Monday, October 2nd, 11h30, Room 454 A, Condorcet Building.

Bérengère DUBRULLE

Directeur de Recherche au CNRS,
CNRS , UMR 3680
SPHYNX
SPEC, CNRS, CEA Saclay, Université Paris-Saclay

Irreversibility and Singularities in Turbulence

Work in collaboration with S. Thalabard, V. Shukla, G. Krstulovic, S. Nazarenko and EXPLOIT team (P. Debue, V. Valori, T. Chaabo, A. Cheminet, Y. Ostovan Ch. Cuvier J-P. Laval, J-M Foucaut, C. Wiertel, V. Padilla, F. Daviaud).

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 Navier-Stokes 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 a mechanism of the TSB in Navier-Stokes was first suggested by L. Onsager in 1949, in which quasi-singularities or singularities create a non-viscous dissipation. I exhibit the tools to track these quasi-singularities. I show how the application of these tools  to velocity measurements in a turbulent swirling flow allows to detect Eulerian and Lagrangian signatures of irreversibility.  This enables me to evidence the structures that are responsible for irreversibility and associate them with peculiar properties of the local velocity field or trajectories.

References:

Cheminet et al, PRL, 129, 124501 (2022)

Costa et al, PRE, submitted, (2023)

Gallavotti, Physics Letters A, 223, 91 (1996)

Onsager , Il Nuovo Cimento, 6, 279 (1949)

Shukla et al, PRE, 100, 043104 (2019)

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