Vortex clustering and universal scaling laws in two-dimensional quantum turbulence

TL;DR

This paper numerically studies two-dimensional quantum turbulence, revealing a universal -5/3 energy spectrum scaling law linked to vortex statistics, including number fluctuations and velocity distributions, consistent with passive vortex advection.

Contribution

It uncovers the connection between vortex statistics and universal scaling laws in 2D quantum turbulence using the Gross-Pitaevskii equation.

Findings

Identification of a -5/3 scaling law in energy spectrum

Vortex number fluctuations follow a similar scaling behavior

Vortex velocity distribution exhibits a -5/3 power-law tail

Abstract

We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal $-5/3$ scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The $-5/3$ scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a $-5/3$ exponent.