Origin of the inverse energy cascade in two-dimensional quantum turbulence

TL;DR

This paper links the inverse energy cascade in 2D quantum turbulence to vortex clustering, revealing a power-law correlation that explains the emergence of turbulence through a novel vortex model.

Contribution

It introduces a statistical relationship between vortex correlations and the inverse energy cascade, supported by a new vortex model capturing turbulent dynamics.

Findings

Kolmogorov spectrum $k^{-5/3}$ relates to vortex pair correlations decaying as $r^{-4/3}$

Vortex clustering drives the inverse energy cascade in quantum turbulence

Proposed vortex model reproduces turbulent clustering dynamics

Abstract

We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum $k^{-5/3}$ on inertial scales $r$ corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as $r^{-4/3}$. To test these scaling relations, we propose a novel forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.