  Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes
equations differ by a spatial filtration parametrized by a scale denoted
$\alpha$. Starting from a strong two-dimensional solution to the
Navier-Stokes-$\alpha$ model driven by a multiplicative noise, we demonstrate
that it generates a strong solution to the stochastic Navier-Stokes equations
under the condition $\alpha$ goes to 0. The initially introduced probability
space and the Wiener process are maintained throughout the investigation,
thanks to a local monotonicity property that abolishes the use of Skorokhod's
theorem. High spatial regularity a priori estimates for the fluid velocity
vector field are carried out within periodic boundary conditions.
