Critical velocities and two mechanisms of transition in superfluid liquid He

Two mechanisms of transition of the superfluid liquid ⁴He to quantum turbulence regimes are proposed for the case when the influence of the normal fluid on superfluid flow is suppressed by introducing superleaks at the ends of the capillary. Using dimensional analysis it is found that in the roton mechanism the critical velocity depends on channel size as vc∝d−1/4, matching the experiments. For the second, super-flow mechanism, the analysis of independent parameters relevant for this phenomena leads to critical velocity depending on d as vc∝d−1. It is shown that turbulence for super-flow mechanism arises when a “quantum Reynolds number” exceeds some critical value which is about 10³ for 1D geometry. The dimensional analysis of the equation for critical velocity of superfluid flow without superleaks at the ends of the capillary is also presented.