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Vortex instabilities in three-dimensional boundary layers: the relationship between Görtler and crossflow vortices

Citation

Bassom, AP and Hall, P, Vortex instabilities in three-dimensional boundary layers: the relationship between Görtler and crossflow vortices, Journal of Fluid Mechanics, 232 pp. 647-680. ISSN 0022-1120 (1991) [Refereed Article]

Copyright Statement

Copyright 1991 Cambridge University Press

DOI: doi:10.1017/S0022112091003841

Abstract

The inviscid and viscous stability problems are addressed for a boundary layer which can support both Görtler and crossflow vortices. The change in structure of Görtler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary-layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Görtler vortices present in a boundary layer which, in the zero-crossflow case, is centrifugally unstable. The results suggest that in many practical applications Görtler vortices cannot be a cause of transition because they are destroyed by the three-dimensional nature of the basic state. In swept-wing flows the Görtler mechanism is probably not present for typical angles of sweep of about 20°.

Some discussion of the receptivity problem for vortex instabilities in weakly three-dimensional boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall & Seddougui (1991). However, the fact that the growth rates of the inviscid modes are the larger in most situations means that they are probably the more likely source of transition.

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:108086
Year Published:1991
Web of Science® Times Cited:18
Deposited By:Mathematics and Physics
Deposited On:2016-04-06
Last Modified:2016-07-08
Downloads:0

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