Collective organisation and screening in two-dimensional turbulence

TL;DR

This paper investigates the ordered arrangements of large vortices in two-dimensional turbulence, revealing a 'crystal-like' structure formed through vortex interactions that influence energy transfer and flow organization.

Contribution

It provides evidence that large vortices form a structured 'crystal' in turbulence, highlighting the role of vortex interactions and screening in flow organization.

Findings

Large vortices exhibit more regular arrangements than random.

Vortices move slower than mean-field predictions.

Energy in large vortices is lower than in random configurations.

Abstract

Following recent evidence that the vortices in decaying two-dimensional turbulence can be classified into small--mobile, and large--quasi-stationary, this paper examines the evidence that the latter might be considered a `crystal' whose formation embodies the inverse cascade of energy towards larger scales. Several diagnostics of order are applied to the ostensibly disordered large vortices. It is shown that their geometric arrangement is substantially more regular than random, that they move more slowly than could be expected from simple mean-field arguments, and that their energy is significantly lower than in a random reorganisation of the same vortices. This is traced to screening of long-range interactions by the preferential association of vortices of opposite sign, and it is argued that this is due to the mutual capture of corrotating vortices, in a mechanism closer to tidal disruption than to electrostatic screening. Finally, the possible relation of these `stochastic crystals' to fixed points of the dynamical system representation of the turbulent flow is briefly examined.