Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling

TL;DR

This paper presents large-scale simulations of quantum turbulence showing classical Kolmogorov energy spectra at large scales and an energy bottleneck at smaller scales, supporting a theoretical crossover model.

Contribution

It provides high-resolution simulation data and a refined model for the energy spectrum crossover in quantum turbulence.

Findings

Classical Kolmogorov spectrum observed at large scales

Energy accumulation at the scale of the mean intervortex distance

Validation of the bottleneck model for eddy-wave crossover

Abstract

In $2048^3$ simulation of quantum turbulence within the Gross-Pitaevskii equation we demonstrate that the large scale motions have a classical Kolmogorov-1941 energy spectrum E(k) ~ k^{-5/3}, followed by an energy accumulation with E(k) ~ 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 [J. Low Temp. Phys. 153, 140-161 (2008)], further developed in the paper.