On velocity alignment and time reversal symmetry breaking in turbulence

When fluids are forced at high Reynolds numbers, turbulence typically emerges. According to the Richardson-Kolmogorov cascade theory, kinetic energy injected at large scales cascades down to dissipative scales where it is converted into heat. This energy flux breaks time reversal symmetry, rendering turbulence irreversible. To sustain dissipation, the flow self-organizes into structures that preferentially transfer energy across scales, so time asymmetry appears in various statistical measures. A particular example is pair dispersion: flow tracers starting close by each other separate over time, but their separation is approximately 1.5 times faster when the flow is played backward as compared to forward in time. The mechanisms linking this irreversibility to the underlying flow structure, however, remain poorly understood.

In this work, we propose decomposing tracer separation into two components: the relative speed between tracers and the alignment between their velocity difference and separation vector. Both components are necessary for dispersion, raising the question of which drives time asymmetry. Using direct numerical simulation results, we show that irreversibility arises solely from alignment differences—not from speed. The two components are correlated, however, due to the nature of the separation process itself. These findings thus provide a kinematic link between flow structure and time reversal symmetry breaking in turbulence.