Lagrangian Time Scale of Passive Rotation for Mesoscale Particles in Turbulence

Turbulence induces rotation in the living and the non-living materials in the ocean. The time scale of rotation for a living organism is important in understanding an organism's feeding efficiency, mating, prey capture rate etc. This time scale is also crucial for understanding the migration of non-living materials such as microplastics. Herein, we investigate the tumbling motion of mesoscale particles that resemble organisms of intermediate size, such as zooplankton that appear in the ocean. Using time-resolved measurements of the orientation of rigid inertial fibers in a turbulence-tank, we analyze 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. Our measurements and the theoretical model provide a basic understanding of the rotational response of an intermediately sized organism to the surrounding turbulence in its non-active state.