Out-of-equilibrium fluxes shape the self-organization of locally-interacting turbulence

We study the self-organization of turbulence in a geophysically motivated two-dimensional fluid with local interactions. Using simulations and theory, we show that the out-of-equilibrium flux to small scales imposes a constraint on the large-scale emergent flow. Consequently, a rich phase diagram of large-scale configurations emerges, replacing the unique state found in flows with energy injection below the interaction scale. We explain what sets the boundaries between the different phases, and the occurrence of spontaneous symmetry breaking. Our work demonstrates that the selection mechanism of large-scale structures in quasi-geostrophic flows can be dramatically altered by forcing above the interaction scale.