Multi-time structure functions and the Lagrangian scaling of turbulence

TL;DR

This paper introduces multi-time Lagrangian structure functions to better understand turbulence, revealing distinct scaling ranges and showing that intermittency is independent of large-scale flow effects, applicable across various flow conditions.

Contribution

The study defines and characterizes multi-time Lagrangian structure functions, demonstrating their effectiveness in separating scaling ranges and analyzing turbulence without prior flow knowledge.

Findings

Multi-time structure functions reduce large-scale contamination in inertial range analysis.

Identified a specific time scale where mean flow effects dominate.

Lagrangian intermittency is independent of large-scale flow effects.

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.