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Finite-time break-up can occur in any unsteady interacting boundary layer

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

F. T. Smith
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
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Summary

This theoretical work shows formally that unsteady interactive boundary layers can break up within a finite time by encountering a nonlinear localized singularity. The theory is an extension of, and is guided to a large extent by, Brotherton-Ratcliffe and Smith's (1987) work on a special case. Two major types of singularity are proposed, a “moderate” type yielding a singular pressure gradient and a “severe” type associated with a pressure discontinuity. Each type produces a singular response in the skin friction in the case of wall-bounded flows. The present finite-time singularity applies to any unsteady interactive flow, e.g., incompressible or compressible boundary layers, internal flows, wakes, in two or three dimensions; and the singularity and its associated change in flow structure have numerous repercussions, which are discussed, physically and theoretically, concerning boundary-layer transition in particular.

MSC classification

Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 256 - 273
Copyright
Copyright © University College London 1988

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References

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