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Uniformly valid analytical solution to the problem of a decaying shock wave

Sharma, VD and Ram, Rishi and Sachdev, PL (1987) Uniformly valid analytical solution to the problem of a decaying shock wave. In: Journal of Fluid Mechanics, 185 . 153 -170.

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An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

Item Type: Journal Article
Publication: Journal of Fluid Mechanics
Publisher: Cambridge University Press
Additional Information: Copyright of this article belongs to Cambridge University Press.
Keywords: Nonisentropicity;One Dimensional Flow; Plane Waves; Rankine-Hugoniot Relation;Shock Wave Attenuation;Euler Equations Of Motion;Gas Dynamics;Mach Number;Wave Interaction.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 21 Oct 2010 08:41
Last Modified: 21 Oct 2010 08:41
URI: http://eprints.iisc.ac.in/id/eprint/33349

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