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In this paper, we establish linear enhanced dissipation results for thethree-dimensional Boussinesq equations around a stably stratified Couette flow,in the viscous and thermally diffusive setting. The dissipation rates arefaster compared to those observed in the homogeneous Navier-Stokes equations,in light of the interplay between velocity and temperature, driven by buoyantforces.  Our approach involves introducing a change of variables grounded in a Fourierspace symmetrization framework. This change elucidates the energy structureinherent in the system. Specifically, we handle non-streaks modes through anaugmented energy functional, while streaks modes are amenable to explicitsolutions. This explicit treatment reveals the oscillatory nature of shearmodes, providing the elimination of the well-known three-dimensionalinstability mechanism known as the ``lift-up effect''.

Suppression of lift-up effect in the 3D Boussinesq equations around a stably stratified Couette flow