  We study the two-dimensional incompressible Navier-Stokes equation on the
torus, driven by Gaussian noise that is white in time and colored in space. We
consider the case where the magnitude of the random forcing $\sqrt{\e}$ and its
correlation scale $\delta(\e)$ are both small. We prove a large deviations
principle for the solutions, as well as for the family of invariant measures,
as $\e$ and $\delta(\e)$ are simultaneously sent to $0$, under a suitable
scaling.
