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Non-stationary cross-flow vortices in three-dimensional boundary-layer flows


Bassom, AP and Gajjar, JSB, Non-stationary cross-flow vortices in three-dimensional boundary-layer flows, Proceedings of the Royal Society of London A, 417, (1852) pp. 179-212. ISSN 1364-5021 (1988) [Refereed Article]

Copyright Statement

Copyright 1988 the Royal Society

DOI: doi:10.1098/rspa.1988.0056


The upper-branch neutral stability of three-dimensional disturbances imposed on a three-dimensional boundary-layer profile is considered and in particular we investigate non-stationary cross-flow vortices. The wave speed is taken to be small initially and with a disturbance structure analogous to that occurring in two-dimensional boundary-layer stability the linear and nonlinear eigenrelations are derived for profiles with more than one critical layer.

For the flow due to a rotating disc we show that linear viscous neutral modes exist for all wave angles between 10.6 and 39.6. As the extremes of this range are approached the flow structure evolves to another, either the viscous mode of Hall (Proc. R. Soc. Lond. A 406, 93 (1986)) or the non-stationary inviscid modes considered by Stuart in Gregory et al. (Phil. Trans. R. Soc. Lond. A 248, 155 (1955)). In the former case, corresponding to wave angles of 39.6, the waves become almost stationary and in the latter case, with wave angles of 10.6 the waves are travelling much faster with a disturbance structure based on the Rayleigh scalings. The analysis is extended to include O(1) wavespeeds and we show that as the wavespeed of the cross-flow vortex approaches the free-stream value, the corresponding disturbance amplitude increases, the growth here being slower than that for two-dimensional 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
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108008
Year Published:1988
Web of Science® Times Cited:32
Deposited By:Mathematics and Physics
Deposited On:2016-04-04
Last Modified:2016-07-08

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