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A two-dimensional boundary layer encountering a three-dimensional hump

Published online by Cambridge University Press:  12 April 2006

F. T. Smith ,
R. I. Sykes  and
P. W. M. Brighton
F. T. Smith
Affiliation:
Department of Mathematics, Imperial College, London
R. I. Sykes
Affiliation:
Meteorological Office, Bracknell, Berkshire, England
P. W. M. Brighton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 1 , 1 November 1977 , pp. 163 - 176
Copyright
© 1977 Cambridge University Press

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