  Nonequilibrium condensate systems such as exciton-polariton condensates are
capable of supporting a spontaneous vortex nucleation. The spatial
inhomogeneity of pumping field or/and disordered potential creates velocity
flow fields that may become unstable to vortex formation. This letter considers
ways in which turbulent states of interacting vortices can be created. It is
shown that by combining just two pumping intensities it is possible to create a
superfluid turbulence state of well-separated vortices, a strong turbulence
state of de-structured vortices, or a weak turbulence state in which all
coherence of the field is lost and motion is driven by weakly interacting
dispersive waves. The decay of turbulence can be obtained by replacing an
inhomogeneous pumping by a uniform one. We show that both in quasi-equilibrium
and during the turbulence decay there exists an inertial range dominated by
four-wave interactions of acoustic waves.
