On Flow of He II in Channels with Ends Blocked by Superleaks

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We report an experimental investigation of a flow of the superfluid phase of 4He–He II—thermally induced by a fountain pump through vertical channels of square cross-section with ends blocked by sintered silver superleaks and its decay. We confirm the existence of a weakly temperature dependent critical velocity vcrI of order 1 cm/s, which does not scale with the channel size and is therefore an intrinsic property of the self-sustained vortex tangle of vortex line density L, measured by second sound attenuation. In addition to the previously reported turbulent A-state characterized by L1/2=γ(T)(v−vcrI), where v is the mean superflow velocity through the channel, we have discovered a new B-state characterized by L=β(v−vcrII), where β seems only weakly temperature dependent. It poses an important question why, at higher flow velocities, the quadratic generation mechanism, so well established in thermal counterflow, ceases to work. We offer a phenomenological model assuming that in the B-state the coarse-grained superflow profile matches the classical parabolic profile, with a finite, temperature dependent slip velocity vcrII of order few cm/s and that a confined viscous normal fluid flow of toroidal form is induced inside the channel due to the mutual friction force. When the fountain pump is switched off, after an initial decay, a confined quasi-viscous flow of a single-component fluid with an effective kinematic viscosity νeff(T) establishes, giving rise to the observed exponential decay. The values of νeff(T), calculated using our model from the measured decay times, are in agreement with those deduced from other experiments on decaying He II turbulence.

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