Scaling regimes of active turbulence with external dissipation

Abstract

Active fluids exhibit complex turbulent-like flows at low Reynolds number. Recent work predicted that 2d active nematic turbulence follows universal scaling laws. However, experimentally testing these predictions is conditioned by the coupling to the 3d environment. Here, we measure the spectrum of the kinetic energy, $E(q)$, in an active nematic film in contact with a passive oil layer. At small and intermediate scales, we find the scaling regimes $E(q)\sim q^{-4}$ and $E(q)\sim q^{-1}$, respectively, in agreement with the theoretical prediction for 2d active nematics. At large scales, however, we find a new scaling $E(q)\sim q$, which emerges when the dissipation is dominated by the 3d oil layer. In addition, we derive an explicit expression for the spectrum that spans all length scales, thus explaining and connecting the different scaling regimes. This allows us to fit the data and extract the length scale that controls the crossover to the new large-scale regime, which we tune by varying the oil viscosity. Overall, our work experimentally demonstrates the emergence of universal scaling laws in active turbulence, and it establishes how the spectrum is affected by external dissipation.