Large-scale dynamos at low magnetic Prandtl numbers

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Large-scale dynamos at low magnetic Prandtl
numbers
above, below, and inside the lab PrMn/h10-5

• Small-scale dynamos
• Progressively harder to excite at low PrM
• But may level off
• Large-scale dynamos
• Independent of PrM
• Low PrM can be used to filter out SS dynamo
• Most of energy dissipated Ohmically
• Can decrease n even further

• Axel Brandenburg (Nordita, Stockholm)

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Winter School 11-22 January
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Small-scale vs large-scale dynamo
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Low PrM results

• Small-scale dynamo Rm.crit35-70 for PrM1
  (Novikov, Ruzmaikin, Sokoloff 1983)
• Leorat et al (1981) independent of PrM (EDQNM)
• Rogachevskii Kleeorin (1997) Rm,crit412
• Boldyrev Cattaneo (2004) relation to roughness
• Ponty et al. (2005) levels off at PrM0.2

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Maybe no small scale surface dynamo?
Small PrMn/h stars and discs around NSs and
YSOs
Schekochihin et al (2005)
k
Boldyrev Cattaneo (2004)
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Levels off for Taylor-Green flow

• Confirmation for finite Rm for SS dynamo?
• Or effect of LS dynamo?

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Hyperviscous, Smagorinsky, normal
height of bottleneck increased
Haugen Brandenburg (PRE, astro-ph/0402301)
onset of bottleneck at same position
Inertial range unaffected by artificial diffusion
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Re-appearence at low PrM
Gap between 0.05 and 0.2 ?
Iskakov et al (2005)
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Fully helical turbulence
Here Rmurmsl/h
Brandenburg (2001, ApJ)
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ABC flow dynamo
Mininni et al. (2007, PRE)

• Rm,crit varies still by factor 2
• Spectral magnetic energy peaks at k1

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Cartesian box MHD equations
Magn. Vector potential
Induction Equation
Momentum and Continuity eqns
Viscous force
forcing function
(eigenfunction of curl)
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Growth rate

• Growth rate scaling for large Rm as for SS dynamo
• Helical dynamo still excited for low Rm

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Kinematic regime
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Kinematic vs saturated regime
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Spectra in kinematic regime

• Kazantsev scaling for PrM1
• Progressively more energy at large scale

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Compensated spectra
kinematic
saturated
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Low PrM dynamoswith helicity do work

• Energy dissipation via Joule
• Viscous dissipation weak
• Can increase Re substantially!

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PrM1, saturated case
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U and B fields minor changes
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Conclusions
1) low PrM helps to distinguish LS and SS dynamos

• LS dynamo must be excited
• SS dynamo too dominant, swamps LS field
• Dominant SS dynamo artifact of large PrMn/h

Brun, Miesch, Toomre (2004, ApJ 614, 1073)
2) Important also for accretion disc dynamos