Large Scale Dynamo Action in MRI Disks

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
ltBy gt
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
a effect and turbulent aagnetic diffusivity

• 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)

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 Slt0, so need negative h21 for dynamo
19
Case with just shear
Similar to G. Lesurs 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 hij
• WxJ not (yet?) excited
• Incoherent a works