Superfluid turbulence in He-II thermal counterflow in circular and high aspect ratio rectangular channels

The pioneering experimental and theoretical research work in superfluid helium (He-II) is reviewed and some aspects of He-II flow are compared with classical channel flows. Several superfluid critical velocity (V/sub sc/) theories are discussed with respect to the temperature and channel size dependences of V/sub sc/ as observed in numerous counterflow experiments. The Landau two-fluid equations of motion are applied to steady state He-II counterflow to analyze the temperature difference data obtained with two circular (d = 131 μm) and four 10:1 rectangular (32 less than or equal to d less than or equal to 98 μm) glass channels. The London-Zilsel relation agrees well (+/- 3%) with the experimental linear (laminar flow) thermal resistance R/sub L/ for either geometry. The critical heat current Q/sub c/ and the magnitude of the nonlinear (turbulent flow) thermal resistance are carefully measured. Results are interpreted in terms of mutual friction between the normal fluid and the superfluid vortex line tangle, and the data are reduced in terms of the velocity dependence of the steady state vortex line density L0. An analysis using the Vinen Theory determines the parameters γ(αchi1/chi2) and α. A similar analysis determines γ and α empirically, and values of the Gorter-Mellink constant A(T) are computed. The empirical analysis indicates that the relationship between γ and V/sub sc/ is a unique one, but that is not correctly given by the Vinen Theory