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Strongly nonlinear vortex–Tollmien–Schlichting–wave interactions in the developing flow through a circular pipe

Published online by Cambridge University Press:  26 April 2006

A. G. Walton
A. G. Walton
Affiliation:
Department of Mathematics, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ, UK
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Abstract

Strongly nonlinear vortex-Tollmien-Schlichting-wave interaction equations are derived for the case where the undisturbed motion represents the developing flow in a circular pipe. The effect upon the equations of moving the wave input position further downstream is investigated and the development of the flow is found to be accelerated by increasing the size of the wave disturbance. Numerical solutions of the three-dimensional interaction equations are presented and indicate that the form of interaction considered here appears to promote the three-dimensionality as the flow develops downstream. It is shown that one of the interactions considered here can develop within an initially two-dimensional Blasius boundary layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 319 , 25 July 1996 , pp. 77 - 107
Copyright
© 1996 Cambridge University Press

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