Metastability for the Dissipative Quasi-Geostrophic Equation and the Non-local Enhancement

In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-geostrophic equation with small viscosity ν around the quasi-steady state Θ _sin=-e^-ν tsin 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 cos y∂ _x(-Δ )^-1/2θ re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.