Navier-Stokes不变性中的隐标度不变性
Hidden scale invariance in Navier-Stokes intermittency
摘要：
我们揭示了一个隐藏的缩放对称性的纳维-斯托克斯方程的极限消失的粘度，这源于动力学时空重新缩放周围适当定义的拉格朗日标度中心。在动力学水平上，隐藏的对称性项目的解决方案，不同的伽利略不变性和全球时间尺度到同一个代表性的流。在统计水平上，这种投影修复了尺度不变性，这在原始公式中被不确定性破坏了。根据第一作者以前的工作，我们在这里假设和证实与数字，隐藏的对称性统计上持有充分发展的湍流的惯性间隔。我们表明，这种对称性占的尺度不变性的某一类的可观的，特别是，柯尔莫哥洛夫乘数。
英文摘要：
We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centers. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers.
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