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The structure of sidewall boundary layers in confined rotating Rayleigh–Bénard convection

Published online by Cambridge University Press:  27 June 2013

R. P. J. Kunnen ,
H. J. H. Clercx  and
G. J. F. van Heijst
R. P. J. Kunnen*
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
H. J. H. Clercx
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
G. J. F. van Heijst
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent rotating convection is usually studied in a cylindrical geometry, as this is its most convenient experimental realization. In our previous work (Kunnen et al., J. Fluid Mech., vol. 688, 2011, pp. 422–442) we studied turbulent rotating convection in a cylinder with the emphasis on the boundary layers. A secondary circulation with a convoluted spatial structure has been observed in mean velocity plots. Here we present a linear boundary-layer analysis of this flow, which leads to a model of the circulation. The model consists of two independent parts: an internal recirculation within the sidewall boundary layer, and a bulk-driven domain-filling circulation. Both contributions exhibit the typical structure of the Stewartson boundary layer near the sidewall: a sandwich structure of two boundary layers of typical thicknesses ${E}^{1/ 4} $ and ${E}^{1/ 3} $, where $E$ is the Ekman number. Although the structure of the bulk-driven circulation may change considerably depending on the Ekman number, the boundary-layer recirculation is present at all Ekman numbers in the range $0. 72\times 1{0}^{- 5} \leq E\leq 5. 76\times 1{0}^{- 5} $ considered here.

JFM classification

Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 509 - 532
Copyright
©2013 Cambridge University Press 

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