How different are the worlds of high (inertial) and low (active) Reynolds number turbulence? Scaling, Universality, and Spottiness.

Active turbulence – the spatio-temporally complex motion of a dense suspension of microorganisms such as bacteria — has gathered great traction recently as an intriguing class of emergent, complex flows, occurring in several living systems at the mesoscale, whose understanding lies at the interface of non-equilibrium physics and biology. However, are these low Reynolds number living flows really turbulent or just chaotic with structural, or even superficial, similarities with high Reynolds number (classical) inanimate turbulence? In this talk we address these questions with a focus on the issues of (approximate) scale-invariance, intermittency and maximally chaotic states and how they lead to anomalous diffusion in bacterial suspensions. In particular, we show the existence of a critical level of activity beyond which the physics of bacterial flows become universal, accompanied by maximally chaotic states which allow for efficient, Levy-walk mediated foraging strategies. We then turn to the question of high Reynolds number, inertial turbulence and show that it is possible to construct local measures of multifractality. These measures show that fully developed turbulence is far from uniformly multifractal which suggests new ways to revisit the old problem of how flows may turn singular.