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Linear instability of the wake behind a flat plate placed parallel to a uniform stream

Published online by Cambridge University Press:  26 April 2006

D. T. Papageorgiou  and
F. T. Smith
D. T. Papageorgiou
Affiliation:
Department of Chemical Engineering, City College of New York, Convent Avenue and 140th Street, New York, NY 10031, USA
F. T. Smith
Affiliation:
University College London, Department of Mathematics, Gower Street, London WC1 E6BT, UK
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Abstract

The growth of linear disturbances in the high-Reynolds-number laminar wake of a flat plate aligned with a uniform stream is investigated. The theory is developed rationally by use of appropriate wake profiles which originate at the trailing edge as double Blasius distributions and thereafter satisfy the equations of motion, in contrast to previous theoretical work where model profiles are used. We also emphasize the structures and scales of the instability in order to provide a rational basis for the development of nonlinear analyses as opposed to existing ad hoc ones. Disturbances, in the near wake, respond according to the Rayleigh equation which is considered analytically for short-, long- and neutral-wave solutions. For more general stability characteristics eigensolutions must be obtained numerically. We calculate these at successive wake stations for ‘improved’ basic flow profiles which are obtained as solutions of the wake boundary-layer equations. Our numerical results indicate fairly good agreement with the asymptotic theory and some experimental data (see §7).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 67 - 89
Copyright
© 1989 Cambridge University Press

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