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Shock dynamics in non-uniform media

Catherasoo, C. J. and Sturtevant, B. (1983) Shock dynamics in non-uniform media. Journal of Fluid Mechanics, 127 . pp. 539-561. ISSN 0022-1120. doi:10.1017/S0022112083002876.

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The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction.

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Additional Information:Copyright © 1983 Cambridge University Press. Reprinted with permission. (Received 12 March 1982) The authors are grateful to Professor G.B. Whitham for drawing their attention to the analogy between a contact discontinuity in shock dynamics and a moving force in unsteady gasdynamics. This work was supported by the National Science Foundation under Grant CME-7822089.
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Deposited On:15 Jun 2008
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