On enhanced dissipation for the Boussinesq equations

In this article we consider the stability and damping problem for 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which includes Couette flow hydrostatic balance. first part show that linearized in an infinite periodic channel evolution is asymptotically stable if any diffusion coefficient non-zero. particular, imposes weaker conditions than example vertical diffusion. Furthermore, study interaction shear flow, balance dissipation. second establish enhanced results nonlinear around flows combining setting full Here adapt methods used by Bedrossian, Vicol Wang [4] Navier-Stokes combine them cancellation properties equations.