Sharma, V. D. ; Ram, Rishi ; Sachdev, P. L. (1987) Uniformly valid analytical solution to the problem of a decaying shock wave Journal of Fluid Mechanics, 185 . pp. 153-170. ISSN 0022-1120
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Related URL: http://dx.doi.org/10.1017/S0022112087003124
Abstract
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: | Article |
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Source: | Copyright of this article belongs to Cambridge University Press. |
ID Code: | 33849 |
Deposited On: | 30 Mar 2011 13:35 |
Last Modified: | 30 Mar 2011 13:35 |
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