Nonlinear superposition of direct and inverse cascades in   two-dimensional turbulence forced at large and small scales
  We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable to the sum of two auxiliary velocity fields forced at large and small scale and exhibiting a direct-enstrophy and an inverse-energy cascade, respectively. Remarkably, the two auxiliary fields reconcile universal properties of fluxes with positive statistical correlation in the inertial range. 
Massimo Cencini, Paolo Muratore-Ginanneschi and Angelo Vulpiani
physics.flu-dyn physics.ao-ph