  Suspensions of active agents with nematic interactions exhibit complex
spatio-temporal dynamics such as mesoscale turbulence. Since the Reynolds
number of microscopic flows is very small on the scale of individual agents,
inertial effects are typically excluded in continuum theories of active nematic
turbulence. Whether active stresses can collectively excite inertial flows is
currently unclear. To address this question, we investigate a two-dimensional
continuum theory for active nematic turbulence. In particular, we compare
mesoscale turbulence with and without the effects of advective inertia. We find
that inertial effects can influence the flow already close to the onset of the
turbulent state and, moreover, give rise to large-scale fluid motion for strong
active driving. A detailed analysis of the kinetic energy budget reveals an
energy transfer to large scales mediated by inertial advection. While this
transfer is small in comparison to energy injection and dissipation, its
effects accumulate over time. The inclusion of friction, which is typically
present in experiments, can compensate for this effect. The findings suggest
that the inclusion of inertia and friction may be necessary for dynamically
consistent theories of active nematic turbulence.
