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.     

Propagation of cylindrical shock waves in a gravitating medium

We study gas motion behind the front of a cylindrical shock wave created by the motion of a piston in a gravitating medium. The problem is self-similar, but the solution cannot be obtained in closed form. A numerical calculation is made for various Mach numbers. The calculation shows that the central part of the configuration is displaced a definite distance from the axis of symmetry.Cylindrical shock waves through a compressible homogeneous medium in a gravity field have been examined by Sedov [1] and Lin [2], However, these studies contain the essential assumption that the total energy (i. e., the sum of the kinetic and thermal energies) within the region bounded by the expanding shock wave is independent of time.In the following we extend the previous studies to the case of shock waves in nonhomogenous media, which propagate in the fluctuating gravity field created by the disturbed mass itself. The shock wave is created by the motion of a piston whose velocity varies as some power of the time, i. e., v. The total energy of the configuration also depends on the time.The authors wish to thank M. P. Murgai for cooperation and assistance and C. D. Ghildyal for valuable advice, as well as L. I. Sedov and G. I. Petrov for their critical comments.     

Propagation of shock waves in a porous medium saturated by a liquid with bubbles of a soluble gas

The process of evolution and reflection of shock waves of moderate amplitude from a rigid boundary in a porous medium saturated by a liquid with bubbles of a soluble gas is studied experimentally. Experimental values of the amplitude and velocity of the reflected wave are compared with the calculated results obtained using mathematical models. The process of dissolution of gas bubbles in the liquid behind the shock wave is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 91–102, September–October, 2000.     

Propagation of weak shock waves

An asymptotic method is developed in order to treat the evolution of weak shock waves. One obtains a geometrical theory according to which weak shock waves propagate along rays and satisfy a transport law.     

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 50–60, May–June, 2005.     

Propagation of weak shock waves in a magnetic field

This paper gives a solution of the problem of the propagation of weak shock waves in an inhomogeneous conducting medium in the presence of a magnetic field. The width of the perturbed region is taken to be small compared with the characteristic dimensions of the problem. The magnetic Reynolds number is also assumed small, which allows one to neglect the induced magnetic field. The method of solution employed is similar to that used in [1–3],The author is grateful to B. I. Zaslavskii for useful advice and for discussing the paper.     

Propagation of shock waves in free space

The problem of the exit of a shock wave from an axisymmetric channel and its propagation in a free space occupied by an ideal gas is examined. This problem has been studied earlier in [1], in which the shock wave front was considered planar, as well as in [2], in which the wave front was regarded as a surface of an ellipsoid of revolution. The solutions obtained in these studies assumed the presence of two regions in the wave-front surface: the region of the original shock wave and a region stemming from the decomposition of an infinitesimally thin annular discontinuity of the gas parameters, with the wave intensity over the front surface in each region being considered constant, i.e., the wave character of the process over the front was not considered. In this study a solution will be achieved by the method of characteristics [3–5] of the equations of motion of the shock-wave front, as obtained in [6, 7]. Flow fields are determined for the region immediately adjacent to the shock-wave front for a wide range of shock-wave Mach numbers M _a =1.6–20.0 for = 1.4. On the basis of the data obtained, by introduction of variables connected with the length of the undisturbed zone, as calculated from the channel cross-section along the x axis, together with the pressure transition at the wave front, relationships are proposed which approach self-similarity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1971.In conclusion, the author thanks S. S. Semenov for his valuable advice on this study.     

Propagation of shock waves in nonuniform plasma

Results of numerical simulation of the propagation of one-dimensional magnetohydrodynamic shock waves in a nonuniform plasma containing a magnetic field are discussed. Possible uses for the production of high velocities and temperatures and astrophysical applications are considered. The essential effect of the magnetic field is shown; acceleration of a shock wave is intensified in a medium with decreasing density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 22–26, March–April, 1976.In conclusion, the authors are grateful to S. K. Godunov for a detailed discussion of the computational aspects and of the results, and to A. E. Voitenko for a discussion of experimental possibilities and of the results.     

Converging shock waves in media with decreasing density

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 16–20, September–October, 1992.