Stationary states, Fluctuation-Dissipation Theorem and effective temperature in a turbulent von Karman flow

A vet unanswered question in statistical physics is whether stationary out-of-equilibrium systems share any resemblance with classical equilibrium systems. A good paradigm to explore this question is offered by turbulent flows. Incompressible flows subject to statistically stationary forcing generally reach a kind of equilibrium (in the statistical sense), independent of the initial conditions. Description of turbulence with tools borrowed from statistical mechanics is a long-standing dream, starting with Onsager. In 2D, equilibrium states of the Navier-Stokes equations have been classified through statistical mechanics principle by Robert and his collaborators [6; 1]. More recent advances have been done for 3D axisymmetric flows (an intermediate situation between 2D and 3D) by Leprovost et al. [2]. In the following, we present results obtained within this framework for a von Karman flow.