This talk presents recent results on the stability of physically relevant steady-state solutions in fluid dynamics, focusing on the Boussinesq system near hydrostatic equilibrium and the magnetohydrodynamic equations near a background magnetic field. These systems involve only partial dissipation and traditional stability analysis simply fails. Our approach exploits two forms of enhanced dissipation: one due to the steady-state itself and the other from coupling and interaction within components of the system. Mathematically, the equations governing perturbations can be systematically converted into anisotropic, often degenerate, wave equations. These wave structures reflect the enhanced dissipation and enable us to design a systematic and effective approach for these otherwise seemingly impossible stability problems.