  We consider in a smooth and bounded two dimensional domain the convergence in
the $L^2$ norm, uniformly in time, of the solution of the stochastic
Navier-Stokes equations with additive noise and no-slip boundary conditions to
the solution of the corresponding Euler equations. We prove, under general
regularity on the initial conditions of the Euler equations, that assuming the
dissipation of the energy of the solution of the Navier-Stokes equations in a
Kato type boundary layer, then the inviscid limit holds.
