ON THE NORMAL AND ANOMALOUS SCALING IN TURBULENCE
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摘要: 研究湍流结构函数的标度律。实验或数值模拟得到的湍流结构函数的标度指数是奇异的。很多学者认为:这一实验事实否定Kolmogorov1941年(K41)提出的正常标度律,各向同性湍流惯性区的标度律是奇异的。近年来作者发表一系列文章,提出不同的观点:由于有限雷诺数效应,有限雷诺数湍流的标度指数不等于真正的惯性区标度指数,湍流结构函数的标度指数的实验数据并不否定K41正常标度律,各向同性湍流惯性区的标度律可能是正常的。惯性区奇异标度律和正常标度律对应的湍流物理本质是完全不同的,因而研究解决这个争论具有重要的意义。Abstract: The scaling of structure functions in turbulenceis discussed. The scaling exponents of structure functionsobserved in experiments and numerical simulations areanomalous. This fact was interpreted by many authors as aclear evidence against Kolmogorov 1941 (K41) theory. It isconcluded that the inertial-range scaling in isotropicturbulence is anomalous. Recently we published papers todemonstrate a different point of view on the inertial-rangescaling. The scaling exponents observed in turbulence with afinite Reynolds number, is not the same as the inertial-rangescaling exponents, due to the finite Reynolds number effects.While the finite Reynolds number effects are considered, theanomalous scaling exponents obtained in experiments ornumerical simulations are not inconsistent to K41 normalscaling. The inertial-range scaling in isotropic turbulencemay be normal. This result should have important consequencein the field of turbulence, since the fact of the inertial-rangescaling being normal or anomalous implies completely differentunderstanding of the physics of turbulence.
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Key words:
- turbulence /
- scaling /
- probability density function /
- finite Reynolds number effect
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