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Small-scale structures in three-dimensional magnetohydrodynamic turbulence.

P D Mininni1, A G Pouquet, D C Montgomery

  • 1National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307, USA.

Physical Review Letters
|February 7, 2007
PubMed
Summary
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Small-scale structures in decaying magnetohydrodynamics (MHD) flows develop rapidly, forming current and vorticity sheets. At high Reynolds numbers, dissipation becomes independent of viscosity, indicating a universal behavior in turbulent magnetic fields.

Area of Science:

  • Plasma Physics
  • Fluid Dynamics
  • Magnetohydrodynamics (MHD)

Background:

  • Understanding the development of small-scale structures is crucial for comprehending energy dissipation in turbulent plasmas.
  • Decaying flows provide a simplified yet fundamental system to study turbulence dynamics.

Purpose of the Study:

  • To investigate the rate of small-scale development in decaying three-dimensional MHD flows.
  • To analyze the formation and evolution of current and vorticity sheets under different initial conditions.
  • To determine the behavior of dissipation at high Reynolds numbers.

Main Methods:

  • Direct numerical simulations (DNS) were employed.
  • Simulations utilized grids up to 1536^3 grid points.
  • Both deterministic and random initial conditions were considered.

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Main Results:

  • Parallel current and vorticity sheets were observed to form at identical spatial locations.
  • These sheets undergo destabilization, folding, and rolling up after an initial exponential growth phase.
  • A self-similar evolution of current and vorticity maxima was found at high Reynolds numbers, growing as a cubic power of time.

Conclusions:

  • The study reveals a universal mechanism for the development of small scales in decaying MHD turbulence.
  • A finite dissipation rate, independent of the Reynolds number, is reached at high Reynolds numbers.
  • These findings have implications for understanding energy transfer and dissipation in astrophysical and laboratory plasmas.