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Magnetostatic Boundary Conditions01:28

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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Magnetically Induced Rotating Rayleigh-Taylor Instability
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The magnetorotational instability prefers three dimensions.

Jeffrey S Oishi1, Geoffrey M Vasil2, Morgan Baxter1

  • 1Department of Physics and Astronomy, Bates College, Lewiston, ME 04240, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 22, 2020
PubMed
Summary
This summary is machine-generated.

The magnetorotational instability (MRI) is driven by 3D modes in astrophysical disks and stellar interiors, especially near critical shear rates. These 3D modes significantly impact fluid dynamics and dynamo action in rotating, magnetized fluids.

Keywords:
magnetohydrodynamicsstabilitystars

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Area of Science:

  • Astrophysics
  • Plasma Physics
  • Fluid Dynamics

Background:

  • The magnetorotational instability (MRI) is a key mechanism driving turbulence in accretion disks.
  • Astrophysical disks and stellar interiors feature rotating, electrically conducting fluids with magnetic fields.
  • Internal shear layers in stars can exhibit MRI instability across various profiles.

Purpose of the Study:

  • To investigate the nature of the fastest-growing modes of the magnetorotational instability (MRI) in ideal magnetofluids.
  • To determine the conditions under which three-dimensional (3D) modes become dominant over two-dimensional (2D) modes.
  • To assess the relevance of these findings for astrophysical systems and laboratory experiments.

Main Methods:

  • Analysis of ideal magnetofluid dynamics.
  • Characterization of mode growth rates based on shear rate (S) and its onset value (S_c).
  • Comparison of 2D and 3D mode behavior across different shear profiles and magnetic Prandtl numbers.

Main Results:

  • The fastest-growing MRI modes are three-dimensional (3D) when the shear rate (S) is near the 2D onset value (S_c).
  • For Keplerian shear, 3D modes are unstable above S ≈ 0.10 S_c and dominate 2D modes until S ≈ 2.05 S_c.
  • 3D modes are prevalent in stellar shear profiles and relevant for liquid-metal experiments, persisting well beyond S ≈ 2.05 S_c.

Conclusions:

  • Weakly nonlinear MRI theory suggests saturation occurs by driving the shear rate towards its critical value.
  • The non-normal nature and transient growth of 3D MRI modes are significant wherever three-dimensionality is present.
  • 3D growth indicates potential for direct dynamo action originating from the linear instability.