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Large Scale Dynamo Action in MRI Disks

Large Scale Dynamo Action in MRI Disks. Role of stratification Dynamo cycles Mean-field interpretation Incoherent alpha-shear dynamo Axel Brandenburg ( Nordita, Stockholm ). Unstratified MRI turbulence. 512 3 w/o hypervisc. D t = 60 = 2 orbits. No large scale field Too short?

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Large Scale Dynamo Action in MRI Disks

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  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. Unstratified MRI turbulence 5123 w/o hypervisc. Dt = 60 = 2 orbits • No large scale field • Too short? • No stratification?

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

  4. Small scales dominate

  5. Animated spectra Red EM Black EK

  6. Old stratified runs <By > Brandenburg et al. (1995)

  7. Different boundary conditions

  8. Tall disk withpotential field b.c. 2p x 2p x 8p

  9. z-t diagram

  10. Longer and bigger Parity not always well defined

  11. Mean-field interpretation turbulent emf • 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) a effect and turbulent aagnetic diffusivity

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

  13. Test fields Example:

  14. Validation: Roberts flow SOCA SOCA result normalize

  15. (i) Turbulence: kinematic a and ht independent of Rm Galloway-Proctor:

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

  17. Full eta tensor hxx and hxx the same and positive (new) hyx always positive (new)

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

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

  20. Dependence on Sh and Rm Again, hyx always positive

  21. Gaussian fluctuations

  22. Fluctuations of aij and hij Incoherent a effect (Vishniac & Brandenburg 1997, Sokoloff 1997, Silantev 2000, Proctor 2007)

  23. Onset and saturation of incoherent alpha-shear dynamos

  24. Conclusions • Cycles w/ stratification • Test field method robust • Even when small scale dynamo • a a0 and h ht0 • Rotation and shear: h*ij • WxJ not (yet?) excited • Incoherent a works

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