Coexistence of quantum and classical flows in quantum turbulence in the $T=0$ limit

Abstract

Tangles of quantized vortex line of initial density ${\cal L}(0) \sim 6\times 10^3$\,cm$^{-2}$ and variable amplitude of fluctuations of flow velocity $U(0)$ at the largest length scale were generated in superfluid $^4$He at $T=0.17$\,K, and their free decay ${\cal L}(t)$ was measured. If $U(0)$ is small, the excess random component of vortex line length firstly decays as ${\cal L} \propto t^{-1}$ until it becomes comparable with the structured component responsible for the classical velocity field, and the decay changes to ${\cal L} \propto t^{-3/2}$. The latter regime always ultimately prevails, provided the classical description of $U$ holds. A quantitative model of coexisting cascades of quantum and classical energies describes all regimes of the decay.