Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-14T16:07:40.405Z Has data issue: false hasContentIssue false
  • English
  • Français

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: ludivine.oruba@ens.fr, pad3@cam.ac.uk, emmanuel.dormy@ens.fr
†Email addresses for correspondence: ludivine.oruba@ens.fr, pad3@cam.ac.uk, emmanuel.dormy@ens.fr
†Email addresses for correspondence: ludivine.oruba@ens.fr, pad3@cam.ac.uk, emmanuel.dormy@ens.fr
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.Google Scholar
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover; first printed by Clarendon Press, 1961.Google Scholar
Davidson, P. A. 2013 Turbulence in Rotating, Stratified and Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Drazin, P. G. 2002 Introduction to Hydrodynamic Stability. Cambridge University Press.Google Scholar
Frank, W. M. 1977 The structure and energetics of the tropical cyclone I. Storm structure. Mon. Weath. Rev. 105, 1119.2.0.CO;2>CrossRefGoogle Scholar
Guervilly, C., Hughes, D. W. & Jones, C. A. 2014 Large-scale vortices in rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 758, 407–435.CrossRefGoogle Scholar
Lugt, H. J. 1983 Vortex Flow in Nature and Technology. Wiley.Google Scholar
Pearce, R. 2005a Why must hurricanes have eyes? Weather 60 (1), 19–24.Google Scholar
Pearce, R. 2005b Comments on ‘Why must hurricanes have eyes?’ revisited. Weather 60 (11), 329–330.Google Scholar
Rasmussen, E. A. & Turner, J. 2003 Polar Lows, Mesoscale Weather Systems in the Polar Regions. Cambridge University Press.CrossRefGoogle Scholar
Smith, R. K. 2005 ‘Why must hurricanes have eyes?’ revisited. Weather 60 (11), 326–328.Google Scholar