Tangles of a quantized vortex line of initial density $\mathcal{L}(0)\sim 6\times 10^3{\mathrm{cm}}^{-2}$ and a variable amplitude of fluctuations of flow velocity $U(0)$ at the largest length scale are generated in superfluid ${}^4\mathrm{He}$ at $T=0.17\mathrm{K}$, and their free decay $\mathcal{L}(t)$ is measured. If $U(0)$ is small, the excess random component of the vortex line length first decays as $\mathcal{L}\propto t^{-1}$ until it becomes comparable with the structured component responsible for the classical velocity field, and the decay changes to $\mathcal{L}\propto t^{-3/2}$. 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.

• Received 20 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.134501

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