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This thesis deals with the dynamics of geophysical turbulent flows at large scales, more particularly their organization into east-west parallel flows (zonal jets). These structures have the particularity to evolve much slower than the surrounding turbulence. Besides, over long time scales, abrupt transitions between different configurations of zonal jets are observed in some cases (multistability). Our approach consists in averaging the effect of fast turbulent degrees of freedom in order to obtain an effective description of the large scales of the flow, using stochastic averaging and the theory of large deviations. These tools provide theattractors, the typical fluctuations and the large fluctuations of jet dynamics. This allows to go beyond previous studies, which only describe the average jet dynamics. Our first result is an effective equation for the slow dynamics of jets, the validityof this equation is studied from a theoretical point of view, and the physical consequences are discussed. In order to describe the statistics of rare events such as abrupt transitions between different jet configurations, tools from large deviation theory are employed. Original methods are developped in order to implement this theory, those methods can be applied for instance in situations of multistability., Cette thèse porte sur la dynamique des grandes échelles des écoulements géophysiques turbulents, en particulier sur leur organisation en écoulements parallèles orientés dans la direction est-ouest (jets zonaux). Ces structures ont la particularité d'évoluer sur des périodes beaucoup plus longues que la turbulence qui les entoure. D'autre part, on observe dans certains cas, sur ces échelles de temps longues, des transitions brutales entre différentes configurations des jets zonaux (multistabilité). L'approche proposée dans cette thèse consiste à moyenner l'effet des degrés de liberté turbulents rapides de manière à obtenir une description effective des grandes échelles spatiales de l'écoulement, en utilisant les outils de moyennisation stochastique et la théorie des grandes déviations. Ces outils permettent d'étudier à la fois les attracteurs, les fluctuations typiques et les fluctuations extrêmes de la dynamique des jets. Cela permet d'aller au-delà des approches antérieures, qui ne décrivent que le comportement moyen des jets.Le premier résultat est une équation effective pour la dynamique lente des jets, la validité de cette équation est étudiée d'un point de vue théorique, et les conséquences physiques sont discutées. De manière à décrire la statistique des évènements rares tels que les transitions brutales entre différentes configurations des jets, des outils issus de la théorie des grandes déviations sont employés. Des méthodes originales sont développées pour mettre en œuvre cette théorie, ces méthodes peuvent par exemple être appliquées à des situations de multistabilité.

International audience; Two-dimensional and geophysical turbulent flows have the property to self organize and create large scale coherent jets and vortices. This is for instance one of the major processes for the dynamics of Earth's atmosphere. Following On-sager initial insight, based on conjugated works by mathematicians and physicists, this fundamental physical process has found some explanations in the framework of statistical mechanics. An important step, initiated twenty years ago, has been the study of the equilibrium statistical mechanics for the 2D Euler and the related quasi-geostrophic models (the Miller-Robert-Sommeria theory). Real geophysical and experimental flows are however dissipative and maintained by external forces. These lectures focus on recent theoretical development of the statistical mechanics of those non-equilibrium situations. Those progresses have been achieved using tools from field theory (path integrals and instantons), non-equilibrium statistical mechanics (large deviations, stochastic averaging). The aim of these lectures is to briefly introduce the theoretical aspects of this program in the simplest context: the 2D stochastic Euler or Navier-Stokes equations and the quasi-geostrophic equations. We review path integral representations of stochastic processes, large deviations for transition probabilities, action minimization, instanton theory, for general mechanical systems forced by random forces. We will apply this framework in order to predict equilibrium and non-equilibrium phase transitions for the 2D Euler, Navier-Stokes, and quasi-geostrophic dynamics, and to predict the rates of rare transitions between two attractors in situations of first order phase transitions. Kinetic theory of systems with long range interactions, both with and without stochastic external forces, are explained. Based on this kinetic theory, we predict non-equilibrium phase transitions, and discuss their recent experimental observations and numerical simulations. Even if the model we have considered so far are too simple academic models, the expected relevance of those approaches in the future for Earth atmosphere and climate dynamics is briefly discussed.