Buoyant instability

From Glossary of Meteorology

buoyant instability

That static instability in a system in which buoyancy or reduced gravity is the only restoring force on displacements.

In general, a fluid is buoyantly unstable when the environmental lapse rate of density is greater than the process lapse rate of density. For an incompressible fluid this requires an increase of density with height; for the atmosphere, when lifting is assumed to be adiabatic, it requires the lapse rate (of temperature) to be greater than the adiabatic lapse rate.