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Scaling laws and vanishing‐viscosity limits for wall‐bounded shear flows and for local structure in developed turbulence
Author(s) -
Barenblatt G. I.,
Chorin Alexandre J.
Publication year - 1997
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199704)50:4<381::aid-cpa5>3.0.co;2-6
Subject(s) - turbulence , mathematics , scaling , k omega turbulence model , bounded function , turbulence modeling , reynolds number , k epsilon turbulence model , viscosity , exponent , logarithm , statistical physics , reynolds averaged navier–stokes equations , scaling law , mathematical analysis , kolmogorov microscales , physics , geometry , mechanics , thermodynamics , linguistics , philosophy
Scaling laws for wall‐bounded turbulence are derived and their properties are analyzed via vanishing‐viscosity asymptotics; a comparison of the results with recent experiments shows that the observed scaling law differs significantly from the customary logarithmic law of the wall. The Izakson‐Millikan‐von Mises derivation of turbulence structure, properly interpreted, confirms this analysis. Analogous relations for the local structure of turbulence are given, including results on the scaling of the higher‐order structure functions; these results suggest that there are no Reynolds‐number‐independent corrections to the Kolmogorov exponent and thus that the classical 1941 version of the Kolmogorov theory already gives the limiting behavior. The use of small‐viscosity asymptotics is explained, and the consequences of the theory and of the experimental evidence for the Navier‐Stokes equations and for the statistical theory of turbulence are discussed. © 1997 John Wiley & Sons, Inc.