  In this article we investigate the two-dimensional incompressible rotating
and stratified, just rotating, just stratified Euler equations with each other
and with the normal Euler equations with the self-similar Ansatz. There are
analytic solutions available for all four models, for density, pressure and
velocity fields, some of them are compound power-law dependent functions. In
general the solutions have a rich mathematical structure. Some solutions show
unphysical explosive properties others, however are physically acceptable and
have finite numerical values with power law decays. For a better transparency
we present some figures for the most complicated velocity and pressure fields.
