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

In this paper, we study the metastability for the 2-D linearized dissipative quasigeostrophic equation with small viscosity ν around the quasi steady state θsin = e −νt 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.

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