Energy spectra of quantum turbulence: Large-scale simulation and modeling

Abstract

In a ${2048}^{3}$ simulation of quantum turbulence within the Gross-Pitaevskii equation, it is demonstrated that the large-scale motions have a classical Kolmogorov-1941 energy spectrum $E(k)\ensuremath{\propto}{k}^{\ensuremath{-}5/3}$, followed by an energy accumulation with $E(k)\ensuremath{\simeq}$ const at $k$ about the reciprocal mean intervortex distance. This behavior was predicted by the L'vov-Nazarenko-Rudenko bottleneck model of gradual eddy-wave crossover [L'vov, Nazarenko, and Rudenko, J. Low Temp. Phys. 153, 140 (2008)], further developed in the paper.