  Using a weak convergence approach, we establish a Large Deviation Principle
(LDP) for the solutions of fluid dynamic systems in two-dimensional bounded
domains subjected to no-slip boundary conditions and perturbed by additive
noise. Our analysis considers the convergence of both viscosity and noise
intensity to zero. Specifically, we focus on three important scenarios:
Navier-Stokes equations in a Kato-type regime, Navier-Stokes equations for
fluids with circularly symmetric flows and Second-Grade Fluid equations. In all
three cases, we demonstrate the validity of the LDP, taking into account the
critical topology $C([0,T];L^2).$
