Exploring the Equivalence between Two-dimensional Classical and Quantum Turbulence through Velocity Circulation Statistics

TL;DR

This study compares velocity circulation statistics in two-dimensional classical and quantum turbulence through numerical simulations, revealing conditions under which their behaviors are equivalent or diverge, thus clarifying the relationship between these turbulence types.

Contribution

It demonstrates the conditions where classical and quantum turbulence exhibit similar circulation statistics and identifies the effects of compressibility on their equivalence.

Findings

Circulation intermittency is the same in classical and quantum turbulence during inverse cascade.

Classical and quantum turbulence show similar self-similar scaling in the nearly incompressible direct cascade.

Compressibility effects lead to divergence in circulation statistics, especially at higher moments.

Abstract

We study the statistics of velocity circulation in two-dimensional classical and quantum turbulence. We perform numerical simulations of the incompressible Navier-Stokes and the Gross-Pitaevskii (GP) equations for the direct and inverse cascades. Our GP simulations display clear energy spectra compatible with the double cascade theory of two-dimensional classical turbulence. In the inverse cascade, we found that circulation intermittency in quantum turbulence is the same as in classical turbulence. We compare GP data to Navier-Stokes simulations and experimental data from [Zhu et al. Phys. Rev. Lett. 130, 214001(2023)]. In the direct cascade, for nearly incompressible GP-flows, classical and quantum turbulence circulation displays the same self-similar scaling. When compressible effects become important, quasi-shocks generate quantum vortices and the equivalence of quantum and classical turbulence only holds for low-order moments. Our results establish the boundaries of the equivalence between two-dimensional classical and quantum turbulence.