Following recent evidence that the vortices in decaying two-dimensional turbulence can be classified into small mobile and large quasistationary, 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 reorganization 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 corotating 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 turbulence flow is briefly examined.

• Received 14 March 2021
• Accepted 1 July 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.084601

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Published by the American Physical Society