1. Large Scale Dynamo Action in MRI Disks Role of stratification Dynamo cycles Mean-field interpretation Incoherent alpha-shear dynamo Axel Brandenburg (Nordita, Stockholm)

2. 2 Unstratified MRI turbulence 512 3 w/o hypervisc.  t = 60 = 2 orbits No large scale field (i)Too short? (ii)No stratification?

3. 3 Vorticity and Density See poster by Tobi Heinemann on density wave excitation!

4. 4 Small scales dominate

5. 5 Animated spectra Red E M Black E K

6. 6 Old stratified runs Brandenburg et al. (1995)

7. 7 Different boundary conditions

8. 8 Tall disk with potential field b.c. 2  x 2  x 8 

9. 9 z-t diagram

10. 10 Longer and bigger Parity not always well defined

11. 11 Mean-field interpretation Correlation method –MRI accretion discs (Brandenburg & Sokoloff 2002) –Galactic turbulence (Kowal et al. 2005, 2006) Test field method –Stationary geodynamo (Schrinner et al. 2005, 2007) –Shear flow turbulence (Brandenburg 2005) turbulent emf  effect and turbulent aagnetic diffusivity

12. 12 Calculate full  ij and  ij tensors Original equation (uncurled) Mean-field equation fluctuations Response to arbitrary mean fields

13. 13 Test fields Example:

14. 14 Validation: Roberts flow SOCA normalize SOCA result

15. 15 (i) Turbulence: kinematic  and  t independent of Rm Galloway-Proctor:

16. 16 Full alpha tensor for MRI  yy negative, as before (Brandenburg et al. 1995)

17. 17 Full eta tensor  xx and  xx the same and positive (new)  yx always positive (new)

18. 18 (ii) Shear turbulence Growth rate Use S<0, so need negative  * 21 for dynamo

19. 19 Case with just shear Similar to G. Lesur’s plot of yesterday!

20. 20 Dependence on Sh and Rm Again  yx always positive

21. 21 Gaussian fluctuations

22. 22 Fluctuations of  ij and  ij Incoherent  effect (Vishniac & Brandenburg 1997, Sokoloff 1997, Silantev 2000, Proctor 2007)

23. 23 Onset and saturation of incoherent alpha-shear dynamos

24. 24 Conclusions Cycles w/ stratification Test field method robust –Even when small scale dynamo –    0 and    t0 Rotation and shear:  * ij –WxJ not (yet?) excited –Incoherent  works