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The catalytic role of the beta effect in barotropization processes

Published online by Cambridge University Press:  29 August 2012

A. Venaille ,
G. K. Vallis  and
S. M. Griffies
A. Venaille*
Affiliation:
NOAA, GFDL, AOS Program, Princeton University, NJ 08540, USA Laboratoire de Physique, ENS-Lyon, 69007 Lyon, France
G. K. Vallis
Affiliation:
NOAA, GFDL, AOS Program, Princeton University, NJ 08540, USA
S. M. Griffies
Affiliation:
NOAA, GFDL, AOS Program, Princeton University, NJ 08540, USA
*
†Email address for correspondence: antoine.venaille@ens-lyon.org
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Abstract

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e. the tendency to reach the gravest vertical mode. The peculiar role of the effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropization may be partially parameterized using the Rhines scale . As this parameter decreases ( increases) then barotropization can progress further, because the term provides enstrophy to each layer. However, if the effect is too large then the statistical mechanical predictions fail and wave dynamics prevent complete barotropization.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Quasi-geostrophic flows Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 490 - 515
Copyright
Copyright © Cambridge University Press 2012

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