Lagrangian structure and stretching in bacterial turbulence

In active matter systems, dense nematic suspensions of self-propelled agents spontaneously exhibit large-scale, chaotic flow structures. Descriptions of the dynamics of these systems 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 a model bacterium (Bacillus subtilis). High-resolution velocity fields are measured using particle image velocimetry across a range of bacterial swimming speeds and cell densities. We quantify the kinematic deformations of these flows through the Lagrangian stretching field to visualize the induced stretching and folding, characteristic of mixing. Close inspection of the finite-time Lyapunov exponent (FTLE) field reveals for the first time swimming-speed dependent FTLE-distribution transitions reminiscent of intermittent dynamics in classical chaotic dynamical systems.