Time-symmetry breaking in turbulence

TL;DR

This paper investigates the breaking of time symmetry in three-dimensional turbulence by analyzing Lagrangian particle dispersion, revealing that energy flux causes asymmetrical separation rates and volume deformation growth over short times.

Contribution

It introduces a combined analytical, numerical, and experimental approach to quantify time-symmetry breaking in turbulence through Lagrangian tracer analysis.

Findings

Particles separate slower forward than backward at short times.

The difference in dispersion grows as t^3.

Volume deformation sensitivity grows linearly with time.

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, surrogated 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.