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