Mri-driven Turbulence with Resistivity Takayoshi Sano


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MRI-Driven Turbulence with Resistivity

  • Takayoshi Sano

  • (Osaka Univ.)


Outline

  • MRI in Resistive Disks

    • Motivation
    • Lundquist Number
  • Small Scale Structures in MRI Driven Turbulence

    • Characteristic Scales & Energy Spectrum
    • Effect of Magnetic Field Geometry
  • Comparison with MRI in Viscous Disks



Importance of Resistivity

  • Protoplanetary Disks

    • Resistivity >> Viscosity
    • Net Vertical Fields Originated from Molecular Clouds
    • If ionization fraction is high enough, MRI is important.
      • Talks by Mark Wardle & Neal Turner
  • Saturation Mechanism of MRI

    • Magnetic Reconnections
    • Thermalization by Joule Heating


MRI in Resistive Disks

  • Resistivity  Lundquist Number



Critical Lundquist Number

  • Critical value is always unity.

    • Linear Analysis, Local Box Simulations, Stratified Disk Simulations
  • But, it depends on the saturated field strength.



Saturation Amplitude of MRI

  • Importance of Net Magnetic Flux

    • Veritcal or Toroidal Flux
  • Resolution Dependence  Higher Resolution



1. Small-Scale Structures in MRI-Driven Turbulence

  • Collaborators:

  • Shuichiro Inutsuka (Kyoto)

  • Takeru K. Suzuki (Tokyo)



High Resolution Resistive MHD Model

  • Resistive MHD

    • Local Shearing Box: 0.4H x 0.4H x 0.4H
    • Resolution: 5123
    • Field Geometry: No Net Flux
    • Lundquist Number: 30
    • Time Integration: 75-90 orbits


Origin of Small Structures?

  • Channel Flow (Axisymmetric MRI mode)

    • Nonlinear Growth  Exact Solution of Nonlinear MHD Eqs. (Magnetic field is amplified efficiently.)
    • Characteristic Structures of a Channel Mode
      • Strong Horizontal Field & Thin Current Sheets


Unit Structure of MRI Driven Turbulence

  • Lots of channel-flow structures can be seen in MRI turbulence.



Micro-Channel Flow at Point A



Micro-Channel Flow at Point B



Resolution Dependence

  • MRI wavelength & current thickness decreases with increasing resolution.



Field Geometry

  • Channel flow structures are much larger in models with a net-vertical flux.

  • Quantitative Analysis of the Size

  • Channel Flow Evolution



Energy Spectrum of MRI Turbulence

  • Anisotropic Turbulence

    • Elongated by Shear Flow
  • Weak Field

  • Toroidal Field Dominant

    • Vertical
    • Azimuthal


Power Spectrum at Inertia Range (1)



Power Spectrum at Inertia Range (2)

  • Vertical Direction

    • Kolmogorov Spectrum
  • Azimuthal Direction

    • Weaker Power
    • Steeper Decline
  • Many Similarities to Goldreich-Sridhar Spectrum



2. Comparison with MRI in Viscous Disks

  • Collaborator:

  • Youhei Masada (ASIAA)



MRI in Viscous Disks

  • Reynolds Number



Characteristic Scales of Viscous MRI



Characteristic Scales of Resistive MRI



Two-Dimensional Simulations

  • Viscous MHD

    • Radial-Vertical Plane
    • Shearing Box (without Vertical Gravity)


Viscosity vs. Resistivity



Interpretation of 2D Result (Resistive MRI)



Interpretation of 2D Result (Viscous MRI)



How About Doubly Diffusive System?



Prediction of Critical Lundquist Number



Summary

  • MRI turbulence with resistivity is important for the evolution of protoplanetary disks and to understand the saturation mechanism.

  • HIGH RESOLUTION STUDY

  • MRI turbulence consists of small channel flows, and their size may be related to the saturation amplitude.

  • Energy spectrum at the inertia range shows the Kolmogorov-like power index.

  • RESISTIVITY VS. VISCOSITY

  • Resistivity can suppress the growth of MRI more efficiently compared with viscosity.

  • 2D simulation results can be understood by the characteristics of the critical wavelength for MRI




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