FREE DECAY OF HOMOGENEOUS SUPERFLUID TURBULENCE IN HELIUM-II

The equations governing the one-dimensional transient behaviour of hom ogeneous superfluid turbulence in He II that were originally considere d by Vinen and Schwarz and recently extended by one of the authors are applied to the free decay of a homogeneous vortex tangle in which the gradients of the temperature and the thermodynamic potential vanish. It turns out that the equations admit a solution in closed form which may be expressed in terms of incomplete beta-functions. The general so lution exhibits three distinct branches. On one of the branches the de cay falls apart in an initial stage of fast decay and a final stage of slow decay separated by a short transition region. This mode of decay is qualitatively similar to the experimentally observed decay of a vo rtex tangle that has recently been reported by Schwarz and Rozen (1991 ) and by Olszok et al. (1994). An alternative mode of decay that is ph ysically meaningful is represented by the other two branches when join ed together. The behaviour of that mode resembles, in a qualitative wa y, the experimental decay originally observed by Vinen (1957).