Competition between rotation and turbulence in superfluid He⁴

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.