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A new era for mean fields: test fields and tests

A new era for mean fields: test fields and tests. Axel Brandenburg ( Nordita, Stockholm ). Output so far. 25%. Mean field theory is predictive. Open domain with shear Helicity is driven out of domain (Vishniac & Cho) Mean flow contours perpendicular to surface! Excitation conditions

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A new era for mean fields: test fields and tests

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  1. A new era for mean fields:test fields and tests Axel Brandenburg (Nordita, Stockholm)

  2. Output so far 25%

  3. Mean field theory is predictive • Open domain with shear • Helicity is driven out of domain (Vishniac & Cho) • Mean flow contours perpendicular to surface! • Excitation conditions • Dependence on angular velocity • Dependence on b.c.: symmetric vs antisymmetric

  4. Best if W contours ^ to surface Example: convection with shear  need small-scale helical exhaust out of the domain, not back in on the other side Magnetic Buoyancy? Tobias et al. (2008, ApJ) Käpylä et al. (2008, A&A)

  5. To prove the point: convection with vertical shear and open b.c.s Magnetic helicity flux Käpylä, Korpi, & myself (2008, A&A 491, 353) Effects of b.c.s only in nonlinear regime

  6. Calculate full aij and hij tensors turbulent emf • Imposed-field method • Convection (Brandenburg et al. 1990) • 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) a effect and turbulent magnetic diffusivity

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

  8. Test fields Example:

  9. Validation: Roberts flow SOCA SOCA result normalize

  10. Kinematic a and ht independent of Rm (2…200) Sur et al. (2008, MNRAS)

  11. The hxx and hyy are now the same Brandenburg & Sokoloff (2002, GAFD) Brandenburg (2005, AN)

  12. Scale-dependence

  13. Time-dependent case

  14. From linear to nonlinear Use vector potential Mean and fluctuating U enter separately

  15. Nonlinear aij and hij tensors Consistency check: consider steady state to avoid da/dt terms Expect: l=0 (within error bars)  consistency check!

  16. Application to passive vector eqn cf. Cattaneo & Tobias (2009) Verified by test-field method Tilgner & Brandenburg (2008)

  17. ht(Rm) dependence for B~Beq • l is small  consistency • a1 and a2 tend to cancel • to decrease a • h2 is small

  18. Test field tests • l = 0 • l = l(s) • l = l(B)

  19. The Future • Test fields will continue to provide guidence • Test flows: eddy viscosity • vorticity dynamo? • Maxwell stresses • Turbulent flux collapse • Negative turbulent mag presure • Global dynamo • Shell sectors 1046 Mx2/cycle

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