  We review progress that has been made to constructa theory for the jet
formation and maintenance in planetary atmospheres. The theory is built in the
regime where velocityfluctuations around the base jet are very small compared
to the zonaljet velocity itself. Such situations are frequent in many
naturaljets, for instance in the atmosphere of outer planets, the most
prominentexample being probably Jupiter's troposphere jets. As discussed
inother chapters of this book, fluctuations close to Jupiter zonaljets are
smaller than the zonal jets themselves. In such a regime, it is natural and
often justified to treat the non-zonalpart of the dynamics with a quasi-linear
approximation: at leadingorder the dynamics of the non-zonal flow is described
by theequation 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 sucha quasilinear
description of statistically stationary jets. The basicquestions are: when does
such an approach is expected to be valid,why, what are the limitations and the
expected errors done doing suchapproximations?
