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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):451-469; doi:10.1093/qjmam/1.1.451
© 1948 by Oxford University Press
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THE METHOD OF CHARACTERISTICS FOR PROBLEMS OF COMPRESSIBLE FLOW INVOLVING TWO INDEPENDENT VARIABLES

PART II. INTEGRATION ALONG A MACH LINE. THE RADIAL FOCUSING EFFECT IN AXIALLY SYMMETRICAL FLOW

R. E. MEYER

( Department of Mathematics, The University Manchester )

The paper deals with the growth and decay of disturbances along Mach lines in isentropic, irrotational, steady, two-dimensional or axially symmetrical, supersonic flow; in particular, the distribution of disturbances is investigated along a Mach line in axialiy symmetrical flow on which the velocity is constant. As an example, the field of flow in the entry of a contractor of circular cross-section is calculated from the focusing laws, and the analytical expressions are compared with the results of the numerical methods of Massau and Tupper.

The disturbance generated by the diffuser entry leads to a singularity of the flow pattern on the axis, the nature of which is investigated within the framework of linear theory.


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