Critical Velocity for a Self-Sustaining Vortex Tangle in Superfluid Helium

Abstract

A recent treatment of superfluid turbulence is extended to the study of turbulence in a channel. It is found that as the flow velocity is reduced, a critical velocity is reached such that the rate at which new vortex singularities are created by line-line reconnections becomes insufficient to balance the loss of vortices at the channel walls, and the vortex tangle ceases to be topologically self-sustaining. Comparison with experiment indicates that this approach provides a reasonable explanation of observed critical velocities.