If a piston with constant velocity moves into a shock tube containing material at rest and at uniform density, the result is well known and trivial. The shock propagates with uniform speed, the state and speed of the material behind the shock is constant. One can ask if similar flows exist for cylindrical of spherical symmetry. Quickly one rules out the possibility of a solution which retains all the properties of this trivial solution. One asks if there are any solutions such that the material behind the shock is not accelerated. Indeed, there are. In the following, it is shown …
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University of California Radiation Laboratory Report UCRL-7672-T
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If a piston with constant velocity moves into a shock tube containing material at rest and at uniform density, the result is well known and trivial. The shock propagates with uniform speed, the state and speed of the material behind the shock is constant. One can ask if similar flows exist for cylindrical of spherical symmetry. Quickly one rules out the possibility of a solution which retains all the properties of this trivial solution. One asks if there are any solutions such that the material behind the shock is not accelerated. Indeed, there are. In the following, it is shown that for a y-law gas, there is a family of densities such that if a piston moves into the material with uniform velocity, the material behind the shock is not accelerated. Further, these are the only densities with this property. In the case of planar symmetry, the trivial case mentioned above is a member of the family, as is to be expected.
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