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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 that are initially stable according to linear Schwarzschild and Ledoux criteria. In particular, we study the development of turbulent flow under a variety of stellar evolution conditions with multi-dimensional hydrodynamic simulation; the phases studied include the core helium flash in a 1.25 M ⊙ star, the core carbon flash in a 9.3M ⊙ star, and oxygen shell burning in a 23M ⊙ star. 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. The mixing manifests itself in the form of overdense and cold blob-like structures originating from density fluctuations at the lower boundary of convective shell and "shooting" down into the core. They are enriched with nuclearly processed material, hence leaving behind traces of higher mean molecular weight. In these regions, we find that initially smooth composition gradients steepen into stair-step-like profiles in which homogeneous, mixed regions are separated by composition jumps. These step-like profiles are then seen to evolve by a process of interface migration driven by turbulent entrainment. We discuss our results in terms of related laboratory phenomena and associated theoretical developments. We also discuss the degree to which the simulated mixing rates depend on the numerical resolution, and what future steps can be taken to capture the mixing rates accurately. © 2011. The American Astronomical Society. All rights reserved., SCOPUS: ar.j, info:eu-repo/semantics/published