Largescale dynamos at low magnetic Prandtl numbers above
Large-scale dynamos at low magnetic Prandtl numbers above, below, and inside the lab: Pr. M=n/h~10 -5 • Small-scale dynamos – Progressively harder to excite at low Pr. M – But may level off … • Large-scale dynamos – Independent of Pr. M – Low Pr. M can be used to “filter” out SS dynamo – Most of energy dissipated Ohmically – Can decrease n even further Axel Brandenburg (Nordita, Stockholm)
Winter School 11 -22 January 2
Small-scale vs large-scale dynamo 3
Low Pr. M results • Small-scale dynamo: Rm. crit=35 -70 for Pr. M=1 (Novikov, Ruzmaikin, Sokoloff 1983) • Leorat et al (1981): independent of Pr. M (EDQNM) • Rogachevskii & Kleeorin (1997): Rm, crit=412 • Boldyrev & Cattaneo (2004): relation to roughness • Ponty et al. : (2005): levels off at Pr. M=0. 2 4
Maybe no small scale “surface” dynamo? Small Pr. M=n/h: stars and discs around NSs and YSOs Schekochihin et al (2005) k Boldyrev & Cattaneo (2004) 5
Levels off for Taylor-Green flow • Confirmation for finite Rm for SS dynamo? • Or effect of LS dynamo? 6
Haugen & Brandenburg (PRE, astro-ph/0402301) Hyperviscous, Smagorinsky, normal height of bottleneck increased onset of bottleneck at same position Inertial range unaffected by artificial diffusion 7
Re-appearence at low Pr. M Gap between 0. 05 and 0. 2 ? Iskakov et al (2005) 8
Fully helical turbulence Here: Rm=urmsl/h Brandenburg (2001, Ap. J) 9
ABC flow dynamo Mininni et al. (2007, PRE) • Rm, crit varies still by factor 2 • Spectral magnetic energy peaks at k=1 10
Cartesian box MHD equations Induction Equation: Magn. Vector potential Momentum and Continuity eqns Viscous force forcing function (eigenfunction of curl) 11
Growth rate • Growth rate scaling for large Rm as for SS dynamo • Helical dynamo still excited for low Rm 12
Kinematic regime 13
Kinematic vs saturated regime 14
Spectra in kinematic regime • Kazantsev scaling for Pr. M=1 • Progressively more energy at large scale 15
Compensated spectra kinematic saturated 16
Low Pr. M dynamos with helicity do work • Energy dissipation via Joule • Viscous dissipation weak • Can increase Re substantially! 17
Pr. M=1, saturated case 18
U and B fields: minor changes 19
Conclusions 1) low Pr. M helps to distinguish LS and SS dynamos • LS dynamo must be excited Brun, Miesch, & Toomre (2004, Ap. J 614, 1073) • SS dynamo too dominant, swamps LS field • Dominant SS dynamo: artifact of large 2) Pr Important also for accretion disc dynamos M=n/h 20
- Slides: 20