Three-dimensional active turbulence in microswimmer suspensions: simulations and modelling

Abstract: Active turbulence is a paradigmatic and fascinating example of self-organized motion at large scales occurring in active matter. We employ massive hydrodynamic simulations of suspensions of resolved model microswimmers to tackle the phenomenon in semi-dilute conditions at a mesoscopic level. We measure the kinetic energy spectrum and we detect a $k^{-3}$ power law regime. The velocity distributions are of L\'evy type, a distinct difference with inertial turbulence. Furthermore, we propose a reduced order dynamical deterministic model for active turbulence, inspired to shell models for classical turbulence, whose numerical and analytical study confirms the spectrum powerlaw observed in the simulations and reveals hints of a non-Gaussian, intermittent, physics of active turbulence. Direct numerical simulations and modelling also agree in pointing to a phenomenological picture whereby, in the absence of an energy cascade `a la Richardson forbidden by the low Reynolds number regime, it is the coupling between fluid velocity gradients and bacterial orientation that gives rise to a multiscale dynamics.