Inertial Range Scaling in Rotations of Long Rods in Turbulence

TL;DR

This study investigates how long neutrally buoyant rods rotate in turbulence, revealing a specific scaling law for their rotation rates in the inertial range and linking their dynamics to flow structures at different scales.

Contribution

We derive and experimentally verify a scaling law for the mean square rotation rate of long rods in turbulence, connecting their rotation to flow structures across scales.

Findings

Mean square rotation rate scales as l^{-4/3} in the inertial range.

Rotation autocorrelation time matches eddy turnover time at rod scale.

Rotational measurements provide insights into flow structure at various scales.

Abstract

We measure the rotational statistics of neutrally buoyant rods with lengths $2.8 < l/\eta <72.9 $ in turbulence. For particles with length in the inertial range, we derive a scaling relationship for the mean square rotation rate, $< \dot{p}_i \dot{p}_i > \propto l^{-4/3}$ and show that measurements approach this scaling. Deviations from the proposed scaling are explained as the effect of dissipation range scales. The correlation time of the Lagrangian autocorrelation of rod rotation rate scales as the turn over time of eddies of the size of the rod. Measuring rotational dynamics of single long rods provides a new way to access the spatial structure of the flow at different length scales.