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The boundary layer induced by a convected two-dimensional vortex

Published online by Cambridge University Press:  20 April 2006

T. L. Doligalski  and
J. D. A. Walker
T. L. Doligalski
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania
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Abstract

The response of a wall boundary layer to the motion of a convected vortex is investigated. The principal cases considered are for a rectilinear filament of strength –κ located a distance a above a plane wall and convected to the right in a uniform flow of speed U∞*. The inviscid solution predicts that such a vortex will remain at constant height a above the wall and be convected with constant speed αU∞*. Here α is termed the fractional convection rate of the vortex, and cases in the parameter range 0 [les ] α < 1 are considered. The motion is initiated at time t* = 0 and numerical calculations of the developing boundary-layer flow are carried out for α = 0, 0.2, 0.4, 0.55, 0.7, 0.75 and 0.8. For α < 0.75, a rapid lift-up of the boundary-layer streamlines and strong boundary-layer growth occurs in the region behind the vortex; in addition an unusual separation phenomenon is observed for α [les ] 0.55. For α [ges ] 0.75, the boundary-layer development is more gradual, but ultimately substantial localized boundary-layer growth also occurs. In all cases, it is argued that a strong inviscid–viscous interaction will take place in the form of an eruption of the boundary-layer flow. The generalization of these results to two-dimensional vortices with cores of finite dimension is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 1 - 28
Copyright
© 1984 Cambridge University Press

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