  We study freely decaying quantum turbulence by performing high resolution
numerical simulations of the Gross-Pitaevskii equation (GPE) in the
Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$
grid points. The energy spectrum confirms the presence of both a Kolmogorov
scaling range for scales larger than the intervortex scale $\ell$, and a second
inertial range for scales smaller than $\ell$. Vortex line visualizations show
the existence of substructures formed by a myriad of small-scale knotted
vortices. Next, we study finite temperature effects in the decay of quantum
turbulence by using the stochastic Ginzburg-Landau equation to generate thermal
states, and then by evolving a combination of these thermal states with the
Taylor-Green initial conditions using the GPE. We extract the mean free path
out of these simulations by measuring the spectral broadening in the Bogoliubov
dispersion relation obtained from spatio-temporal spectra, and use it to
quantify the effective viscosity as a function of the temperature. Finally, in
order to compare the decay of high temperature quantum and that of classical
flows, and to further calibrate the estimations of viscosity from the mean free
path in the GPE simulations, we perform low Reynolds number simulations of the
Navier-Stokes equations.
