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Barotropic theory for the velocity profile of Jupiter’s turbulent jets: an example for an exact turbulent closure

Published online by Cambridge University Press:  07 December 2018

E. Woillez Open the ORCID record for E. Woillez [Opens in a new window]  and
F. Bouchet
E. Woillez
Affiliation:
Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
F. Bouchet*
Affiliation:
Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
*
†Email address for correspondence: freddy.bouchet@ens-lyon.fr
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Abstract

We model the dynamics of Jupiter’s jets by the stochastic barotropic $\unicode[STIX]{x1D6FD}$-plane model. In this simple framework, by analytic computation of the averaged effect of eddies, we obtain three new explicit results about the equilibrium structure of jets. First we obtain a very simple explicit relation between the Reynolds stresses, the energy injection rate and the averaged velocity shear. This predicts the averaged velocity profile far from the jet edges (extrema of zonal velocity). Our approach takes advantage of a time-scale separation between the inertial dynamics on one hand, and the spin-up (or spin-down) time on the other. Second, a specific asymptotic expansion close to the eastward jet extremum explains the formation of a cusp at the scale of energy injection, characterized by a curvature that is independent of the forcing spectrum. Finally, we derive equations that describe the evolution of the westward tip of the jets. The analysis of these equations is consistent with the previously discussed picture of barotropic adjustment, explaining the relation between the westward jet curvature and the $\unicode[STIX]{x1D6FD}$-effect. Our results give a consistent overall theory of the stationary velocity profile of inertial barotropic zonal jets, in the limit of small-scale forcing.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Geophysical and Geological Flows: Geostrophic turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 577 - 607
Copyright
© 2018 Cambridge University Press 

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