  A landmark of turbulence is the emergence of universal scaling laws, such as
Kolmogorov's $E(q)\sim q^{-5/3}$ 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 $E(q)\sim
q^{-1}$ at long wavelengths. We find that the energy injection due to activity
has a peak at a characteristic length scale, which is 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 conclude that active
nematic fluids define a distinct universality class of turbulence at low
Reynolds number.
