  We study the stability of special, stratified solutions of a 3d Boussinesq
system describing an incompressible, inviscid 3d fluid with variable density
(or temperature, depending on the context) under the effect of a
uni-directional gravitational force. The behavior is shown to depend on the
properties of an anisotropic dispersive operator with weak decay in time.
However, the dispersive decay also depends on the strength of the gravity in
the system and on the profile of the stratified solution, whose stability we
study. We show that as the strength of the dispersion in the system tends to
infinity, the 3d system of equations tends to a stratified system of 2d Euler
equations with stratified density.
