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

## TL;DR

This study investigates how quantum and classical vortex flows coexist and decay in superfluid helium at near-zero temperature, revealing two decay regimes and proposing a model for their interaction.

## Contribution

It introduces a quantitative model describing the coexistence and decay of quantum and classical energy cascades in superfluid turbulence.

## Key findings

- Decay of vortex line length follows t^{-1} initially for small flow velocities.
- Transition to t^{-3/2} decay occurs when structured flow dominates.
- The model accurately describes all observed decay regimes.

## 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.