Saturation of decaying counterflow turbulence in helium II

Abstract

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L\ensuremath{\sim}{t}^{\ensuremath{-}1}$. Schwarz and Rozen [Phys. Rev. Lett. 66, 1898 (1991); Phys. Rev. B 44, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek et al. [Phys. Rev. E 67, 047302 (2003)] found an initial transient followed by the same classical ${t}^{\ensuremath{-}3/2}$ scaling as observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.