  By direct hydrodynamic simulation, using the Piecewise Parabolic Method (PPM)
code PROMETHEUS, we study the properties of a convective oxygen burning shell
in a SN 1987A progenitor star prior to collapse. The convection is too
heterogeneous and dynamic to be well approximated by one-dimensional
diffusion-like algorithms which have previously been used for this epoch.
Qualitatively new phenomena are seen.
  The simulations are two-dimensional, with good resolution in radius and
angle, and use a large (90-degree) slice centered at the equator. The
microphysics and the initial model were carefully treated. Many of the
qualitative features of previous multi-dimensional simulations of convection
are seen, including large kinetic and acoustic energy fluxes, which are not
accounted for by mixing length theory. Small but significant amounts of
carbon-12 are mixed non-uniformly into the oxygen burning convection zone,
resulting in hot spots of nuclear energy production which are more than an
order of magnitude more energetic than the oxygen flame itself. Density
perturbations (up to 8%) occur at the `edges' of the convective zone and are
the result of gravity waves generated by interaction of penetrating flows into
the stable region. Perturbations of temperature and electron fraction at the
base of the convective zone are of sufficient magnitude to create angular
inhomogeneities in explosive nucleosynthesis products, and need to be included
in quantitative estimates of yields. Combined with the plume-like velocity
structure arising from convection, the perturbations will contribute to the
mixing of nickel-56 throughout supernovae envelopes. Runs of different
resolution, and angular extent, were performed to test the robustness of these
