Active Turbulence - Statistical Analysis*

An active suspension consists of a fluid, usually Newtonian, and a large number of active particles. The latter term describes objects which exert a force onto the surrounding fluid and propel themselves through the suspension. At specific particle densities the emerging patterns of an active suspension at low Reynolds numbers show similarities to turbulence, leading to the term "active turbulence". 

We show simulation results for an active suspension, obtained with the fluid-particle solver module of the BoSSS framework  (https://github.com/FDYdarmstadt/BoSSS). Position, orientation and velocity data are used to calculate probability density functions (PDF) describing the statistics of the active suspension.  These data are compared to theoretical results, which are based on the infinite hierarchy of PDF-equations, derived in Deußen et al. (Phys. Fluids, 33, 061902, 2021). We derive Lie symmetries for the PDF-equations, which are then used to obtain group invariant solutions. Comparing the simulation data to the solutions connects the observed turbulent phenomenons to the underlying theory and, subsequently, contributes to the understanding of active suspensions.