This talk presents several examples of stabilizing mechanisms in fluid systems rooted in underlying wave structures. We start with buoyancy-driven flows near hydrostatic equilibrium, modeled by the incompressible Boussinesq system. The associated Navier–Stokes equations with partial dissipation are not known to be globally stable, but the buoyancy helps damp and stabilize the fluid. We then turn to 3D incompressible and compressible magnetohydrodynamic (MHD) flows near a background magnetic field. The fluid velocity satisfies either the Euler or partially dissipated Navier-Stokes, whose standalone stability is not well understood. But the coupled MHD systems nevertheless are shown to be globally stable and decay. In each case, the governing perturbation systems boil down to damped wave equations, revealing enhanced dissipation and smoothing effects that underlie the resulting stability.