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, $m\ge 1$. In particular, a complete study is provided for the truncated quadratic density $(A\mathrm{\mid }x{\mathrm{\mid }}^2+B){\mathbf{1}}_{\mathbb{D}}(x)$, with $\mathbb{D}$ the unit disc. We exhibit different behaviors with respect to the coefficients $A$ and $B$ describing the rarefaction of bifurcating curves.