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Model for unstable global modes in the rotating-disk boundary layer

Published online by Cambridge University Press:  28 September 2010

J. J. HEALEY
J. J. HEALEY*
Affiliation:
Department of Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK
*
†Email address for correspondence: [email protected]
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Abstract

Recent simulations and experiments appear to show that the rotating-disk boundary layer is linearly globally stable despite the existence of local absolute instability. However, we argue that linear global instability can be created by local absolute instability at the edge of the disk. This argument is based on investigations of the linearized complex Ginzburg–Landau equation with weakly spatially varying coefficients to model the propagation of a wavepacket through a weakly inhomogeneous unstable medium. Therefore, this mechanism could operate in a variety of locally absolutely unstable flows. The corresponding nonlinear global mode has a front at the radius of onset of absolute instability when the disk edge is far from the front. This front moves radially outwards when the Reynolds number at the disk edge is reduced. It is shown that the laminar–turbulent transition front also behaves in this manner, possibly explaining the scatter in observed transitional Reynolds numbers.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 148 - 159
Copyright
Copyright © Cambridge University Press 2010

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