Bacteria collective motion is scale-free

Abstract: Suspensions of swimming bacteria interact hydrodynamically over long ranges, organizing themselves into collective states that drive large-scale chaotic flows, often referred to as "bacterial turbulence". Despite extensive experimental and theoretical work, it remains unclear whether an intrinsic length scale underlies the observed patterns. To shed light on the mechanism driving active turbulence, we investigate the emergence of large-scale flows in E. coli suspensions confined within cylindrical chambers, systematically varying confinement height over more than two orders of magnitude. We first demonstrate that the critical density for the onset of collective motion scales inversely with this confinement height without saturation, even for the smallest densities observed. Near the onset, both the observed length and time scales increase sharply, with the length scale bounded only by the vertical confinement. Importantly, both scales exhibit clear power-law dependence on the confinement height, demonstrating the absence of an intrinsic length scale in bacterial collective motion. This holds up to scales nearly 10,000 times the size of a single bacterium, as evidenced by transient coherent vortices spanning the full chamber width near the onset. Our experimental results demonstrating that bacterial turbulence is scale-free provide important constraints for theories aiming to capture the dynamics of wet active matter.