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Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation V. L. Saveliev1 and M. A. Gorokhovski2 1. Institute of Ionosphere, Almaty , Kazakhstan 2. Laboratoire de Mécanique des Fluides et AcoustiqueEcole Centrale de Lyon, France PHYSICAL REVIEV E 72, (2005)

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Introduction

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**II. Renormalized averaging formula for <vu>**

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**Operator for averaging the field product**

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**Simplest formula for averaging**

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Example of averaging

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**Deviatoric part of stress tensor**

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Important remark

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**III. Group-theoretical model of developed turbulence**

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Symmetry parameters

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**Self-similar solutions**

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**Decomposition of turbulent field**

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**Invariance of turbulent state**

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**Renormalization-group invariance**

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**Renormalization of the averaged Navier-Stokes equation Averaging over small scale**

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**Inner threshold of turbulence**

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**Equation for averaged turbulent fields**

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**Remarks about viscosity**

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V. Conclusion

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References

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I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

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