Kolmogorov Spectrum of Quantum Turbulence
Michikazu Kobayashi, Makoto Tsubota

TL;DR
This paper investigates quantum turbulence by numerically solving a modified Gross-Pitaevskii equation, demonstrating that its energy spectrum follows the Kolmogorov law and confirming the inertial range in quantum turbulence.
Contribution
It introduces a new numerical approach to study quantum turbulence, confirming the Kolmogorov spectrum and inertial range in quantum turbulence.
Findings
Energy spectrum matches Kolmogorov law
First confirmation of inertial range in quantum turbulence
Steady and decaying turbulence behaviors analyzed
Abstract
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and…
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