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Nonlinear wave propagation on an arbitrary steady transonic flow

Published online by Cambridge University Press:  29 March 2006

Phoolan Prasad
Phoolan Prasad
Affiliation:
School of Mathematics, University of Leeds Present address: Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012, India.
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Abstract

Here, we have studied the propagation of an arbitrary disturbance bounded in space on an arbitrary two- or three-dimensional transonic flow. First we have presented a general theory valid for an arbitrary system of n first-order quasi- linear partial differential equations and then used the theory for the special case of gasdynamic equations. If a disturbance is created in the neighbourhood of a sonic point, only a part of the disturbance stays in the transonic region and it is bounded by a wave front perpendicular to the streamlines. This part of the disturbance is governed by a very simple partial differential equation and the problem essentially reduces to the discussion of one-dimensional waves. The disturbance decays in the neighbourhood of the points where the flow acceler- ates from a subsonic state to a supersonic state and it attains a steady state where the flow is decelerating.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 4 , 6 March 1973 , pp. 721 - 737
Copyright
© 1973 Cambridge University Press

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