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Nonlocal turbulent transport

Nonlocal turbulent transport. Extracting concepts from grand challenge DNS Alpha effect Test-field method Integral kernel. Brandenburg, R ä dler, & Schrinner (2008, A&A 482, 732) Hubbard & Brandenburg (2009, ApJ 706, 712). Test-field method: a ij and h ij tensors.

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Nonlocal turbulent transport

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  1. Nonlocal turbulent transport • Extracting concepts from grand challenge DNS • Alpha effect • Test-field method • Integral kernel Brandenburg, Rädler, & Schrinner (2008, A&A 482, 732) Hubbard & Brandenburg (2009, ApJ 706, 712)

  2. Test-field method: aij and hij tensors Original equation (uncurled) Mean-field equation fluctuations Response to arbitrary mean fields

  3. Constand and linear test fields Example:

  4. Result for Roberts flow But: a and ht should have been constants

  5. Periodic test fields Example:

  6. Result for Roberts flow Now: a and ht are k-dependent!

  7. Validation & k-dependence SOCA SOCA result Brandenburg, Rädler, Schrinner (2008, A&A) normalize

  8. Remember: a and ht are really kernels IAU Symp 71 in Prague, Czechoslovakia (1975)

  9. Convolution  multiplication in k space

  10. Non-locality for turbulence

  11. Confirmed also for other cases Mitra et al. (2009 A&A 495, 1) U=(0, Sx, 0) Sh=S/uk=-0.13 ~1/[1+(k/kf)2] seems now compulsory Significant when MFM would produce SS Unconfirmed for large k Smagorinsky scaling ~1/k-4/3 Madarassy & Brandenburg,, (2010, PRE)

  12. Similar to earlier work with D Sokoloff

  13. Nonlocality in time Hubbard & Brandenburg (2009, ApJ 706, 712)

  14. Importance of time-dependence

  15. Conclusions • Nonlocality is of practical relevance • Reconstructing the full EMF (Chatterjee et al. 2010) Reconstruction with k up to 16 Reconstruction with basic mode Original EMF

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