Propagation of cylindrical shock waves in a gravitating medium
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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  and Lin , 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., vατβ. The total energy of the configuration also depends on the time.
KeywordsShock Wave Total Energy Numerical Calculation Mach Number Thermal Energy
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