Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Нужнов Ю.В.  

Dissipative vortexes structures of fine-scale turbulence

Sizing of the smallest dissipative vortexes structures of turbulent stream is doing based on the theory for fine-scale structure of turbulence with consideration of the intermittency effects. Characteristic differential of the developed theory is to take into consideration an "internal" intermittency of dissipation field and the statistical character of ratio of size reduction of the vortexes. According to this theory the expressions for characteristics of the fine-scale turbulence into inertial-subrange depend from value of the intermittency coefficients (both external and internal) as well as dimensional relationship the fine-scale fluctuations to integral turbulence lengthscale defined as parameter r/L. Calculations of the Kolmogorov coefficients have been carried out depending on "external" intermittency coefficient and correspond closely to experimental data.
It was shown taking into account the "internal" intermittency result in occurence of dissipative structures the smallest size of which can be level of r=10-610-8m that is several orders smaller then the averaged Kolmogorov lengthscale . As long as the maximum dissipation rate of turbulent energy due to vortexes with size of the order of 10 then said dissipative structures can be interpreted as same "fractal walls" of this vortexes in form of nanovortex formations (layers, fibers, tubes) on which is presented the dissipation.
Further evolution these dissipative structures can be concerned with formation of strange attractors and in case of flow-around solid microparticles which are presented in turbulent flow - to incipient (hydrodynamic) stage shaping of the double-walled tubular nanostructure. A mechanism of this stage was verified by experiments carried out on carbonic base surface of the electron microscope with ingrained metal particles. Analysis of photographs made at that is confirmed the mechanism.

Abstracts file: Vortex.doc
Full text file: ДиссвВихрСтрМелкТурб.pdf

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