论文标题
从蝴蝶效应到固有的随机性：奇异剪切流的自发生长
From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows
论文作者
论文摘要
如今，蝴蝶效应通常以确定性混沌系统对初始条件的敏感依赖性而识别。但是，这只是洛伦兹（Lorenz）开创的不可预测性概念的一个方面，他实际上预测多尺度流体流可以自发地失去确定性的性质并在本质上随机。与混乱完全不同的这种效果对详细的物理观察仍然无法触及。在这里，我们通过证明它是最初奇异的剪切层的基本开尔文 - 螺旋体的水动力不稳定性来证实了这种情况。此外，我们提供的证据表明，所得的宏观流显示由触发的通用统计特性，但与微尺度上的特定物理特性无关。这种自发的随机性被解释为与理查森（Richardson）相对分散拉格朗日颗粒的欧拉（Eulerian）对应物，从而使湍流随机性的内在性质具有物质。
The butterfly effect is today commonly identified with the sensitive dependence of deterministic chaotic systems upon initial conditions. However, this is only one facet of the notion of unpredictability pioneered by Lorenz, who actually predicted that multiscale fluid flows could spontaneously lose their deterministic nature and become intrinsically random. This effect, which is radically different from chaos, have remained out of reach for detailed physical observations. Here, we substantiate this scenario by showing that it is inherent to the elementary Kelvin--Helmholtz hydrodynamical instability of an initially singular shear layer. We moreover provide evidence that the resulting macroscopic flow displays universal statistical properties that are triggered by, but independent of specific physical properties at micro-scales. This spontaneous stochasticity is interpreted as an Eulerian counterpart to Richardson's relative dispersion of Lagrangian particles, giving substance to the intrinsic nature of randomness in turbulence.
