  Rayleigh-Taylor and Buoyancy-driven instabilities are very common
instabilities for an inhomogeneous medium. We examine here how these
instabilities grow for incompressible viscoelastic fluids like a strongly
coupled dusty plasma by using incompressible generalized hydrodynamic (i-GHD)
fluid model. Since the dust particles are pretty massive, the gravitational
attraction of earth has a significant role in its dynamics. In this paper the
acceleration due to gravity g and the role of strong coupling in the context of
gravitationally stratified dusty plasma fluid have been considered. We find
that the appearance of elasticity speed up the growth of viscoelastic RT
instability by reducing the effect of viscosity at timescales shorter than the
Maxwell relaxation time ${\tau_m}$. The buoyancy driven situation with
spatially localized (in both dimensions) of low/high density regions placed in
a background medium has also been evolved in the presence of gravity. Our
studies show that both the instabilities get suppressed with increasing
coupling strength of the medium. This suppression has been illustrated
analytically as well as by carrying out a two-dimensional fully nonlinear
simulation.
