  During most stages of stellar evolution the nuclear burning of lighter to
heavier elements results in a radial composition profile which is stabilizing
against buoyant acceleration, with light material residing above heavier
material. However, under some circumstances, such as off-center ignition, the
composition profile resulting from nuclear burning can be destabilizing, and
characterized by an outwardly increasing mean molecular weight. The potential
for instabilities under these circumstances, and the consequences that they may
have on stellar structural evolution, remain largely unexplored. In this paper
we study the development and evolution of instabilities associated with
unstable composition gradients in regions which are initially stable according
to linear Schwarzschild and Ledoux criteria. In particular, we explore the
mixing taking place under various conditions with multi-dimensional
hydrodynamic convection models based on stellar evolutionary calculations of
the core helium flash in a 1.25 \Msun star, the core carbon flash in a
9.3\,\Msun star, and of oxygen shell burning in a star with a mass of
23\,\Msun. The results of our simulations reveal a mixing process associated
with regions having outwardly increasing mean molecular weight that reside
below convection zones. The mixing is not due to overshooting from the
convection zone, nor is it due directly to thermohaline mixing which operates
on a timescale several orders of magnitude larger than the simulated flows.
Instead, the mixing appears to be due to the presence of a wave field induced
in the stable layers residing beneath the convection zone which enhances the
mixing rate by many orders of magnitude and allows a thermohaline type mixing
process to operate on a dynamical, rather than thermal, timescale. We discuss
our results in terms of related laboratory phenomena and associated theoretical
developments.
