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Vortex-induced boundary-layer separation. Part 1. The unsteady limit problem Re → ∞

Published online by Cambridge University Press:  26 April 2006

Vallorie J. Peridier ,
F. T. Smith  and
J. D. A. Walker
Vallorie J. Peridier
Affiliation:
Department of Mechanical Engineering, Temple University, Philadelphia, PA 19122, USA
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

The unsteady boundary-layer flow produced by a two-dimensional vortex in motion above an infinite plane wall in an otherwise stagnant fluid is considered in the limit of infinite Reynolds number. This study is part of a continuing investigation into the nature of the physical processes that occur near the surface in transitional and fully turbulent boundary layers. The adverse pressure gradient due to the vortex leads to the development of a zone of recirculation in the viscous flow near the surface, and the boundary-layer flow then focuses rapidly toward an eruption along a band which is very narrow in the stream wise direction. The evolution of the unsteady boundary layer is posed in Lagrangian coordinates and computed using an efficient, factored ADI numerical method. The boundary-layer solution is found to develop a separation singularity and to evolve toward a terminal stage which is generic in two-dimensional unsteady flows. The computed results are compared with the results of asymptotic theory of two-dimensional boundary-layer separation and the agreement is found to be excellent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 99 - 131
Copyright
© 1991 Cambridge University Press

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