Universal scaling in defect-free active turbulence*

Active fluids exhibit turbulent flows at low Reynolds numbers. In active liquid crystals, these flows are strongly constrained by topological defects, whose density defines a characteristic length that prevents the scale invariance typical of turbulence. Here we show that, at zero Reynolds number, defect-free active nematics exhibit a new type of turbulence with a distinctive scaling regime at large length scales. The system self-organizes into a disordered spatiotemporal pattern of orientation domains with a characteristic wavelength selected by the nonlinear dynamics, at which the active energy injection is maximal. In contrast to inertial turbulence, the energy is entirely dissipated at the scale where it is injected, without energy transfer to other scales. Nevertheless, arbitrarily large flow vortices are generated by the instantaneous, long-range kernel of Stokes hydrodynamics. Hence, instead of the Kolmogorov ∼q^-5/3 scaling of inertial turbulence, the velocity power spectrum scales as ∼q^-1, with q being the wave number. Thus, in the absence of the screening effects due to topological defects, active nematic fluids exhibit turbulence without energy cascades and with a new universal scaling.