Kolmogorov Spectrum of Quantum Turbulence

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 steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.