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Tenth International Symposium on Turbulence and Shear Flow Phenomena
July, 7-9, 2017 , Swissotel Chicago, Chicago, Illinois, U.S.A.

DOI: 10.1615/TSFP10

Self-preservation and the Kolmogorov 1st similarity law

pages 665-668
DOI: 10.1615/TSFP10.1130
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ABSTRACT

It is demonstrated that the Kolmogorov (1941a) first similarity law, enunciated solely on the basis of phenomenological arguments, can be recovered from the Navier-Stokes equations under the assumption of self-preservation (SP). In particular, it is shown that this law is recovered from the two-point transport equation of the second-order velocity structure function in decaying turbulence which is homogeneous and isotropic. The Kolmogorov length and velocity scales emerge as the "natural" scaling parameters. When SP is complete, i.e. SP holds at all scales of motion, the choice of scaling parameters is immaterial because they are all proportional to the Kolmogorov scales. When SP is incomplete, i.e. SP is tenable only at small scales and the Kolmogorov scales are the only correct scaling variables for the small scales.

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