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New Perspectives in Turbulence: Scaling Laws, Asymptotics, and Intermittency

Intermittency, a basic property of fully developed turbulent flow, decreases with growing viscosity; therefore classical relationships obtained in the limit of vanishing viscosity must be corrected when the Reynolds number is finite but large. These corrections are the main subject of the present paper. They lead to a new scaling law for wall-bounded turbulence, which is of key importance in engineering, and to a reinterpretation of the Kolmogorov--Obukhov scaling for the local structure of turbulence, which has been of paramount interest in both theory and applications. The background of these results is reviewed, in similarity methods, in the statistical theory of vortex motion, and in intermediate asymptotics, and relevant experimental data are summarized.