Abstract

Dense bacterial suspensions, which are examples of active systems, show spatiotemporal evolution that is reminiscent of flows in turbulent fluids. Hydrodynamical models have been developed to describe turbulence in dense, quasi-two-dimensional (2D) bacterial suspensions. This bacterial turbulence happens at a low Reynolds number as opposed to fluid turbulence that happens at a high Reynolds number. In this talk first I will discuss the Toner-Tu-Swift-Hohenberg (TTSH) model to describe the dynamics of dense bacterial suspensions, which we derive from the Navier-Stokes equation. In the latter part, I will discuss the recent results which we have got by solving numerically this TTSH model equation. We carry out extensive direct numerical simulations of Lagrangian tracer particles that are advected by the velocity field in this model. We demonstrate how the statistical properties of these particles help us to uncover an important, qualitative way in which irreversibility in bacterial turbulence is different from its fluid-turbulence counterpart: For large but negative (or large and positive) values of the activity (or friction) parameter, the probability distribution functions of energy increments, along tracer trajectories, or the power are positively skewed; so irreversibility in bacterial turbulence can lead, on average, to particles gaining energy faster than they lose it, which is the exact opposite of what is observed for tracers in 2D fluid turbulence.