  In this paper, we prove a central limit theorem and establish a moderate
deviation principle for 2D stochastic hydrodynamical type systems with
multiplicative noise in unbounded domains, which covers 2D Navier-Stokes
equations, 2D MHD models and the 2D magnetic B?enard problem and also shell
models of turbulence. The weak convergence method plays an important role in
obtaining the moderate deviation principle.
