Non uniform Rotating Vortices and Periodic Orbits for the Two-Dimensional Euler Equations

This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different m-fold symmetries, $$m\geqq 1$$ . In particular, a complete study is provided for the truncated quadratic density $$(A|x|^2+B){\mathbf{1}}_{{\mathbb {D}}}(x)$$ , with $${\mathbb {D}}$$ the unit disc. We exhibit different behaviors with respect to the coefficients A and B describing the rarefaction of bifurcating curves.