**Bérengère Dubrulle**

Centre national de la recherche scientifique

**August 13, 2009**

**Foothills Laboratory 2, Room 1022**

**Lecture 3:30pm**

### Statistical Mechanics of Axisymmetric Turbulence: Theory and Experiments

A turbulent flow is characterized by a very large number of degrees of freedom which sets a number of practical challenges for simulations and models. A long standing dream in turbulence theory is to devise a "statistical mechanics" of turbulence, enabling the identification of a few macroscopic global quantities (analog of temperature, pressure in kinetic theory) describing the flow, thereby describing the effective complexity of turbulence.

In my talk, I present such a theory, based on recent theoretical breakthrough by Robert and Sommeria. Specifically, I derive the conservation laws of an axisymmetric turbulent flow and a mixing entropy characterizing the probability distribution of the turbulent velocity. Then, using standard tools of statistical mechanics, I derive the corresponding Gibbs distributions, the equilibrium states and fluctuations around them. I show that the equilibrium states are multi-stable and discuss the possible transitions between them. The theoretical predictions are compared with experimental fields, and a good agreement is found. I discuss the prespectives in terms of turbulence models and effective numerical simulations.