Eulerian vs Lagrangian Irreversibility in an Experimental Turbulent Swirling Flow

In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. Recently, Drivas [J. Nonlinear Sci. 29, 65 (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, Nonlinearity 13, 249 (2000).]; (ii) a Lagrangian one, based on symmetry properties of the trajectories under time reversal [Jucha et al.,Phys. Rev. Lett. 113, 054501 (2014).]. We test this equivalence in a turbulent Von Karman experiment at a resolution of the order of the Kolmogorov scale using a high resolution 4D-PTV technique. We use the equivalence to perform the first 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.