Dissipation of Quantum Turbulence in the Zero Temperature Limit

Abstract

Turbulence, produced by an impulsive spin down from angular velocity $\ensuremath{\Omega}$ to rest of a cube-shaped container, is investigated in superfluid $^{4}\mathrm{He}$ at temperatures 0.08 K--1.6 K. The density of quantized vortex lines $L$ is measured by scattering negative ions. Homogeneous turbulence develops after time $t\ensuremath{\approx}20/\ensuremath{\Omega}$ and decays as $L\ensuremath{\propto}{t}^{\ensuremath{-}3/2}$. The corresponding energy flux $ϵ={\ensuremath{\nu}}^{\ensuremath{'}}(\ensuremath{\kappa}L{)}^{2}\ensuremath{\propto}{t}^{\ensuremath{-}3}$ is characteristic of quasiclassical turbulence at high Re with a saturated energy-containing length. The effective kinematic viscosity in $T=0$ limit is ${\ensuremath{\nu}}^{\ensuremath{'}}=0.003\ensuremath{\kappa}$, where $\ensuremath{\kappa}={10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ is the circulation quantum.