Lagrangian structure and stretching in bacterial turbulence

Dense suspensions of active, self-propelled agents spontaneously exhibit large-scale, chaotic flow structures. Descriptions of their dynamics have predominately focused on characterization of spatiotemporal correlation of the velocity field, but their transport and mixing properties remain largely unknown. In this work, we use Lagrangian analysis techniques to study the chaotic flow fields generated by "bacterial turbulence'" in dense suspensions of Bacillus subtilis. High-resolution velocity fields are simultaneously measured along with individual tracer and cell trajectories across a range of bacterial swimming speeds. The flow kinematics are quantified through the Lagrangian stretching field and used to characterize the mixing induced by the stretching and folding of the active bacterial colony. The distribution of the finite-time Lyapunov exponent (FTLE) field reveals swimming-speed dependent transitions reminiscent of intermittent dynamics in classical chaotic dynamical systems. Finally, measured trajectories of both passive beads and individual swimming cells directly demonstrate how the striking active Lagrangian flow structures regulate transport in bacterial turbulence.