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Eye formation in rotating convection

Published online by Cambridge University Press:  06 January 2017

L. Oruba ,
P. A. Davidson  and
E. Dormy
L. Oruba*
Affiliation:
Physics Department, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
P. A. Davidson*
Affiliation:
Engineering Department, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
E. Dormy*
Affiliation:
Department of Mathematics and Applications, CNRS UMR 8553, Ecole Normale Supérieure, 45 rue d’Ulm, 75005 Paris, France
*
†Email addresses for correspondence: [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected]
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Abstract

We consider rotating convection in a shallow, cylindrical domain. We examine the conditions under which the resulting vortex develops an eye at its core; that is, a region where the poloidal flow reverses and the angular momentum is low. For simplicity, we restrict ourselves to steady, axisymmetric flows in a Boussinesq fluid. Our numerical experiments show that, in such systems, an eye forms as a passive response to the development of a so-called eyewall, a conical annulus of intense, negative azimuthal vorticity that can form near the axis and separates the eye from the primary vortex. We also observe that the vorticity in the eyewall comes from the lower boundary layer, and relies on the fact the poloidal flow strips negative vorticity out of the boundary layer and carries it up into the fluid above as it turns upward near the axis. This process is effective only if the Reynolds number is sufficiently high for the advection of vorticity to dominate over diffusion. Finally we observe that, in the vicinity of the eye and the eyewall, the buoyancy and Coriolis forces are negligible, and so although these forces are crucial to driving and shaping the primary vortex, they play no direct role in eye formation in a Boussinesq fluid.

JFM classification

Geophysical and Geological Flows: Rotating flows Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 890 - 904
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Copyright
© 2017 Cambridge University Press 

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