Metastability for the dissipative quasi-geostrophic equation and the non-local enhancement

Abstract

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.

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Cited by in corpus (3)

• A dynamical approach to the study of instability near Couette flow
• Orientation mixing in active suspensions
• Enhanced dissipation, hypoellipticity for passive scalar equations with fractional dissipation