Rotational diffusion of particles in turbulence

TL;DR

This study experimentally investigates how spherical and ellipsoidal particles rotate in turbulence, confirming that their angular velocity follows an Ornstein-Uhlenbeck process and enabling quantification of turbulent rotational diffusivity.

Contribution

The paper demonstrates that particle angular velocity in turbulence is well modeled by an Ornstein-Uhlenbeck process using stereoscopic PIV measurements.

Findings

Angular velocity statistics fit OU process predictions

Autocovariance decays exponentially as predicted

Quantification of turbulent rotational diffusivity

Abstract

Through laboratory measurements, we compare the rotation of spherical and ellipsoidal particles in homogeneous, isotropic turbulence. We find that the particles' angular velocity statistics are well described by an Ornstein-Uhlenbeck (OU) process. This theoretical model predicts that the Lagrangian autocovariance of particles' angular velocity will decay exponentially. We measure the autocovariance using stereoscopic particle image velocimetry (SPIV) applied to particles whose size is within the inertial subrange of the ambient turbulence. The SPIV resolves the motion of points interior to the particles, from which we calculate the solid body rotation of the particles. This provides us with the angular velocity time series for individual particles. Through ensemble statistics, we determine the autocovariance of angular velocity and confirm that it matches the form predicted by an OU process. We can further use the autocovariance curve to quantify the turbulent rotational diffusivity.