1 / 22

Detection of negative effective magnetic pressure instability in turbulence simulations

Detection of negative effective magnetic pressure instability in turbulence simulations. Instability in stratified turbulence with B -field (here horizontal) Reproduced in mean-field magnetohydrodynamics R m dependence of turbulent transport coefficient.

monifa
Download Presentation

Detection of negative effective magnetic pressure instability in turbulence simulations

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. Detection of negative effective magnetic pressure instabilityin turbulence simulations • Instability in stratified turbulence with B-field (here horizontal) • Reproduced in mean-field magnetohydrodynamics • Rm dependence of turbulent transport coefficient Axel Brandenburg, Koen Kemel, Nathan Kleeorin, Dhrubaditya Mitra, Igor Rogachevskii

  2. Setup • 3-D box, size (2p)3, isothermal MHD • Random, nonhelical forcing at kf/k1=5, 15 or 30 • Stratified in z, r~exp(-z/H), H=1, Dr=535 • Periodic in x and y • stress-free, perfect conductor in z • Weak imposed field B0 in y • Run for long times: what happens? • Turnover time tto=(urmskf)-1, turb diff ttd=(htk12)-1 • Is longer by factor 3(kf/k1)2 = 3 152 = 675 • Average By over y and Dt=80tto

  3. Negative effective magnetic pressure instability in action (ReM=70, kf/k1=15) Brandenburg et al. (2011, ApJL 740, 50L)

  4. Poorly visible in snapshots (kf/k1=15)

  5. Exponential growth • Several thousand turnover times • Or ½ a turbulent diffusive time • Exponential growth  linear instability of an already turbulent state

  6. Large aspect ratio: more cells • not all cells equally strong • reasonably well seen in just y-averages (top) • Better with additional time averaging (bottom)

  7. Larger scale separation: 30 instead of 15

  8. Better visible in snapshots for kf/k1=30

  9. Seems to work only in certain B range • is expected • B0/Beq~0.15 • Vertical inhomo. for stronger field

  10. But B structure produced deeper down • Here more scale separation (30 instead of 15) • Field strength and growth rate the same for different B0 • Can just reposition z range of the box to get the same growth rate and field strength

  11. Rm dependence Breakdown of quasi-linear theory ReM here based on forcing k Here 15 eddies per box scale ReM=70 means 70x15x2p=7000 based on box scale

  12. Mean-field concept a effect, turbulent diffusivity, Yoshizawa effect, etc Turbulent viscosity and other effects in momentum equation

  13. Earlier results for low Rm • Rädler (1974) computed magnetic suppression (for other reasons) • Rüdiger (1974)  works only for Pm < 8 • Roberts & Soward (1975), Rüdiger et al. (1986) Maxwell tension formally negative for Rm > 1, but invalid • Rüdiger et al. (2012), no negative effective magnetic pressure for Rm < 1. • Kleeorin et a. (1989, 1990, 1996), Kleeorin & Rogachevskii (1994, 2007)

  14. Magnetic contribution to pressure & energy different! Can lead to reversed mean-field buoyancy in stratified system

  15. Formation of flux concentrations Earlier work with Kleeorin & Rogachevskii (2010, AN 331, 5)

  16. Stratified runs isothermal  constant scale height, density contrast, exp(2p)=535, Beq varies, so B/Beq varies, get whole curve in one run

  17. Convection not just for forced turbulence,  result is robust!

  18. Effective magnetic pressure

  19. Fit formula and Rm dependence

  20. Basic mechanism Anelastic: descending structure  compression B amplifies B amplifies Growth rate

  21. Conclusions: new food for thought • Essential ingredient for shallow sunspot acticity identified (ApJL 740, L50) • Effect does not exist below Rm=1 (SOCA) • Becomes stronger with better scale separation (e.g. 30 instead of 15) • Active regions shallow phenomena Hindman et al. (2009, ApJ)

  22. Thanks to the Astrophysics group at Nordita

More Related