  We examine the scaling with activity of the emergent length scales that
control the nonequilibrium dynamics of an active nematic liquid crystal, using
two popular hydrodynamic models that have been employed in previous studies. In
both models we find that the chaotic spatio-temporal dynamics in the regime of
fully developed active turbulence is controlled by a single active scale
determined by the balance of active and elastic stresses, regardless of whether
the active stress is extensile or contractile in nature. The observed scaling
of the kinetic energy and enstropy with activity is consistent with our
single-length scale argument and simple dimensional analysis. Our results
provide a unified understanding of apparent discrepancies in the previous
literature and demonstrate that the essential physics is robust to the choice
of model.
