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Nonlinear wave propagation in a two-dimensional steady transonic flow

Published online by Cambridge University Press:  12 April 2006

Phoolan Prasad  and
E. V. Krishnan
Phoolan Prasad
Affiliation:
Mehta Research Institute of Mathematics and Mathematical Physics, 26 Dilkusha, New Katra, Allahabad-211002 (U.P.), India
Present address: Department of Applied Mathematics, Indian Institute of Science, Bangalore-560012, India.
E. V. Krishnan
Affiliation:
Mehta Research Institute of Mathematics and Mathematical Physics, 26 Dilkusha, New Katra, Allahabad-211002 (U.P.), India
Present address: Department of Applied Mathematics, Indian Institute of Science, Bangalore-560012, India.
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Abstract

When we look at photographs of real transonic flows which are predicted to be shockless, we find a very large number of weak shocks almost perpendicular to the streamlines. These are no more than almost-trapped upstream-propagating nonlinear waves. In this paper we try to obtain a simple approximate equation which gives their complete history and takes into account both their turning effect, owing to a non-zero gradient of the fluid velocity in a direction normal to the streamlines, and also the finite radius of curvature of the wave front. We first give a brief discussion of a few results which can be easily obtained from the solution of the approximate equation and then compute the history of two nonlinear pulses by numerically integrating the equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 17 - 28
Copyright
© 1977 Cambridge University Press

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References

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