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On the effect of crossflow on nonlinear Görtler vortices in curved channel flows

Citation

Bassom, AP, On the effect of crossflow on nonlinear Görtler vortices in curved channel flows, Quarterly Journal of Mechanics and Applied Mathematics, 42, (4) pp. 495-510. ISSN 0033-5614 (1989) [Refereed Article]

Copyright Statement

© Oxford University Press 1989

DOI: doi:10.1093/qjmam/42.4.495

Abstract

It is known that the two-dimensional flow through a curved channel of narrow width is unstable to nonlinear vortices for sufficiently high Taylor-Görtler numbers and that the instability arises because of centrifugal effects. In many practical applications the basic flow of interest is three-dimensional and here we look for nonlinear, small-wavelength vortices in a three-dimensional and here we look for nonlinear, small-wavelength vortices in a three-dimensional flow through a curved channel and show that the crossflow needed to dramatically change the results for the case of a two-dimensional basic flow is extremely tiny. We derive the governing equation for constant-sized, streamwise-independent nonlinear vortices and by using a combination of asymptotics, numerical methods and phase-plane techniques we describe the solutions of this equation. Significantly, these solutions suggest that above a certain critical value for the crossflow the vortices cannot persist and that for lesser crossflows two different structures for the vortices are possible. The relevance of the results found here to the important case of external boundary-layer flows (where the effect of boundary-layer growth plays a crucial role) is indicated and suggestions for extensions of this work are made.

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:107844
Year Published:1989
Web of Science® Times Cited:4
Deposited By:Mathematics and Physics
Deposited On:2016-03-30
Last Modified:2016-07-08
Downloads:0

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