  In order to understand star formation it is important to understand the
dynamics of atomic and molecular clouds in the interstellar medium (ISM).
Nonlinear hydrodynamic flows are a key component to the ISM. One route by which
nonlinear flows arise is the onset and evolution of interfacial instabilities.
Interfacial instabilities act to modify the interface between gas components at
different densities and temperatures. Such an interface may be subject to a
host of instabilities, including the Rayleigh-Taylor, Kelvin-Helmholtz, and
Richtmyer-Meshkov instabilities. Recently, a new density interface instability
was identified. This self-gravity interfacial instability (SGI) causes any
displacement of the interface to gr ow on roughly a free-fall time scale, even
when the perturbation wavelength is much less than the Jeans length. In
previous work, we used numerical simulations to confirm the expectations of
linear theory and examine the nonlinear evolution of the SGI. We now continue
our study by generalizing our initial conditions to allow the acceleration due
to self-gravity to be non-zero across the interface. We also consider the
behaviour of the SGI for perturbation wavelengths near the Jeans wavelength. We
conclude that the action of self-gravity across a density interface may play a
significant role in the ISM either by fueling the growth of new instabilities
or modifying the evolution of existing instabilities.
