  In active nematic liquid crystals activity is able to drive chaotic
spatiotemporal flows referred to as active turbulence. Active turbulence has
been characterized through theoretical and experimental work as a low Reynolds
number phenomenon. We show that, in two-dimensions, the active forcing alone is
able to trigger hydrodynamic turbulence leading to the coexistence of active
and inertial turbulence. This type of flows develops for sufficiently active
and extensile flow-aligning nematics. We observe that the combined effect of an
extensile nematic and large values of the flow-aligning parameter leads to a
broadening of the elastic energy spectrum that promotes a growth of kinetic
energy able to trigger an inverse energy cascade.
