High-resolution numerical simulations were made of unforced, planetary-scale fluid dynamics. In particular, the simulation was based on the quasi-geostrophic equations for a Boussinesq fluid in a uniformly rotating and stably stratified environment, which is an idealization for large regions of either the atmosphere or ocean. The solutions show significant discrepancies from the long-standing theoretical prediction of isotropy. The discrepancies are associated with the self-organization of the flow into a large population of coherent vortices. Their chaotic interactions govern the subsequent evolution of the flow toward a final configuration that is nonturbulent.