  Shell convection driven by nuclear burning in a stellar core is a common
hydrodynamic event in the evolution of many types of stars. We encounter and
simulate this convection (i) in the helium core of a low-mass red giant during
core helium flash leading to a dredge-down of protons across an entropy
barrier, (ii) in a carbon-oxygen core of an intermediate-mass star during core
carbon flash, and (iii) in the oxygen and carbon burning shell above the
silicon-sulfur rich core of a massive star prior to supernova explosion. Our
results, which were obtained with the hydrodynamics code HERAKLES, suggest that
both entropy gradients and entropy barriers are less important for stellar
structure than commonly assumed. Our simulations further reveal a new dynamic
mixing process operating below the base of shell convection zones.
