MERCREDI 10 JUIN 2009
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Freddy Bouchet
INLN, Nice Sophia-Antipolis

Title: Out of equilibrium statistical mechanics and phase transitions
for the large scales of 2D and geophysical turbulence

Abstract: We consider two dimensionnal or geophysical flows driven out
of equilibrium by stochastic forces. When these are balanced with
linear dissipation one reaches non equilibrium statistically
stationary states (NESS), without detailed balance. We discuss theses
examples from a statistical mechanics point of view: for instance we
discuss the existence of out of equilibrium phase transitions, or
consider kinetic theory approaches.

For the two-dimensional Navier-Stokes equations with weak stochastic
forcing and dissipation, the existence of an invariant measure has
been mathematically proved recently, together with mixing and ergodic
properties. This problem has however never been considered from a
physical point of view. We thus address the following issues: when is
the measure concentrated on an inertial equilibrium, how are the large
scales selected by the forcing, what is the level of the fluctuations?

The most striking result is the existence of out of equilibrium phase
transitions. One observe transitions from one type of flow
(unidirectional) to an other one (dipole), at random time. This is
similar to the classical two wheel potential with noise. By contrast,
in our case, no such potential exists and the turbulent nature of the
flow (infinite number of degrees of freedom) renders the phenomena
much richer. Analogies with the Earth magnetic field reversal, and
with similar phenomena in experiment of two dimensionnal and
geophysical flows will be discussed.

The approach of these phenomena using kinetic theory will be
discussed. This is the most natural way for a theory for the self
organized jets of geophysical turbulence, for instance in Jovian
atmospheres. We prove new results for the linearized Euler and
Navier-Stokes equations with random forces, and their relations to
turbulent fluctuations.