24. Pauli Colloquium/Kolloquium der Forschungsplattform MMM on "Irreversibility and Singularities in Turbulence":
Bérengère Dubrulle (CNRS)
Location: HS11 (2nd floor), Fak.Math. OMP1, Uni Wien

Tue, 29. Aug (Opening: 9:30)  Tue, 29. Aug 23


Topics:
1) 9h30  9h35: Introduction: Norbert J. Mauser (U. Wien & WPI & CNRS)
2) 9h35  10h25: Bérengère Dubrulle (CNRS) :
«Irreversibility and Singularities in Turbulence»
3) 10h25  10h55: Coffee, Tea & Cake

Organisation(s)
Wolfgang Pauli Institut
Inst.CNRS Pauli
Research Platform “MathematicsMagnetismMaterials” (MMM) Univ. Wien 
Organiser(s)
Norbert J. Mauser (WPI c/o MMM Univ. Wien & CNRS) 

Remark: Click here for further information
 
Abstract:
In a viscous fluid, the energy dissipation is the signature of the breaking of the timereversal
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 nondimensional energy dissipation per unit mass becomes
independent of the viscosity, meaning that the timereversal 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 NavierStokes equations, a modification of the NavierStokes equation suggested by G.
Gallavotti [2] to ensure energy conservation and relevance of statistical physics interpretation. I
then discuss a mechanism of the TSB in NavierStokes was first suggested by L. Onsager in 1949
[3], in which quasisingularities or singularities create a nonviscous dissipation. I exhibit the tools
to track these quasisingularities. 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.
[1] G. Costa et al, PRE, submitted, (2023)
[2] G. Gallavotti, Physics Letters A, 223, 91 (1996)
[3] L. Onsager , Il Nuovo Cimento, 6, 279 (1949)
[4] V. Shukla et al, PRE, 100, 043104 (2019