Eulerian versus Lagrangian irreversibility in an experimental turbulent von Karman flow
In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. To understand the physical origin of this mechanism, one needs to define an equivalent of the order parameter that allows to trace the time irreversibility locally in space and time. Recently, two different local indicators of time-irreversibility have been suggested:
1. an Eulerian one, based on regularity properties of the velocity field (Duchon & Robert 2000);
2. a Lagrangian one, based on symmetry properties of the trajectories under time reversal (Drivas 2019).
A proof that the two indicators are equivalent was given in (Drivas 2019). In this talk, I will test the equivalence of the two indicators in a turbulent Von Karman experiment in our facility at CEA. The flow is generated by two counter-rotating impellers fitted with blades. Thanks to a high resolution 4D-PTV technique (Ostovan 2019), we obtain time-resolved Lagrangian trajectories and Eulerian velocity measurements, at a resolution of the order of the Kolmogorov scale. We use these measurements to compare Eulerian and Lagrangian signatures of irreversibility and link them with peculiar properties of the local velocity field or trajectories.
