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On the formation of weak plane shock waves by impulsive motion of a piston

Published online by Cambridge University Press:  28 March 2006

John P. Moran  and
S. F. Shen
John P. Moran
Affiliation:
Graduate School of Aerospace Engineering, Cornell University, Ithaca, New York
S. F. Shen
Affiliation:
Graduate School of Aerospace Engineering, Cornell University, Ithaca, New York
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Abstract

The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2 mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 4 , August 1966 , pp. 705 - 718
Copyright
© 1966 Cambridge University Press

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