Enhanced Activity Reduces the Duration of Intermittent L\'evy Walks in Bacterial Turbulence

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. In contrast to inertial turbulence, understanding the microscopic dynamics of bacterial fluid elements undergoing collective motion is in its incipient stages. Here, we report experiments revealing correlations between the microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our detailed analysis of the passive tracers and the velocity field of the bacterial suspensions allowed us to systematically correlate the Lagrangian and the Eulerian perspectives. Bacteria within the collective dynamics revealed initial ballistic dynamics followed by intermittent L\'evy walk before the eventual decay to random Gaussian fluctuations. Intriguingly, the persistence length and time of the fluid motion decrease with an increase in the activity, which, in turn, reduces the duration of L\'evy walk. Our results reveal transitions in microscopic dynamics underlying the bacterial turbulence and their control via the intrinsic time scales set by the effective activity of the flow.