Date:

Wed, 23/06/202112:00-13:30

See also: Nonlinear Seminar

**Bérengère Dubrulle, SPEC, CNRS, CEA Saclay, Université Paris-Saclay**

*Lecturer:*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.