  We consider the Navier-Stokes equation in a domain with irregular boundaries.
The irregularity is modeled by a spatially homogeneous random process, with
typical size $\eps \ll 1$. In a parent paper, we derived a homogenized boundary
condition of Navier type as $\eps \to 0$. We show here that for a large class
of boundaries, this Navier condition provides a $O(\eps^{3/2} |\ln
\eps|^{1/2})$ approximation in $L^2$, instead of $O(\eps^{3/2})$ for periodic
irregularities. Our result relies on the study of an auxiliary boundary layer
system. Decay properties of this boundary layer are deduced from a central
limit theorem for dependent variables.
