  The dynamical response of edge waves under the influence of self-gravity is
examined in an idealized two-dimensional model of a proto-stellar disc,
characterized in steady state as a rotating vertically infinite cylinder of
fluid with constant density except for a single density interface at some
radius r0. The fluid in basic state is prescribed to rotate with a Keplerian
profile $\Omega_k(r)\sim r^{-3/2}$ modified by some additional azimuthal
sheared flow. A linear analysis shows that there are two azimuthally
propagating edge waves, kin to the familiar Rossby waves and surface gravity
waves in terrestrial studies, which move opposite to one another with respect
to the local basic state rotation rate at the interface. Instability only
occurs if the radial pressure gradient is opposite to that of the density jump
(unstably stratified) where self-gravity acts as a wave stabilizer irrespective
of the stratification of the system. The propagation properties of the waves
are discussed in detail in the language of vorticity edge waves. The roles of
both Boussinesq and non-Boussinesq effects upon the stability and propagation
of these waves with and without the inclusion of self-gravity are then
quantified. The dynamics involved with self-gravity non- Boussinesq effect is
shown to be a source of vorticity production where there is a jump in the basic
state density, in addition, self-gravity also alters the dynamics via the
radial main pressure gradient, which is a Boussinesq effect . Further
applications of these mechanical insights are presented in the conclusion
including the ways in which multiple density jumps or gaps may or may not be
stable.
