Multi-time structure functions and the Lagrangian scaling of turbulence

Abstract

We define and characterize multi-time Lagrangian structure functions using data stemming from two swirling flows with mean flow and turbulent fluctuations: A Taylor-Green numerical flow, and a von K\'arm\'an laboratory experiment. Data is obtained from numerical integration of tracers in the former case, and from three-dimensional particle tracking velocimetry measurements in the latter. Multi-time statistics are shown to decrease the contamination of large scales in the inertial range scaling. A time scale at which contamination from the mean flow becomes dominant is identified, with this scale separating two different Lagrangian scaling ranges. The results from the multi-time structure functions also indicate that Lagrangian intermittency is not a result of large-scale flow effects. The multi-time Lagrangian structure functions can be used without prior knowledge of the forcing mechanisms or boundary conditions, allowing their application in different flow geometries.