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The Quarterly Journal of Mechanics and Applied Mathematics 1951 4(3):371-383; doi:10.1093/qjmam/4.3.371
© 1951 by Oxford University Press
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APPLICATION OF RELAXATION TO THE ROTATIONAL FIELD OF FLOW BEHIND A BOW SHOCK WAVE

A. R. MITCHELL

( Mathematics Department, United College, The University St. Andrews )

A development of the relaxation technique due to R. V. Southwell for evaluating subsonic isentropic regions of compressible flow in two dimensions is used to evaluate mixed subsonic-supersonic regions where the flow is rotational.

The new technique is employed to determine the complete field downstream of the bow shock wave formed when a parallel supersonic flow of Mach number 1–8 impinges on a blunt-nosed two-dimensional obstacle. The velocity is calculated everywhere in the field and it is found that the stream-line starting at the point of maximum vorticity on the bow shock wave is a locus of high vorticity in the rotational field downstream of the shock wave.


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