Flow of He II in a channel with ends blocked by superfleaks

We report experiments of He II flow thermally induced by a fountain pump in channels of square cross-section with ends blocked by sintered silver superleaks and its decay (PRL 100 (2008) 215302). We confirm a critical velocity $v_{\rm{cr}}^{\rm I}$ 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 the second sound attenuation. In addition to the previously reported turbulent A-state characterized by $L^{1/2}=\gamma(T) (v-v_{\rm{cr}}^{\rm I})$ we have discovered a new B-state characterized by $L = \beta (v-v_{\rm{cr}}^{\rm II}) $. We offer a phenomenological model assuming that in the B-state the superflow matches the classical parabolic profile, with a slip velocity $v_{\rm{cr}}^{\rm II}$ 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 effective kinematic viscosity $\nu_ {eff}(T)$ establishes, giving rise to the observed exponential decay. The calculated values of $\nu_{eff}(T)$ are in agreement with those deduced from other experiments on decaying He II turbulence.