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