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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.

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Presentation on theme: "Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation V. L. Saveliev 1 and M. A. Gorokhovski 2 1. Institute."— 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 , 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

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


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