Unconstrained Mesoscale Turbulence

In this chapter, we discuss the emerging dynamics of microswimmer suspensions described via the reduced minimal model. For now, we restrict ourselves to the unconstrained bulk flow case, i.e., for vanishing external field and without any effects of boundaries or obstacles. We first perform a linear stability analysis and, based on the results, derive amplitude equations to investigate possible emerging states. This method is very effective in treating regular spatiotemporal patterns, but fails to account for the instabilities induced by the nonlinear advection term. The latter instabilities lead to highly dynamic spatiotemporal flow patterns that have interesting consequences for the transport properties of microswimmer suspensions. Here, we borrow concepts from research on Navier–Stokes turbulence and particle transport in random fields to explain the observed phenomena.