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The nonparallel evolution of nonlinear short waves in buoyant boundary layers

Citation

Denier, JP and Bassom, AP, The nonparallel evolution of nonlinear short waves in buoyant boundary layers, Studies in Applied Mathematics, 110, (2) pp. 139-156. ISSN 0022-2526 (2003) [Refereed Article]

DOI: doi:10.1111/1467-9590.00234

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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107361
Year Published:2003
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2016-03-11
Last Modified:2016-07-08
Downloads:0

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