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Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation V. L. Saveliev 1 and M. A. Gorokhovski 2 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

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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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IV.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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