ATMOSPHERE JET DYNAMICS

Strong jets dominate the large scale dynamics of most atmospheres, for instance the jet streams of Earth's atmosphere or zonal jets on gas giant planets like Jupiter or Saturn. The main question is how do atmosphere jets form and what is their fluctuation statistics (internal variability). The average velocity profile is the result of a balance between Reynolds stresses (convergence of eddy momentum flux), on one hand, and dissipation, on the other hand. We are involved in the study of several fundamental aspects of atmosphere jet dynamics. We have specifically studied regimes for which a time scale separation exists between inertial dynamics ,on one hand, and friction and forcing, on the other hand. Such regimes where very steady zonal jets do form is relevant for instance for Jupiter. In those regimes we have addressed the theoretical and mathematical aspects of the validity of a kinetic theory approach that provides a natural closure, also referred as SSST or second order cumulant expansion. Another important question we have addressed is the very long time internal variability, possibly related to abrupt transition between different attractors characterized by the number of jets. Current and past projects include:

a) Kinetic theory of zonal jet dynamics
b) Rare transitions for zonal jet dynamics

Some of our recent researches on zonal jets (the ones related to equilibrium and kinetic theory) have been summarized in two chapter of a book entitled "Zonal Flows", edited by Boris Galperin, and to be published by Cambridge University Press. This books gathers an international team of specialists of all aspects of zonal jets: observations, numerical, and theoretical approaches, for Earth atmosphere, ocean, and Jovian zonal jets. These two chapters can be found here:

F. BOUCHET, and A. VENAILLE, Zonal flows as statistical equilibria, HAL, [.pdf]

F. BOUCHET, C. NARDINI AND T. TANGARIFE, Kinetic theory and quasilinear theories of jet dynamics, HAL, [.pdf]

Kinetic theory of zonal jet dynamics

We have engaged in a series of works aimed at proving the validity of a kinetic theory approach to zonal jet dynamics in the inertial limit with a time scale separation between inertial dynamics, on one hand, and forcing and dissipation, on the other hand. This very difficult mathematical challenge is only partially completed. It started with preliminary theoretical works on the inviscid relaxation of the 2D Euler equations (.pdf). The main results are the proper definition of the inertial limit, the proofs of self-consistency for the kinetic approach for quasi-geostrophic dynamics (.pdf), the discussion of ergodicity for the stochastic averaging approach (see chapter 5.3.3. of T. Tangarife PhD manuscript, .pdf) and the description of Reynolds stress fluctuations and Reynolds stress large deviations T. Tangarife PhD manuscript, (.pdf).

Please see also some statistical mechanics aspects of kinetic theory.

Some aspects of the kinetic theory of zonal jet dynamics are covered in the lectures given at Leuven's university, others in the seminar Large deviation theory for atmosphere jets (Seminar given during the Workshop on Instantons and Extreme Events in Turbulence and Dynamical Systems, held at Rio de Janeiro in December 2015 [movie] [slides] )

Rare transitions for zonal jet dynamics

Jupiter has experienced in the past, the sudden disappearance of one of its zonal jets. What is the probability of such a sudden climate change for Jupiter's troposphere? Are similar events relevant for Earth's climate. What are the scientific approach to such fascinating events? You can learn more following the abrupt climate change link, or reading some preliminary theoretical development in T. Tangarife PhD manuscript, (.pdf)., or watching the seminar "Large deviation theory for atmosphere jets" below. This is also related to the large deviation theory and rare events link.

Large deviation theory for atmosphere jets: Seminar given during the Workshop on Instantons and Extreme Events in Turbulence and Dynamical Systems, held at Rio de Janeiro in December 2015 [movie] [slides]

Freddy BOUCHET - ENS de Lyon and CNRS

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