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On the instability of Görtler vortices to nonlinear travelling waves

Citation

Seddougui, SO and Bassom, AP, On the instability of Gortler vortices to nonlinear travelling waves, IMA Journal of Applied Mathematics, 46, (3) pp. 269-296. ISSN 0272-4960 (1991) [Refereed Article]

Copyright Statement

© Oxford University Press 1991

DOI: doi:10.1093/imamat/46.3.269

Abstract

Recent theoretical work by Hall & Seddougui (1989) has shown that strongly nonlinear high-wavenumber Görtler vortices developing within a boundary layer flow are susceptible to a secondary instability which takes the form of travelling waves confined to a thin region centred at the outer edge of the vortex. This work considered the case in which the secondary mode could be satisfactorily described by a linear stability theory, and in the current paper our objective is to extend this investigation of Hall & Seddougui (1989) into the nonlinear regime. We find that, at this stage, not only does the secondary mode become nonlinear, but it also interacts with itself so as to modify the governing equations for the primary Görtler vortex. In this case, then, the vortex and the travelling wave drive each other, and indeed the whole flow structure is described by an infinite set of coupled nonlinear differential equations. We undertake a Stuart-Watson type of weakly nonlinear analysis of these equations and conclude, in particular, that on this basis there exist stable flow configurations in which the travelling mode is of finite amplitude. Implications of our findings for practical situations are discussed, and it is shown that the theoretical conclusions drawn here are in good qualitative agreement with available experimental observations.

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:108554
Year Published:1991
Web of Science® Times Cited:4
Deposited By:Mathematics and Physics
Deposited On:2016-04-22
Last Modified:2016-11-25
Downloads:0

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