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Second-order Cowley-Imai analogy in magnetogasdynamics

Published online by Cambridge University Press:  29 March 2006

Lee A. Bertram  and
Y. M. Lynn
Lee A. Bertram
Affiliation:
Department of Engineering Mechanics, Iowa State University
Y. M. Lynn
Affiliation:
Division of Mathematics, University of Maryland, Baltimore County
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Abstract

The extended Cowley–Imai analogy is derived and employed to obtain explicit equations which allow transcription of gasdynamic perturbation solutions into magnetogasdynamic solutions. The transcription is written down to second order for axisymmetric super-Alfvénic flows of a perfect gas at arbitrary Mach numbers. Speed and field perturbations are shown to vanish in the Alfvénic limit for such solutions, although this is not a property of the exact solution. Van Dyke's supersonic-cone-flow solution is then transcribed and compared with the exact numerical solution over the range 1 < A∞, ≥ 20, 1 < M∞, ≥ 20 for a cone of 5° semi-apex angle, showing excellent agreement which improves with increasing field strength. The large-cone-angle behaviour of the solution is also quite good for the upstream state A∞ = M∞ = 2·0.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 1 , 14 March 1972 , pp. 33 - 42
Copyright
© 1972 Cambridge University Press

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References

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