Lagrangian time scale of rotation for inertial fibers in isotropic turbulence

TL;DR

This paper investigates the autocorrelation of inertial fibers' tumbling rate in turbulence, proposing models that predict correlation time and variance based on fiber length and inertia, validated through experiments.

Contribution

It introduces a simple model incorporating fiber inertia and viscous torque to predict tumbling dynamics in turbulence, extending understanding beyond inertia-free cases.

Findings

Correlation time predicted by Kolmogorov scaling for non-inertial fibers.

Model accurately predicts correlation time and tumbling rate variance for inertial fibers.

Experimental validation confirms the model's effectiveness.

Abstract

Using time-resolved measurements of the orientation of rigid inertial fibers in a turbulence-tank, we investigate the autocorrelation of their tumbling rate. The correlation time ($\tau_d$) is well predicted by Kolmogorov inertial-range scaling based on the fiber length (L) when the fiber inertia can be neglected. For inertial fibers, we propose a simple model considering fiber inertia (measured by a tumbling Stokes number) and a viscous torque which accurately predicts both the correlation time and the variance of the tumbling rate.