Instability of vortex array and transitions to turbulence in rotating helium II

Abstract

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. 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. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow.

Alternative Vinen equation and its extension to rotating counterflow superfluid turbulence

“…Thus, the "tanh" term in (2.17) is analogous to the expression describing magnetization in terms of magnetic field and temperature in a 1/2 spin paramagnetic system. Other expressions, as for instance, Langevin's one for classical paramagnetism, could also be used [18,28,29]. This ansatz is similar to that proposed in Ref.…”

“…Tsubota et al [18] also have paid attention to this experiment. They proposed that the regime V c1 < V < V c2 is a state of polarized turbulence, while for V > V c2 the polarization is decreased by the large number of reconnections.…”

“…Here, we will chose for it the value N ′ = 22 proposed by Tsubota et al in Ref. [18]. Expression (2.17) is similar to that proposed in Ref.…”

“…In recent years there has been growing attention in superfluid turbulence in rotating containers [16]- [18], in which the formation of vortex lines is due both to the counterflow and the rotation, which has fostered the extension of Vinen's ideas to a wider range of situations [15,19,20]. In Ref.…”

Vortex Tangle Dynamics under the Effect of Mutual Friction in Superfluid HeII

“…The decay process has been studied in Refs. [7,8,9]. This paper deals with the growth case of the vortex tangle.…”