Superfluid Turbulence in Helium-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(,sc)) theories are discussed with respect to the temperature and channel size dependences of V(,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 (mu)m) and four 10:1 rectangular (32 (LESSTHEQ) d (LESSTHEQ) 98 (mu)m) glass channels. The London-Zilsel relation agrees well ((+OR-)3%) with the experimental linear (laminar flow) thermal resistance R(,L) for either geometry. The critical heat current Q(,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 L(,o). An analysis using the Vinen Theory determines the parameters (gamma)((alpha)(chi)(,1)/(chi)(,2)) and (alpha). A similar analysis determines (gamma) and (alpha) empirically, and values of the Gorter-Mellink constant A(T) are computed. The empirical analysis indicates that the relationship between (gamma) and V(,sc) is a unique one, but that it is not correctly given by the Vinen Theory. The data obtained in this and other counterflow research work exhibit pronounced geometry-dependent features: two distinct cubic flow regimes are identified for low aspect ratio geometries--only one cubic regime is observed in high aspect ratio rectangular channels. In either geometry V(,sc)d, calculated from Q(,c), obeys a weak size dependence consistent with a Feynman-type V(,sc)((gamma)), but the characteristic length scale is (TURNEQ)10('-5) cm, rather than the vortex core radius ((TURNEQ)10('-8) cm). It is suggested that a nonuniform velocity field V(,nl) could in principle explain the geometry-dependent A(T) in pure counterflow. The dependence of the line velocity V(,l) on V(,n) may also explain certain discrepant values of A(T) obtained for different types of flow in a given channel geometry. A simple experiment is suggested to clarify these geometry-induced differences in the turbulent flow states.