Spontaneous generation of vortex crystals from forced two-dimensional homogeneous turbulence

The long-term limit of statistically stationary two-dimensional turbulence is shown to depend on the form of the large-scale forcing, in agreement with previous results. That effect is studied systematically by continuously varying the forcing from deterministic to Brownian in direct numerical simulations in doubly periodic boxes. As expected, this switches on or off the enstrophy cascade and the presence of strong coherent structures, but the transition is not monotonic. Under intermediate forcing conditions, the flow evolves to a stationary vortex crystal with triangular lattice, which appears to be stable and to last indefinitely. Deterministic forcings frustrate crystallization through the formation of fast-moving dipoles, and very random ones melt the crystal. The dispersion properties of the different regimes are studied, and it is shown that efficient particle dispersion depends on the presence of multiscale turbulence. The relation with other two-dimensional systems is discussed.