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Weakly nonlinear stability of viscous vortices in three-dimensional boundary layers

Citation

Bassom, AP and Otto, SR, Weakly nonlinear stability of viscous vortices in three-dimensional boundary layers, Journal of Fluid Mechanics, 249 pp. 597-618. ISSN 0022-1120 (1993) [Refereed Article]

Copyright Statement

Copyright 1993 Cambridge University Press

DOI: doi:10.1017/S0022112093001302

Abstract

Recently it has been demonstrated that three-dimensionality can play an important role in dictating the stability of any Görtler vortices which a particular boundary layer may support. According to a linearized theory, vortices within a high Görtler number flow can take one of two possible forms within a two-dimensional flow supplemented by a small crossflow of size O(Re12 G35), where Re is the Reynolds number of the flow and G the Görtler number. Bassom & Hall (1991) showed that these forms are characterized by O(1)-wavenumber inviscid disturbances and larger O(G15)-wave-number modes which are trapped within a thin layer adjacent to the bounding surface. Here we concentrate on the latter, essentially viscous, vortices. These modes are unstable in the absence of crossflow but the imposition of small crossflow has a stabilizing effect. Bassom & Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wavenumber combinations and here we describe the weakly nonlinear stability properties of these disturbances. It is shown conclusively that the effect of crossflow is to stabilize the nonlinear modes and the calculations herein allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting and asymptotic work permits discussion of the stability properties of modes with wavenumbers that are small relative to the implied O(G15) scaling.

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:108043
Year Published:1993
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2016-04-05
Last Modified:2016-07-08
Downloads:0

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