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

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...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 860; pp. 577 - 607
Main Authors Woillez, E., Bouchet, F.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 10.02.2019
Subjects
Asymptotic series
Barotropic mode
Computation
Curvature
Dynamics
Eddies
Eigenvalues
Energy
Equilibrium
Frameworks
Injection
Jets
JFM Papers
Mathematical models
Reynolds stresses
Spin dynamics
Stochasticity
Theory
Turbulent jets
Velocity
Velocity distribution
Vortices
atmospheric flows
turbulence theory
geostrophic turbulence
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2018.877