We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson et al., who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. We find that the eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. We suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow and conclude by making an analogy between the alignment of vortices in the presence of rotation and the alignment of dipole moments in the presence of an applied magnetic field.

• Received 22 May 2003

DOI:https://doi.org/10.1103/PhysRevB.69.134515