Interaction between a fast magnetohydrodynamic shock wave and a tangential discontinuity

The self-similar problem of the oblique interaction between a fast shock wave and a tangential discontinuity is solved within the framework of the ideal magnetohydrodynamic model. The constraints on the initial parameters necessary for the existence of a regular solution are found. Various feasible wave flow patterns are found. In the space of the governing parameters boundaries between the solutions of various types are constructed. The basic features of the developing flows and their dependence on the initial data are clarified.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 159–168, March–April, 1995.     

The non-uniform piston-driven magnetohydrodynamic shock wave

Summary The effects of small variations in cross-sectional area and piston velocity on the propagation of a shock wave into a duct have been considered. The motion of the perfectly conducting fluid is subjected to a transverse magnetic field. In particular an expression for the pressure perturbation behind the shock has been derived.     

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.     

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.     

Stationary simple waves in a plasma with anisotropic pressure

Stationary simple waves in a plasma with anisotropic pressure are investigated on the basis of the hydrodynamic equations of Chew, Goldberger, and Low. In Sec. 1, for the case where the vectors of the average flow velocity and the magnetic field intensity are parallel, the system of equations is reduced to two quasilinear equations for the velocity components. In Sec. 2 the equations for the characteristics are obtained, the system being assumed to be hyperbolic. For the special case of irrotational flow the character of simple waves in flows adjacent to various contours is studied. Section 3 contains a qualitative investigation of changes in the flow parameters in simple waves. In Sec. 4 the possibility of a transition to an unstable state of the plasma is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 12–19, March–April, 1971.The author thanks V. B. Baranov for the formulation of the problem and for his advice and constant attention to the work and also A. G. Kulikovskii for discussion of the results.     

The existence of a discontinuity in the profile of a slow shock magnetohydrodynamic wave

An analysis is made of the structure of the profile of a slow shock magnetohydrodynamic wave of arbitrary intensity in a nonviscous medium. It is shown that the condition for the formation of a discontinuous profile coincides with the condition for the creation of an isothermal discontinuity in conventional gas dynamics.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 2, pp. 3–9, March–April, 1971.The authors thank G. Ya. Lyubarskii for useful advice and discussions of the questions touched upon in this paper.     

Magnetic hydrodynamics of two-dimensional flows in a plasma with an anisotropic pressure

The hydrodynamic equations of Chew, Goldberger, and Low [1] are used to analyze certain types of two-dimensional flows of a plasma with an anisotropic pressure (the pressure along the magnetic field p differs from the pressure across it p). In Sec. 1 the relationships derived in [2] for the transition of plasma state across surfaces of strong discontinuity are invoked to investigate the variation of the hydrodynamic parameters in weak shock waves in the linear approximation. The flow around bodies which only slightly perturb the main flow is investigated in Sec. 2 in the linear approximation. Similar problems for the case of an isotropic pressure are studied in detail in [3–5], for example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–10, November–December, 1970.     

Estimating pressure in nonsteady reflection of a shock wave

A comparative analysis of the results of physical [1–4] and mathematical experiments [5–8] is used to elucidate the mechanism of additional pressure lift at a Mach wavefront. The possibility and range of application of simplified flow models for the estimation of the pressure at certain characteristic points of the reflection surface (for example, a prism, a cylinder, or a sphere) was investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 100–106, March–April, 1977.     

Stability of the Burgers shock wave

This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance.It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.     

Stability of regular shock wave reflection

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 26–33, March–April, 1989.     

Stability of a plane,ionizing shock wave in a magnetic field

It is shown that with a constant transverse magnetic field present, a plane, ionizing, gas-dynamical shock wave becomes more stable with respect to small displacements of its front from the equilibrium position.Moscow. Translated from Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1972.     

Stability of a radiation-absorbing ionizing shock wave in an electromagnetic field

The linear stability of a radiation-absorbing ionizing shock wave (light detonation waves) in the presence of a uniform electromagnetic field is investigated. The applied electric field is considered to be normal to the wave front and the magnetic field to be parallel to the front and perpendicular to the plane in which perturbations propagate. The medium satisfies a two-parameter equation of state. Analytic stability criteria are obtained. For a perfect gas the effect of the electromagnetic field and radiation on shock wave stability is determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–30, January–February, 1996.     

Existence and interaction of acceleration wave with a characteristic shock in transient pinched plasma

In this paper, the evolution of an acceleration wave and a characteristic shock for the system of partial equations describing one dimensional, unsteady, axisymmetric motion of transient pinched plasma has been considered. The amplitude of the acceleration wave propagating along the characteristic associated with the largest eigenvalue has been evaluated. The interaction of the acceleration wave with the characteristic shock has been investigated. The amplitudes of the reflected and transmitted waves and the jump in the shockwave acceleration after interaction are evaluated.