Conformal invariance in two-dimensional turbulence
Conformal invariance in two-dimensional turbulence
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DOI：
10.1038/nphys217
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发表时间：
2006-02-01
期刊：
影响因子：
19.6
通讯作者：
Falkovich, G
中科院分区：
文献类型：
--
作者：
Bernard, D;Boffetta, G;Falkovich, G
基本物理定律的简单性在基本对称性中表现出来。虽然具有无限多个强相互作用自由度的系统（在粒子物理学和临界现象中）很难描述，但它们通常表现出对称性，特别是尺度不变性。在二维（2D）局部性通常扩展尺度不变性到更广泛的一类保形变换，允许非均匀重新缩放。共形不变性使得能够对2D中的临界现象的普适性类别进行彻底的分类。强相互作用非平衡系统的一个典型例子，二维湍流中是否存在共形不变性？在这里，我们数值计算表明，一些功能的二维逆湍流叶栅显示共形不变性。我们观察到，涡度簇的统计是非常接近的临界渗流，最简单的普遍性类的临界现象之一。这些结果代表了共形对称框架内的二维物理统一的关键一步。
The simplicity of fundamental physical laws manifests itself in fundamental symmetries. Although systems with an infinite number of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2D) locality often extends scale invariance to a wider class of conformal transformations that allow non-uniform rescaling. Conformal invariance enables a thorough classification of universality classes of critical phenomena in 2D. Is there conformal invariance in 2D turbulence, a paradigmatic example of a strongly interacting non-equilibrium system? Here, we show numerically that some features of a 2D inverse turbulent cascade show conformal invariance. We observe that the statistics of vorticity clusters are remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a key step in the unification of 2D physics within the framework of conformal symmetry.