  We consider the motion of incompressible viscous fluid in a rectangle,
imposing the periodicity condition in one direction and the no-slip boundary
condition in the other. Assuming that the flow is subject to an external random
force, white in time and regular in space, we construct an estimator for the
viscosity using only observations of the enstrophy. The goal of the paper is to
prove that the estimator is strongly consistent and asymptotically normal. The
proof of consistency is based on the explicit formula for the estimator and
some bounds for trajectories, while that of asymptotic normality uses in
addition mixing properties of the Navier-Stokes flow.
