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Global stability of the rotating-disc boundary layer with an axial magnetic field

Published online by Cambridge University Press:  29 April 2013

Christian Thomas  and
Christopher Davies
Christian Thomas
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Christopher Davies*
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
*
†Email address for correspondence: DaviesC9@cardiff.ac.uk
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Abstract

A numerical study is conducted to investigate the influence of a uniform axial magnetic field on the global linear stability of the rotating-disc boundary layer. Simulation results obtained using a radially homogenized base flow were found to be in excellent agreement with an earlier linear stability analysis, which indicated that an axial magnetic field can locally suppress both convective and absolute instabilities. However, the numerical results obtained for the genuine, radially inhomogeneous, flow indicate that a global form of instability develops for sufficiently large magnetic fields. The qualitative nature of the global instability is similar to that which was observed in a previous study, where mass suction was applied at the rotating disc surface. It is shown that, just as for the case with mass suction, it is possible to explain the promotion of global instability by considering a model that includes detuning effects, which are associated with the radial variation of locally defined absolute temporal frequencies. The recurrence of the same type of instability behaviour when two distinct flow control strategies are implemented, one using suction and the other an axial magnetic field, indicates that the phenomena described by the model may be considered generic.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability Flow Control: Flow Control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 724 , 10 June 2013 , pp. 510 - 526
Copyright
©2013 Cambridge University Press 

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