  In the absence of rotation and shear, and under the assumption of constant
temperature or specific entropy, purely potential forcing by localized
expansion waves is known to produce irrotational flows that have no vorticity.
Here we study the production of vorticity under idealized conditions when there
is rotation, shear, or baroclinicity, to address the problem of vorticity
generation in the interstellar medium in a systematic fashion. We use
three-dimensional periodic box numerical simulations to investigate the various
effects in isolation. We find that for slow rotation, vorticity production in
an isothermal gas is small in the sense that the ratio of the root-mean-square
values of vorticity and velocity is small compared with the wavenumber of the
energy-carrying motions. For Coriolis numbers above a certain level, vorticity
production saturates at a value where the aforementioned ratio becomes
comparable with the wavenumber of the energy-carrying motions. Shear also
raises the vorticity production, but no saturation is found. When the
assumption of isothermality is dropped, there is significant vorticity
production by the baroclinic term once the turbulence becomes supersonic. In
galaxies, shear and rotation are estimated to be insufficient to produce
significant amounts of vorticity, leaving therefore only the baroclinic term as
the most favorable candidate. We also demonstrate vorticity production visually
as a result of colliding shock fronts.
