Journal of Fluid Mechanics

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

John P.  Moran a1 and S. F.  Shen a1
a1 Graduate School of Aerospace Engineering, Cornell University, Ithaca, New York

Article author query
moran jp   [Google Scholar] 
shen sf   [Google Scholar] 


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.

(Published Online March 28 2006)
(Received November 1 1965)