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arXiv 1806.04893physics.flu-dyn
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强非线性情况:高湍流中的不稳定性

A case of strong non linearity: intermittency in highly turbulent flows

Yves Pomeau, Martine Le Berre, Thierry Lehner

摘要:

长期以来,人们一直怀疑不可压缩流体在大雷诺数或无限大雷诺数(即在小粘度或零粘度)下的流动可能存在有限时间奇异性。我们简要地回顾了关于这一点的理论状况。讨论了小粘性对无粘流体欧拉方程自相似解的影响。然后,我们表明,在Modane风洞中的速度脉动的单点记录显示出大速度和大加速度之间的相关性,这与从Leray方程(1934)导出的流体方程自相似奇异解的标度律完全一致。相反,这些实验速度加速度的相关性是矛盾的柯尔莫哥洛夫标度律。

英文摘要:

It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We discuss the effect of a small viscosity on the self-similar solution of the Euler equations for inviscid fluids. Then we show that single point records of velocity fluctuations in the Modane wind tunnel display correlations between large velocities and large accelerations in full agreement with scaling laws derived from Leray's equations (1934) for self-similar singular solutions of the fluid equations. Conversely those experimental velocity-acceleration correlations are contradictory to the Kolmogorov scaling laws.

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