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We study turbulent convection during the core helium flash close to its peakby comparing the results of two and three-dimensional hydrodynamic simulations.  We use a multidimensional Eulerian hydrodynamics code based onstate-of-the-art numerical techniques to simulate the evolution of the heliumcore of a $1.25 M_{\odot}$ Pop I star.  Our three-dimensional hydrodynamic simulations of the evolution of a starduring the peak of the core helium flash do not show any explosive behavior.The convective flow patterns developing in the three-dimensional models arestructurally different from those of the corresponding two-dimensional models,and the typical convective velocities are smaller than those found in theirtwo-dimensional counterparts. Three-dimensional models also tend to agreebetter with the predictions of mixing length theory. Our hydrodynamicsimulations show the presence of turbulent entrainment that results in a growthof the convection zone on a dynamic time scale. Contrary to mixing lengththeory, the outer part of the convection zone is characterized by asub-adiabatic temperature gradient.

The core helium flash revisited: II. Two and three-dimensional hydrodynamic simulations