  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.
