  In this paper, we study the metastability for the 2-D linearized dissipative
quasi-geostrophic equation with small viscosity $\nu$ around the quasi steady
state $\theta_{sin}=e^{-\nu t}\sin y$. We proved the linear enhanced
dissipation and obtained the dissipation rate. Moreover, the new non-local
enhancement phenomenon was discovered and discussed. Precisely we showed that
the non-local term re-enhances the enhanced diffusion effect by the
shear-diffusion mechanism.
