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We consider the zero viscosity limit of long time averages of solutions ofdamped and driven Navier-Stokes equations in ${\mathbb R}^2$. We prove that therate of dissipation of enstrophy vanishes. Stationary statistical solutions ofthe damped and driven Navier-Stokes equations converge to renormalizedstationary statistical solutions of the damped and driven Euler equations.These solutions obey the enstrophy balance

Inviscid Limit for Damped and Driven Incompressible Navier-Stokes Equations in $$\mathbb R^2$$