Observation of quantum decay of homogeneous, isotropic (grid) turbulence

In classical grid turbulence fluid is forced through a stationary grid. In the quantum case a grid moves through an initially stationary superfluid driven by a linear motor. We have developed a motor using superconducting drive coils and bearings, moving a grid at constant speed (0 and 15 cm/s). Stalp \textit{et al}\footnote{S. R. Stalp, L. Skrbek, and R. J. Donnelly, \textit{Phys. Rev. Lett}. \textbf{\textit{82}}, \textit{4831} (\textit{1999}).} report the decay of vortex-line density $L$ in the grid's wake measured by 2$^{\mathrm{nd}}$ sound attenuation. $L$ decayed at large times as $t^{-3/2}$, interpreted as a quasi-classical Richardson cascade of energy-containing eddies size limited by channel width, associated with a Kolmogorov energy spectrum. It is assumed eddies produced on a scale of the grid mesh grow through the classical fluids mechanism.\footnote{P.A. Davidson, \textit{Turbulence}, Oxford Univ. Press., UK (2004).} We can now test a semi-quantitative theory with different mesh grids or channel sizes, relating to the possible existence of inverse turbulent cascades. Our 2$^{\mathrm{nd}}$ sound system is conventional, but with a novel phase and amplitude feedback loop making stringent constant temperature unnecessary. Both $t^{-3/2}$ and non-$ t^{-3/2}$ decays have been observed with 2 mesh sizes.