  This paper presents the vortical and self-similar solutions for 2D
compressible Euler equations using the separation method. These solutions
complement Makino's solutions in radial symmetry without rotation. The
rotational solutions provide new information that furthers our understanding of
ocean vortices and reference examples for numerical methods. In addition, the
corresponding blowup, time-periodic or global existence conditions are
classified through an analysis of the new Emden equation. A conjecture
regarding rotational solutions in 3D is also made.
