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Self-preservation and the Kolmogorov 1st similarity law

Lyazid Djenidi
Discipline of Mechanical Engineering, University of Newcastle, Newcastle, 2308, NSW, AUSTRALIA

Robert Anthony Antonia
Discipline of Mechanical Engineering, University of Newcastle, Newcastle, 2308, NSW, AUSTRALIA

Luminita Danaila
CNRS, UMR 6614, Laboratoire de Thermodynamique, CORIA, Site universitaire du Madrillet, 76801 Saint-Etienne du Rouvray, France

Sinopsis

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.