Collective behaviour in suspensions of microswimmers is often dominated by the impact of longranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to N = 3 × 10 6 ) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length-and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.Here, λ is the tumbling frequency by which individual swimmers randomise their swimming direction and κ is the stresslet magnitude, defined below. In order to probe the properties of J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-10 | 1 arXiv:1904.03069v2 [cond-mat.soft] 26 Aug 2019 J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-10 | 9

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