Effects of non-universal large scales on conditional structure functions in turbulence

TL;DR

This study measures how large-scale flow properties influence small-scale turbulence structures, revealing strong dependencies even in regions considered homogeneous, thus challenging assumptions of universality in turbulence modeling.

Contribution

It provides comprehensive experimental data on the impact of large-scale flow variations on small-scale turbulence structures in a controlled laboratory setting.

Findings

Structure functions depend strongly on large-scale velocity.

Dependence persists even in homogeneous regions.

Inhomogeneity signatures are evident near oscillating grids.

Abstract

We report measurements of conditional Eulerian and Lagrangian structure functions in order to assess the effects of non-universal properties of the large scales on the small scales in turbulence. We study a 1m $\times$ 1m $\times$ 1.5m flow between oscillating grids which produces $R_\lambda=285$ while containing regions of nearly homogeneous and highly inhomogeneous turbulence. Large data sets of three-dimensional tracer particle velocities have been collected using stereoscopic high speed cameras with real-time image compression technology. Eulerian and Lagrangian structure functions are measured in both homogeneous and inhomogeneous regions of the flow. We condition the structure functions on the instantaneous large scale velocity or on the grid phase. At all scales, the structure functions depend strongly on the large scale velocity, but are independent of the grid phase. We see clear signatures of inhomogeneity near the oscillating grids, but even in the homogeneous region in the center we see a surprisingly strong dependence on the large scale velocity that remains at all scales. Previous work has shown that similar correlations extend to very high Reynolds numbers. Comprehensive measurements of these effects in a laboratory flow provide a powerful tool for assessing the effects of shear, inhomogeneity and intermittency of the large scales on the small scales in turbulence.