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Short-scale effects on model boundary-layer spots

Published online by Cambridge University Press:  26 April 2006

R. G. A. Bowles  and
F. T. Smith
R. G. A. Bowles
Affiliation:
School of Mathematics and Statistics, University of Middlesex, London N11 2NQ, UK
F. T. Smith
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
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Abstract

This theoretical work, on the spot in an otherwise laminar boundary layer, concerns the initial-value problem for three-dimensional inviscid disturbances covering a wide range of scales. The study asks whether or not comparatively short scales can have a substantial impact on the spot spreading rate, as well as on other important features including the spot structure. It is found that such scales act to reduce the spread angle to approximately 11°, close to the experimental observations for transitional/turbulent spots, as opposed to the angle of 19.47° for waves near or behind the spot trailing edge. The scales emerge from coupling uniform shear flow directly with the local uniform stream and then analysing large-time features. The leading edge and trailing edge of the spot are also examined in detail, along with other structural properties. It is concluded that nonlinearity and short-scale effects probably combine to restrict the global spread angle as above, while viscous sublayer bursting among other things completes the spot structure. Related work on nonlinear, trailing-edge and leading-edge behaviours and comparisons with experiments are also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 395 - 407
Copyright
© 1995 Cambridge University Press

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