Non uniform rotating solutions for the two-dimensional Euler equations

We explore 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≥1. In particular, a complete study is provided for the truncated quadratic density (A|x|2+B)1D(x), with D the unit disc. We exhibit different behaviors with respect to the coefficients A and B describing the rarefaction of bifurcating curves. This is a joint work with Taoufik Hmidi and Juan Soler.