Anomalous diffusion and L\'evy walks distinguish active from inertial turbulence

TL;DR

This paper demonstrates that bacterial swarms exhibit super-diffusive behavior through Le9vy walks, revealing fundamental differences between active and inertial turbulence and uncovering new flow oscillations.

Contribution

It introduces a hydrodynamic model showing super-diffusion in active suspensions and links it to flow oscillations, distinguishing active from inertial turbulence.

Findings

Active turbulence exhibits super-diffusion via Le9vy walks.

Flow oscillations are linked to super-diffusive behavior.

Differences between active and inertial turbulence are clarified.

Abstract

Bacterial swarms display intriguing dynamical states like active turbulence. Using a hydrodynamic model we now show that such dense active suspensions manifest super-diffusion, via L\'evy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared-displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behaviour of microorganisms, our study underlines the essential differences between active and inertial turbulence.