Superfluid Turbulence in HeliumII Thermal Counterflow in Circular and High Aspect Ratio Rectangular Channels.
Abstract
The pioneering experimental and theoretical research work in superfluid helium (HeII) is reviewed and some aspects of HeII 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 twofluid equations of motion are applied to steady state HeII 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 LondonZilsel 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 GorterMellink 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 geometrydependent features: two distinct cubic flow regimes are identified for low aspect ratio geometriesonly 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 Feynmantype 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 geometrydependent 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 geometryinduced differences in the turbulent flow states.
 Publication:

Ph.D. Thesis
 Pub Date:
 1983
 Bibcode:
 1983PhDT........81L
 Keywords:

 Physics: Condensed Matter