Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/655
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Type: Journal article
Title: The nonparallel evolution of nonlinear short waves in buoyant boundary layers
Author: Denier, J.
Bassom, A.
Citation: Studies in Applied Mathematics, 2003; 110(2):139-156
Publisher: Blackwell Publishers
Issue Date: 2003
ISSN: 0022-2526
1467-9590
Statement of
Responsibility: 
James P. Denier and Andrew P. Bassom
Abstract: Buoyant boundary-layer flows, typified by the flow over a heated flat plate, have the curious property that they can exhibit regions of "overshoot" in which the streamwise velocity exceeds its free-stream value. A consequence of this is the streamwise velocity develops a local maximum and is inflectional in nature. It is therefore inviscidly unstable, and the fastest growing wave mode is known to be one whose wavelength is short compared to the boundary-layer thickness. In this work we consider the nonparallel evolution of these short waves and show that they can be described in terms of the solution of a system of ordinary differential equations. Numerical and asymptotic studies enable us to explain the ultimate fate of the wave and show, depending on a key parameter which is a function of the underlying boundary layer, that two possibilities can arise. Nonparallelism may be sufficiently stabilizing so as to extinguish the linearly unstable waves or, in other cases, the mode may intensify but concentrate itself in a very thin zone surrounding the maximum in the streamwise velocity. These findings enable us to give some indication of the part these modes play in the transition to turbulence in buoyant boundary layers.
Description: The definitive version is available at www.blackwell-synergy.com
RMID: 0020030808
DOI: 10.1111/1467-9590.00234
Appears in Collections:Applied Mathematics publications
Environment Institute publications

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