common to both active nematics and self-propelled nematics, i.e., occur regardless of the symmetry of the microdynamics. Finally, we show that there exists a third instability unique to self-propelled nematic fluids due to the fact that in these systems, large scale nematic order can induce local polar order, which in turn destabilizes the density. This mechanism may be responsible for the smectic order of polar clusters observed recently in simulations of SP rods [@Yang2010; @Sam2012]. We conclude with a brief discussion.

The Macroscopic Theory {#sec:macro}
======================

The hydrodynamic equations of a self-propelled nematic have been derived from systematic coarse-graining of specific microscopic models [@Baskaran2008a; @Baskaran2009]. Here we introduce these equations phenomenologically, with the goal of examining the dynamics without the limitations imposed by the specific parameter values obtained from a microscopic model or resulting from the choice of the closure used in the kinetic equation.

We limit ourselves to overdamped systems in two dimensions. The hydrodynamic equations are then written in terms of three continuum fields: the conserved number density $\rho \left( \mathbf{r},t\right) $ of active units, the polarization density $\bm\tau({\bf r},t)=\rho({\bf r},t)
\mathbf{P}\left( \mathbf{r},t\right) $, with $\mathbf{P}\left( \mathbf{r},t\right)$ a polarization order parameter, and the nematic alignment density tensor $Q_{ij}({\bf 