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We inquire about the properties of 2d Navier-Stokes turbulence simultaneouslyforced at small and large scales. The background motivation comes byobservational results on atmospheric turbulence. We show that the velocityfield is amenable to the sum of two auxiliary velocity fields forced at largeand small scale and exhibiting a direct-enstrophy and an inverse-energycascade, respectively. Remarkably, the two auxiliary fields reconcile universalproperties of fluxes with positive statistical correlation in the inertialrange.

Nonlinear superposition of direct and inverse cascades in two-dimensional turbulence forced at large and small scales