Lecturer: Bérengère Dubrulle, SPEC, CNRS, CEA Saclay, Université Paris-Saclay
    
Abstract:
In a viscous fluid, the energy dissipation is the signature of the breaking of the time-reversal
symmetry (hereafter TSB) t-> -t, u-> -u, where u is the velocity. This symmetry of the NavierStokes equations is explicitly broken by viscosity. Yet, in the limit of large Reynolds numbers,
when flow becomes turbulent, the non-dimensional energy dissipation per unit mass becomes
independent of the viscosity, meaning that the time-reversal symmetry is spontaneously broken.
Natural open questions related to such observation are: what is the mechanism of this
spontaneous symmetry breaking? Can we associate the resulting time irreversibility to
dynamical processes occurring in the flow? Can we devise tools to locally measure this time
irreversibility?
In this talk, I first show that the TSB is indeed akin to a spontaneous phase transition in the
Reversible Navier-Stokes equations, a modification of the Navier-Stokes equation suggested
by G. Gallavotti to ensure energy conservation and relevance of statistical physics
interpretation. I then discuss the mechanism of the TSB in Navier-Stokes via quasi-singularities
that create a non-viscous dissipation and exhibit the tools to track them. I apply them to time
and space-resolved Lagrangian and Eulerian velocity measurements in a turbulent von Karman
flow. I finally compare Eulerian and Lagrangian signatures of irreversibility, and link them with
peculiar properties of the local velocity field or trajectories.