1. 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)

2. Introduction

3. II. Renormalized averaging formula for <vu>

4. Operator for averaging the field product

5. Simplest formula for averaging

6. Example of averaging

7. Deviatoric part of stress tensor

8. Important remark

9. III. Group-theoretical model of developed turbulence

10. Symmetry parameters

11. Self-similar solutions

12. Decomposition of turbulent field

13. Invariance of turbulent state

14. Renormalization-group invariance

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

16. Inner threshold of turbulence

17. Equation for averaged turbulent fields

18. Remarks about viscosity

19. V. Conclusion

20. References