  Two types of vortex states have been much studied in superfluid $^4$He. The
first is the vortex array in a rotating container. The second is the vortex
tangle in turbulent flow. An experiment attempt to combine these two states by
rotating a counterflow was attempted years ago. The data suggest the existence
of different flow regimes separated by instabilities, but a theoretical
interpretation is still missing. We present work in which we use the vortex
filament model to numerically investigate rotating counterflow. We show
evidence of a new state of polarized turbulence.
