Mri-driven Turbulence with Resistivity Takayoshi Sano

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MRI-Driven Turbulence with Resistivity

  • Takayoshi Sano

  • (Osaka Univ.)


  • 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


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


  • 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 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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