1 / 27

Numerical simulations of astrophysical dynamos

Numerical simulations of astrophysical dynamos. Dynamos: numerical issues Alpha dynamos do exist: linear and nonlinear Constrained by magnetic helicity: need fluxes How high do we need to go with Rm? MRI and low PrM issue. Axel Brandenburg ( Nordita, Stockholm ). Struggle for the dynamo.

collinm
Download Presentation

Numerical simulations of astrophysical dynamos

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Numerical simulations of astrophysical dynamos • Dynamos: numerical issues • Alpha dynamos do exist: linear and nonlinear • Constrained by magnetic helicity: need fluxes • How high do we need to go with Rm? • MRI and low PrM issue Axel Brandenburg (Nordita, Stockholm)

  2. Struggle for the dynamo • Larmor (1919): first qualitative ideas • Cowling (1933): no  antidynamo theorem • Larmor (1934): vehement response • 2-D not mentioned • Parker (1955): cyclonic events, dynamo waves • Herzenberg (1958): first dynamo • 2 small spinning spheres, slow dynamo (l~Rm-1) • Steenbeck, Krause, Rädler (1966): awdynamo • Many papers on this since 1970 • Kazantsev (1968): small-scale dynamo • Essentially unnoticed, simulations 1981, 2000-now

  3. Mile stones in dynamo research • 1970ies: mean-field models of Sun/galaxies • 1980ies: direct simulations • Gilman/Glatzmaier: poleward migration • 1990ies: compressible simulations, MRI • Magnetic buoyancy overwhelmed by pumping • Successful geodynamo simulations • 2000- magnetic helicity, catastr. quenching • Dynamos and MRI at low PrM=n/h

  4. Easy to simulate? • Yes, but it can also go wrong • 2 examples: manipulation with diffusion • Large-scale dynamo in periodic box • With hyper-diffusion curl2nB • ampitude by (k/kf)2n-1 • Euler potentials with artificial diffusion • Da/Dt=hDa, Db/Dt=hDb, B = grada xgradb

  5. Dynamos withEuler Potentials • B = gradax gradb • A = a gradb, so A.B=0 • Here: Robert flow • Details MNRAS 401, 347 • Agreement for t<8 • For smooth fields, not for d-correlated initial fields • Exponential growth (A) • Algebraic decay (EP)

  6. Reasons for disagreement • because dynamo field is helical? • because field is three-dimensional? • none of the two: it is because h is finite

  7. Is this artificial diffusion kosher? Make h very small, it is artificial anyway, Surely, the R term cannot matter then?

  8. Problem already in 2-D nonhelical • Works only when a and b are not functions of the same coordinates Alternative possible in 2-D Remember:

  9. Method of choice? No, thanks • It’s not because of helicity (cf. nonhel dyn) • Not because of 3-D: cf. 2-D decay problem • It’s really because a(x,y,z,t) and b(x,y,z,t)

  10. Other good examples of dynamos Helical turbulence (By) Helical shear flow turb. Convection with shear Magneto-rotational Inst. Käpyla et al (2008)

  11. One big flaw: slow saturation (explained by magnetic helicity conservation) molecular value!!

  12. Helical dynamo saturation with hyperdiffusivity for ordinary hyperdiffusion ratio 53=125 instead of 5 PRL 88, 055003

  13. Test-field results for a and htkinematic: independent of Rm (2…200) Sur et al. (2008, MNRAS)

  14. Rm dependence for B~Beq • l is small  consistency • a1 and a2 tend to cancel • making a small • h2 small

  15. Boundaries instead of periodic Brandenburg, Cancelaresi, Chatterjee, 2009, MNRAS

  16. Boundaries instead of periodic Hubbard & Brandenburg, 2010, GAFD

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

  18. Low PrM issue • Small-scale dynamo: Rm.crit=35-70 for PrM=1 (Novikov, Ruzmaikin, Sokoloff 1983) • Leorat et al (1981): independent of PrM (EDQNM) • Rogachevskii & Kleeorin (1997): Rm,crit=412 • Boldyrev & Cattaneo (2004): relation to roughness • Ponty et al.: (2005): levels off at PrM=0.2

  19. Re-appearence at low PrM Gap between 0.05 and 0.2 ? Iskakov et al (2005)

  20. Small-scale vs large-scale dynamo

  21. Low PrM dynamoswith helicity do work • Energy dissipation via Joule • Viscous dissipation weak • Can increase Re substantially!

  22. Comparison with stratified runs <By > Brandenburg et al. (1995) Dynamo waves Versus Buoyant escape

  23. Phase relation in dynamos Mean-field equations: Solution:

  24. Unstratified: also LS fields? Lesur & Ogilvie (2008) Brandenurg et al. (2008)

  25. Low PrM issue in unstratified MRI Käpylä & Korpi (2010): vertical field condition

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

  27. 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

More Related