Analytic Solutions of the Rotating and Stratified Hydrodynamical Equations

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.