# Group Theoretical Model of Developed Turbulence and Renormalization of the Navier Stokes Equation

A theoretical model for understanding developed turbulence and the Navier Stokes equation, using group theory and renormalization techniques.

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## About Group Theoretical Model of Developed Turbulence and Renormalization of the Navier Stokes Equation

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## Presentation Transcript

1. 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 480020, Kazakhstan 2. Laboratoire de Mcanique des Fluides et AcoustiqueEcole Centrale de Lyon, France PHYSICAL REVIEV E 72, 016302 (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. IV. 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