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    LESSER, M.B. and CRIGHTON, D.G. 1975. Physical Acoustics - Principles and Methods.

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    Chong, T. H. and Sirovich, L. 1971. Non-linear effects in steady supersonic dissipative gasdynamics Part 1. Two-dimensional flow. Journal of Fluid Mechanics, Vol. 50, Issue. 01, p. 161.

    Sedov, A. and Nariboli, G.A. 1971. Visco-elastic waves by the use of wave-front theory. International Journal of Non-Linear Mechanics, Vol. 6, Issue. 5, p. 615.

    Sedov, A. V. Gopalakrishna, A. and A. Nariboli, G. 1971. Three-Dimensional Burgers's Equation in Gas Dynamics. Journal of the Physical Society of Japan, Vol. 30, Issue. 2, p. 557.

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    Ockendon, H. and Spence, D. A. 1969. Non-linear wave propagation in a relaxing gas. Journal of Fluid Mechanics, Vol. 39, Issue. 02, p. 329.

    Lesser, M. B. and Seebass, R. 1968. The structure of a weak shock wave undergoing reflexion from a wall. Journal of Fluid Mechanics, Vol. 31, Issue. 03, p. 501.

    Lick, Wilbert 1966. Advances in Applied Mechanics Volume 10.


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

  • John P. Moran (a1) and S. F. Shen (a1)
  • DOI:
  • Published online: 01 March 2006

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.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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