从蝴蝶效应到内在随机性：奇异剪切流的自发增长
From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows
摘要：
蝴蝶效应今天通常被认为是确定性混沌系统对初始条件的敏感依赖。然而，这只是洛伦兹开创的不可预测性概念的一个方面，他实际上预测了多尺度流体流动可以自发地失去其确定性，并变得内在随机。这种效应与混沌截然不同，目前还无法进行详细的物理观察。在这里，我们证实了这种情况下，它是固有的基本开尔文-亥姆霍兹流体动力学不稳定性的初始奇异剪切层。此外，我们提供的证据表明，由此产生的宏观流动显示出普遍的统计特性，这些特性由微观尺度的特定物理特性触发，但独立于微观尺度的特定物理特性。这种自发的随机性被解释为一个欧拉对应理查森的拉格朗日粒子的相对分散，给物质的随机性在湍流的内在本质。
英文摘要：
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.
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