Collège de France
A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov’s E(q) ~ q^-5/3 scaling of the kinetic energy spectrum of inertial turbulence with the wave vector q. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling E(q) ~ 1/q at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-ranged velocity correlations, which lead to the scaling behavior.
We discuss two examples of active turbulent fluids: tissue monolayers studied in the group of P. Silberzan at Institut Curie and active nematic layers studied in the group of F. Sagues in Barcelona.