1 / 18

Numerical simulations of the magnetorotational instability (MRI)

Numerical simulations of the magnetorotational instability (MRI). S.Fromang CEA Saclay, France J.Papaloizou ( DAMTP, Cambridge, UK) G.Lesur ( DAMTP, Cambridge, UK), T.Heinemann (DAMTP, Cambridge, UK). Background: ESO press release 36/06. The magnetorotational instability.

murphy-moore
Download Presentation

Numerical simulations of the magnetorotational instability (MRI)

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 the magnetorotational instability (MRI) S.Fromang CEA Saclay, France J.Papaloizou (DAMTP, Cambridge, UK) G.Lesur (DAMTP, Cambridge, UK), T.Heinemann (DAMTP, Cambridge, UK) Background: ESO press release 36/06

  2. The magnetorotational instability (Balbus & Hawley, 1991) nonlinear evolution  numerical simulations

  3. I. Setup & numerical issues

  4.  The shearing box (1/2) r x y H H z y H x • Local approximations • Ideal MHD equations + EQS (isothermal) • vy=-1.5x • Shearing box boundary conditions (Hawley et al. 1995)

  5.  The shearing box (2/2) z x Transport diagnostics • Maxwell stress: TMax=<-BrB>/P0 • Reynolds stress: TRey=<vrv>/ P0 • =TMax+TRey  rate of angular momentum transport Magnetic field configuration Zero net flux: Bz=B0 sin(2x/H) Net flux: Bz=B0

  6. The 90’s and early 2000’s Local simulations (Hawley & Balbus 1992) • Breakdown into MHD turbulence (Hawley & Balbus 1992) • Dynamo process (Gammie et al. 1995) • Transport angular momentum outward: <>~10-3-10-1 • Subthermal B field, subsonic velocity fluctuations BUT: low resolutions used (323 or 643)

  7. The issue of convergence (Nx,Ny,Nz)=(64,100,64) Total stress: =4.2  10-3 (Nx,Ny,Nz)=(128,200,128) Total stress: =2.0  10-3 (Nx,Ny,Nz)=(256,400,256) Total stress: =1.0  10-3 Fromang & Papaloizou (2007) ZEUS code (Stone & Norman 1992), zero net flux The decrease of  with resolution is not a property of the MRI. It is a numerical artifact!

  8. Dissipation Small scales dissipation important  Explicit dissipation terms needed (viscosity & resistivity) • Reynolds number: Re =csH/ • Magnetic Reynolds number: ReM=csH/ Magnetic Prandtl number Pm=/

  9.  Case I Zero net flux

  10. Pm=/=4, Re=3125 ZEUS PENCIL CODE SPECTRAL CODE NIRVANA Fromang et al. (2007) ZEUS : =9.6  10-3 (resolution 128 cells/scaleheight) NIRVANA :=9.5  10-3 (resolution 128 cells/scaleheight) SPECTRAL CODE: =1.0  10-2 (resolution 64 cells/scaleheight) PENCIL CODE :=1.0  10-2 (resolution 128 cells/scaleheight)  Good agreement between different numerical methods

  11. Pm=/=4, Re=6250 (Nx,Ny,Nz)=(256,400,256) Density Vertical velocity By component Movie: B field lines and density field (software SDvision, D.Polmarede, CEA)

  12. Effect of the Prandtl number Pm=/=4 Pm=/= 8 Pm=/= 16 Pm=/= 2 Pm=/= 1 Take Rem=12500 and vary the Prandtl number…. (Lx,Ly,Lz)=(H,H,H) (Nx,Ny,Nz)=(128,200,128) •  increases with the Prandtl number • No MHD turbulence for Pm<2

  13.  The Pm effect Pm =/ <<1 Viscous length << Resistive length Schekochihin et al. (2004) Velocity Magnetic field Velocity Magnetic field Schekochihin et al. (2007) Schekochihin et al. (2007) Pm=/>>1 Viscous length >> Resistive length • No proposed mechanisms…but: • Dynamo in nature (Sun, Earth) • Dynamo in experiments (VKS) • Dynamo in simulations

  14. Parameter survey Pm ? MHD turbulence ? No turbulence Re • Small scales important in MRI turbulence • Transport increases with the Prandtl number • No transport when Pm≤1 For a given Pm, does α saturates at high Re?

  15. Pm=4, Transport Re=3125 Re=6250 Re=12500 (Nx,Ny,Nz)=(128,200,128) (Nx,Ny,Nz)=(256,400,256) (Nx,Ny,Nz)=(512,800,512) Total stress =9.2 ± 2.8  10-3 Total stress =7.6 ± 1.7  10-3 Total stress =2.0 ± 0.6  10-2 No systematic trend as Re increases…

  16.  Case II Vertical net flux

  17. Influence of Pm - Pseudo-spectral code, resolution: (64,128,64) - (Lx,Ly,Lz)=(H,4H,H) - =100 Lesur & Longaretti (2007)

  18. Conclusions & open questions Pm MHD turbulence ? No turbulence Re • Include explicit dissipation in local simulations of the MRI: • resistivity AND viscosity • Zero net flux AND nonzero net flux •  an increasing function of Pm • Behavior at large Re is unclear • Global simulations? What is the effect of large scales? • State of PP disks very uncertain (Pm<<1) • Dead zone location/structure very uncertain…

More Related