  Ionization front instabilities have long been of interest for their suspected
role in a variety of phenomena in the galaxy, from the formation of bright rims
and 'elephant trunks' in nebulae to triggered star formation in molecular
clouds. Numerical treatments of these instabilities have historically been
limited in both dimensionality and input physics, leaving important questions
about their true evolution unanswered. We present the first three-dimensional
radiation hydrodynamical calculations of both R-type and D-type ionization
front instabilities in galactic environments (i.e., solar metallicity gas).
Consistent with linear stability analyses of planar D-type fronts, our models
exhibit many short-wavelength perturbations growing at early times that later
evolve into fewer large-wavelength structures. The simulations demonstrate that
both self-consistent radiative transfer and three-dimensional flow introduce
significant morphological differences to unstable modes when compared to
earlier two-dimensional approximate models. We find that the amplitude of the
instabilities in the nonlinear regime is primarily determined by the efficiency
of cooling within the shocked neutral shell. Strong radiative cooling leads to
long, extended structures with pronounced clumping while weaker cooling leads
to saturated modes that devolve into turbulent flows. These results suggest
that expanding H II regions may either promote or provide turbulent support
against the formation of later generations of stars, with potential
consequences for star formation rates in the galaxy today.
