the vibration spectra of shallow shells

In the design of electric machines, devices, and plasma generator bearing constructions, it is sometimes necessary to study the influence of magnetic fields on the vibration frequency spectra of thin-walled elements. The main equations of magnetoelastic vibrations of plates and shells are given in [1], where the influence of the magnetic field on the fundamental frequencies and vibration shapes is also studied. When studying the higher frequencies and vibration modes of plates and shells, it is very efficient to use Bolotin’s asymptotic method [2–4]. A survey of studies of its applications to problems of elastic system vibrations and stability can be found in [5, 6]. Bolotin’s asymptotic method was used to obtain estimates for the density of natural frequencies of shallow shell vibrations [3] and to study the influence of the membrane stressed state on the distribution of frequencies of cylindrical and spherical shells vibrations [7, 8]. In a similar way, the influence of the longitudinal magnetic field on the distribution of plate and shell vibration frequencies was studied [9, 10]. It was shown that there is a decrease in the vibration frequencies of cylindrical shells under the action of a longitudinal magnetic field, and the accumulation point of the natural frequencies moves towards the region of lower frequencies [10]. In the present paper, we study the influence of a transverse magnetic field on the distribution of natural frequencies of shallow cylindrical and spherical shells, obtain asymptotic estimates for the density of natural frequencies of shell vibrations, and compare the obtained results with the empirical numerical results.     

Similarity solutions of the equations of a boundary layer in a nonuniform external flow

Similarity solutions of the equations of a laminar incompressible boundary layer, formed in a rotational external flow, are investigated. Such problems arise in the analysis of the flow in a boundary layer when there is an abrupt change in the boundary conditions (for example, in the case of a discrete inflation of the boundary layer, in hypersonic flow about blunt bodies, etc.). Various approaches to their solution have been proposed earlier in [1–4]. Solved below is the so-called inverse problem of boundary layer theory (see [3], p. 200), where the contour of the body that causes a given flow outside the boundary layer is unknown beforehand and is found during the course of solution of the problem in connection with the coupling of the longitudinal and transverse velocity components. The cases of a parabolic (u_e ~ y²) and a linear (u_e=a(x)+b(x)y) variation in the velocity of the external flow with distance along the transverse direction are considered in detail. The latter includes an investigation of the flow in the neighborhood of the critical point of a blunt body, taking account of the vorticity of the flow in the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 78–83, March–April, 1971.     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Stability of stationary convective flow of a mixture in a vertical porous layer

In contrast to the corresponding viscous flow, the convective flow of a homogeneous liquid in a planar vertical layer whose boundaries are maintained at different temperatures is stable [1]. When a porous layer is saturated with a binary mixture, in the presence of potentially stable stratification one must expect an instability of thermal-concentration nature to be manifested. This instability mechanism is associated with the difference between the temperature and concentration relaxation times, which leads to a buoyancy force when an element of the fluid is displaced horizontally. In viscous binary mixtures, the thermal-concentration instability is the origin of the formation of layered flows, which have been studied in detail in recent years [2–4]. The convective instability of the equilibrium of a binary mixture in a porous medium was considered earlier by the present authors in [5]. In the present paper, the stability of stationary convective flow of a binary mixture in a planar vertical porous layer is studied. It is shown that in the presence of sufficient longitudinal stratification the flow becomes unstable against thermal-concentration perturbations; the stability boundary is determined as a function of the parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–157, January–February, 1980.     

Propagation of shock waves in a medium with exponentially varying density

The results of Raizer [1], Hays [2], and Chernous'ko [3] are generalized to-the case of self-similar propagation of shock waves in a gas with exponentially varying density and constant pressure. A solution is found by the method of successive approximations. The zero-order approximation coincides with the Whitham method [4]. The first-order approximation is in good agreement with numerical calculations in [2]. The non-selfsimilar motion of a weak shock wave is investigated in the framework of linear theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 48–54, November–December, 1970.     

Stability of a plane-parallel convective flow of a liquid in a horizontal layer

We consider the stationary plane-parallel convective flow, studied in [1], which appears in a two-dimensional horizontal layer of a liquid in the presence of a longitudinal temperature gradient. In the present paper we examine the stability of this flow relative to small perturbations. To solve the spectral amplitude problem and to determine the stability boundaries we apply a version of the Galerkin method, which was used earlier for studying the stability of convective flows in vertical and inclined layers in the presence of a transverse temperature difference or of internal heat sources (see [2]). A horizontal plane-parallel flow is found to be unstable relative to two critical modes of perturbations. For small Prandtl numbers the instability has a hydrodynamic character and is associated with the development of vortices on the boundary of counterflows. For moderate and for large Prandtl numbers the instability has a Rayleigh character and is due to a thermal stratification arising in the stationary flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 95–100, January–February, 1974.     

Normal interaction of shock waves in the presence of vibrational relaxation

The effect of nonequilibrium physicochemical processes on the flow resulting from the normal collision and reflection of shock waves is studied by the example of nonequilibrium excitation of molecular oscillations in nitrogen. It is shown that the thermal effect of vibrational relaxation is small and the problem can be linearized around a known solution [1]. A similar approach to the solution of the problem of flow around a wedge and certain one-dimensional non-steady-state problems was used earlier in [2–4]. The solution of these problems was constructed in an angular domain, bounded by the shock wave and a solid wall (or the contact surface) and was reduced to a well-known functional equation [6]. The solution of this problem, because of the presence of two angular domains divided by a tangential discontinuity, reduces to a functional equation of more general form than in [6]. The results are obtained in finite form. In the special case of shocks of equal intensity, the normal reflection parameters are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 90–96, July–August, 1976.     

Connective instability of a two-layer system with thermally insulated boundaries

The investigation of the convective stability of mechanical equilibrium of two horizontal layers of immiscible fluids has revealed the characteristics of such systems [1–3]. In particular, it has been found that, as distinct from a homogeneous horizontal layer, under certain conditions two-layer systems experience convective instability when uniformly heated from above and, moreover, oscillatory instability when heated from below. In [1–3] the problem was solved for a system with isothermal outer boundaries. In this paper the stability of equilibrium of two-layer systems is investigated for thermally insulated outer boundaries. Special attention is given to the study of the long wave instability mode.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 22–28, March–April, 1986.The authors wish to thank O. V. Kustova for assisting with the computations.     

Asymptotic of the electromagnetic field above a layerlike anisotropic medium of high conductivity

The model of an anisotropic, layerlike medium is often employed in problems of electromagnetic probing, and many papers have been written on the propagation of an electromagnetic field in such media. A systematic exposition of such problems was set out by Tikhonov, Sku-garevskaya, and Dmitriev [1–6]. In this paper we shall construct an asymptotic for the electromagnetic field of a point source lying above a layerlike medium of finite anisotropy having a fairly high longitudinal and transverse conductivity, or in which the source lies at a considerable height above the medium. The principles here laid down for the construction of the asymptotic indicate quite clearly under what circumstances the asymptotic is feasible, and if necessary allow the next approximations to be taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 175–188, March–April, 1966.