Kinetic theory and quasilinear theories of jet dynamics

F Bouchet (1) , C Nardini (1) , T Tangarife (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We review progress that has been made to construct a theory for the jet formation and maintenance in planetary atmospheres. The theory is built in the regime where velocity fluctuations around the base jet are very small compared to the zonal jet velocity itself. Such situations are frequent in many natural jets, for instance in the atmosphere of outer planets, the most prominent example being probably Jupiter's troposphere jets. As discussed in other chapters of this book, fluctuations close to Jupiter zonal jets are smaller than the zonal jets themselves. In such a regime, it is natural and often justified to treat the non-zonal part of the dynamics with a quasi-linear approximation: at leading order the dynamics of the non-zonal flow is described by the equation linearized close to the quasi-stationary zonal jets. The theory, based on a multi-scale method called stochastic averaging, share similarities with Stochastic Structural Stability Theory (S3T) and with second order closure (CE2), also discussed in other chapters of the book. The aim of this contribution is to discuss the theoretical aspects of such a quasilinear description of statistically stationary jets. The basic questions are: when does such an approach is expected to be valid, why, what are the limitations and the expected errors done doing such approximations?

Mots clés: Stochastic barotropic equations; Atmosphere dynamics; Stochastic 2D Navier Stokes equations; Averaging and homogenization; Stochastic partial differential equations; Turbulence; Geostrophic turbulence; Non-equilibrium steady states

Domaines: Dynamique des Fluides [physics.flu-dyn]; Mécanique statistique [cond-mat.stat-mech]; Géophysique [physics.geo-ph]

F Bouchet, C Nardini, T Tangarife. Kinetic theory and quasilinear theories of jet dynamics. 2014. ⟨hal-01266458v1⟩