  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.
