  Coupling between flow and orientation is a central issue in understanding the
collective dynamics of active biofilaments and cells. Active stressess
generated by motor activity destroy (quasi-)long-range orientational order and
induce chaotic vortex flows. In cellular and subcellular environment, alignment
is also hindered by heterogeneous filamentous structures in extracellular
matrix and various organelles in a cell. Here we address the effects of a
quenched random field on the flow patterns and orientational order in
two-dimensional active nematic liquid crystals. We found that the director
dynamics is frozen above a critical disorder strength. For sufficiently strong
randomness, the orientational correlation function decays exponentially with
the distance, reproducing the behavior of passive random-field nematics. In
contrast, the flow velocity decreases only gradually as the randomness is
increased, and develops a logarithmic spatial correlation for strong disorder.
The threshold between the activity- and disorder-dominated regimes is specified
and its dependence on the activity parameter is discussed.
