title: Time-reversal-symmetry breaking in turbulence.
abstract: In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis, and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as t^{3}. We also find the geometric deformation of material volumes, defined by four points spanning an initially regular tetrahedron, to show sensitivity to the time reversal with an effect growing linearly in t. We associate this with the structure of the strain rate in the flow.
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.
authors.forename: Jennifer
authors.initials: J
authors.lastname: Jucha
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.
authors.forename: Haitao
authors.initials: H
authors.lastname: Xu
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany and Ecole Normale Supérieure de Lyon and CNRS, 69007 Lyon, France.
authors.forename: Alain
authors.initials: A
authors.lastname: Pumir
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, 37077 Göttingen, Germany and Laboratory of Atomic and Solids State Physics and Sibley School for Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Eberhard
authors.initials: E
authors.lastname: Bodenschatz