Inertial Range Scaling in Rotations of Long Rods in Turbulence

We derive a scaling relationship for the mean square rotation rate of rods with lengths in the inertial range in turbulence: <(p)over dot(i)(p)over dot(i)> proportional to l(-4/3). We present experimental measurements of the rotational statistics of neutrally buoyant rods with lengths 2.8 < l/eta < 72.9, and find that the measurements approach the predicted scaling. The approach to inertial range scaling is shown to be more complex than anticipated with an overshoot and approach to the scaling from above. For all rod lengths, the correlation time of the Lagrangian autocorrelation of the rotation rate scales as the turnover time of the 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.