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Accueil > Actualités > Séminaires > Séminaires 2022

Mardi 19 Avril 11h00 - LEGI Salle K118

Adam Cheminet, CEA SPEC SPHYNX

Title : Towards a link between time-irreversibility and singularity in turbulent flows

Contact : Nathanael Machicoane

Abstract : In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. Recently, Drivas [Drivas, 2019] proved the equivalence of two different local indicators of time-irreversibility : i) an Eulerian one, based on regularity properties of the velocity field [Duchon and Robert, 1999] ; ii) a Lagrangian one, based on symmetry properties of the trajectories under time reversal [Jucha et al., 2014].

Drivas [Drivas, 2019], rigorously proved that under suitable limits, the Eulerian and Lagrangian irreversibility indicators converge to the same quantity epsilon, the local energy dissipation. This result is interesting because it provides two different indicators, one Eulerian, and one Lagrangian, that discriminate between regions where the fluid is or is not time-irreversible. By tracking dynamically in time and space such regions, one may then get hints of the physical processes that are responsible for the symmetry breaking.

In this talk, I will first test the equivalence of the two indicators in an experimental turbulent Von Kármán flow at a resolution of the order of the Kolmogorov scale using a high-resolution 4D-PTV technique. I will then use the equivalence to perform a joined Eulerian-Lagrangian exploration of the dynamics leading to time irreversibility, and find that it is linked with vortex interaction, suggesting a link between irreversibility and singularity (Figure 1).

Figure 1 : 3D visualization of Eulerian irreversiblity iso-surfaces (in red) and highly irreversible trajectories selected from the Lagrangian criterion in black (positive) and blue (negative).

[Drivas, 2019] Drivas, T. D. (2019). Turbulent cascade direction and lagrangian time-asymmetry. Journal of Nonlinear Science, 29(1):65–88.
[Duchon and Robert, 1999] Duchon, J. and Robert, R. (1999). Inertial energy dissipation for weak solutions of incompressible euler and navier-stokes equations. Nonlinearity, 13(1):249–255.
[Jucha et al., 2014] Jucha, J., Xu, H., Pumir, A., and Bodenschatz, E. (2014). Time-reversal-symmetry breaking in turbulence. Phys. Rev. Lett., 113:054501.