Nonlinear evolution of the magnetohydrodynamic Rayleigh-Taylor instability

James McLellan Stone, Thomas Gardiner

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional magnetohydrodynamic simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than λc = B·B/(ρhl)g are suppressed (where ρh and ρl are the densities of the heavy and light fluids, respectively), whereas modes perpendicular to B are unaffected. We study strong fields with λc varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.

Original languageEnglish (US)
Article number094104
JournalPhysics of Fluids
Volume19
Issue number9
DOIs
StatePublished - Sep 2007

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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