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 $(A|x|^2+B){\bf{1}}_{\mathbb{D}}(x)$, with $\mathbb{D}$ the unit disc. We exhibit different behaviors with respect to the coefficients $A$ and $B$ describing the rarefaction of bifurcating curves.

中文翻译：

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二维欧拉方程的非均匀旋转涡和周期轨道

本文涉及湍流中一些特殊有序结构的研究。特别是，提出了一种系统和相关的方法来构造具有不一定均匀密度和不同 $m$--fold 对称性 $m\ge 1$ 的非平凡和非径向旋转涡旋。特别是对截断二次密度$(A|x|^2+B){\bf{1}}_{\mathbb{D}}(x)$进行了完整的研究，其中$\mathbb{D }$ 单位光盘。我们在描述分叉曲线稀疏的系数 $A$ 和 $B$ 方面表现出不同的行为。