  We demonstrate the formation of a high angular momentum turbulent state in an
exciton-polariton quantum fluid with TE-TM Spin-Orbit Coupling (SOC). The
transfer of particles from quasi-resonantly cw pumped \spl component to \sm
component is accompanied with the generation of a turbulent gas of quantum
vortices by inhomogeneities. We show that this system is unstable with respect
to the formation of bogolons at a finite wave vector, controlled by the laser
detuning. In a finite-size cavity, the domains with this wave vector form a
ring-like structure along the border of a cavity, with a gas of mostly
same-sign vortices in the center. The total angular momentum is imposed by the
sign of TE-TM SOC, the wave vector of instability, and the cavity size. This
effect can be detected experimentally via local dispersion measurements or by
interference. The proposed configuration thus allows simultaneous experimental
studies of quantum turbulence and high-angular momentum states in
continuously-pumped exciton-polariton condensates.
