Journal of Fluid Mechanics



Shock dynamics in non-uniform media


C. J.  Catherasoo a1 and B.  Sturtevant a1
a1 Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125

Article author query
catherasoo cj   [Google Scholar] 
sturtevant b   [Google Scholar] 
 

Abstract

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.

(Published Online April 20 2006)
(Received March 12 1982)



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