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The centrifugal instability of the boundary-layer flow over slender rotating cones

Published online by Cambridge University Press:  14 August 2014

Z. Hussain ,
S. J. Garrett  and
S. O. Stephen
Z. Hussain*
Affiliation:
Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
S. J. Garrett
Affiliation:
Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
S. O. Stephen
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.

JFM classification

Boundary Layers: Boundary layer stability Flow Control: Instability control Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 274 - 293
Copyright
© 2014 Cambridge University Press 

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