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On the non-parallel instability of the rotating-sphere boundary layer

Published online by Cambridge University Press:  29 March 2017

Antonio Segalini Open the ORCID record for Antonio Segalini [Opens in a new window]  and
Stephen J. Garrett Open the ORCID record for Stephen J. Garrett [Opens in a new window]
Antonio Segalini*
Affiliation:
Linné FLOW Centre, KTH Mechanics, 10044 Stockholm, Sweden
Stephen J. Garrett
Affiliation:
Department of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK
*
†Email address for correspondence: segalini@mech.kth.se
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Abstract

We present a new solution for the steady boundary-layer flow over the rotating sphere that also accounts for the eruption of the boundary layer at the equator and other higher-order viscous effects. Non-parallel corrections to the local type I and type II convective instability modes of this flow are also computed as a function of spin rate. Our instability results are associated with the previously observed spiral vortices and remarkable agreement between our predictions of the number of vortices and experimental observations is found. Vortices travelling at 70 %–80 % of the local surface speed are found to be the most amplified for sufficient spin rates, also consistent with prior experimental observations.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability

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Papers
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Journal of Fluid Mechanics , Volume 818 , 10 May 2017 , pp. 288 - 318
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© 2017 Cambridge University Press 

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