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Trapped waves in the neighbourhood of a sonic-type singularity

Published online by Cambridge University Press:  19 April 2006

Renuka Ravindran
Renuka Ravindran
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore-560012
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Abstract

A model equation is derived to study trapped nonlinear waves with a turning effect, occurring in disturbances induced on a two-dimensional steady flow. Only unimodal disturbances under the short wave assumption are considered, when the wave front of the induced disturbance is plane. In the neighbourhood of certain special points of sonic-type singularity, the disturbances are governed by a single first-order partial differential equation in two independent variables. The equation depends on the steady flow through three parameters, which are determined by the variations of velocity and depth, for example (in the case of long surface water waves), along and perpendicular to the wave front. These parameters help us to examine various relative effects. The presence of shocks in a continuously accelerating or decelerating flow has been studied in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 3 , 11 December 1979 , pp. 465 - 475
Copyright
© 1979 Cambridge University Press

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References

Nieulwand, G. Y. & Spee, B. M. 1968 Transonic shock-free flow, fact or fiction? Specialists meeting on Transonic Flows (Paris), AGARD Conf. Proc. no. 35, NLR MP 68004.
Prasad, P. 1973 Nonlinear wave propagation on an arbitrary steady transonic flow. J. Fluid Mech. 57, 721–737.Google Scholar
Prasad, P. 1975 Approximation of the perturbation equations of a quasilinear hyperbolic system in the neighbourhood of a bicharacteristic. J. Math. Anal. Applies. 50, 470–482.Google Scholar
Prasad, P. & Krishnan, E. V. 1977 Nonlinear wave propagation in a two-dimensional steady transonic flow. J. Fluid Mech. 82, 17–28.Google Scholar
Spee, B. M. 1971 Investigations on transonic flow around aerofoils, NLR TR 69122 U.