  The spiral core instability, observed in large aspect ratio Rayleigh-Benard
convection, is studied numerically in the framework of the Swift-Hohenberg
equation coupled to a large-scale flow. It is shown that the instability leads
to non-trivial core dynamics and is driven by the self-generated vorticity.
Moreover, the recently reported transition from spirals to hexagons near the
core is shown to occur only in the presence of a non-variational nonlinearity,
and is triggered by the spiral core instability. Qualitative agreement between
the simulations and the experiments is demonstrated.
