Vortex clustering in two dimensional quantum turbulence

Emergence of large-scale patterns and energy transport in systems with long-range interactions is an active research field. Condensation of energy on large scale coherent structures and its transfer from small to large scales, are two key features of 2D turbulence. Atmospheric turbulence comes close to the 2D approximation, and shows both an inverse energy cascade and coherent structures such as Earth's hurricanes, and Jupiter's Great Red Spot. Quantum turbulence in highly-oblate Bose Einstein condensates is an even closer experimental realization of 2D turbulence with tantalizing evidence for these classical phenomena.
The formation of coherent structures was originally attributed to the clustering of co-rotating vortices giving rise to negative temperature equilibria. Vortex clustering is observed in decaying turbulence in classical and quantum fluids, where there is no inverse energy cascade. We discuss the Onsager mechanism for equilibrium vortex condensates versus the inertial clustering in driven quantum turbulence, using numerical studies of the Gross-Pitaevskii equation as well as of a driven, dissipative point vortex model. The inverse energy cascade originates from clustering into patches of co-rotating and of counter-rotating vortices that have a self-similar spatial correlation. This is analogous to the scale-invariant statistics of vorticity in 2D classical turbulence, and its surprising appearance in quantum turbulence draws further analogies between the two.