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Self-similar turbulent dynamo.

Alexander A Schekochihin1, Steven C Cowley, Jason L Maron

  • 1Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, United Kingdom. as629@damtp.cam.ac.uk

Physical Review Letters
|March 5, 2004
PubMed
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Numerical simulations reveal that magnetic field amplification in conductive fluids exhibits spatial intermittency, concentrating fields in folded structures. This intermittency stabilizes, forming self-similar probability-density functions, contrary to prior assumptions.

Area of Science:

  • Plasma physics
  • Magnetohydrodynamics
  • Computational fluid dynamics

Background:

  • Magnetic field amplification is crucial in astrophysical and geophysical phenomena.
  • Understanding the spatial distribution and statistical properties of amplified magnetic fields is key.

Purpose of the Study:

  • To numerically investigate the spatial intermittency and statistical behavior of magnetic fields during amplification in highly conducting fluids.
  • To examine the influence of diffusion on magnetic field intermittency and its probability-density function (PDF).

Main Methods:

  • Numerical simulations of magnetic field amplification in a conducting fluid.
  • Analysis of the spatial distribution and field-strength probability-density function (PDF).
  • Investigation across varying magnetic Prandtl numbers and inclusion of diffusion effects.

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Main Results:

  • Magnetic fields concentrate in long, thin, folded structures during growth, exhibiting spatial intermittency.
  • Contrary to expectations, intermittency does not grow indefinitely if diffusion is present; the PDF of field strength becomes self-similar.
  • Normalized moments increase with magnetic Prandtl number; self-similarity is linked to finite system size and flow scales.
  • In the nonlinear saturated state, intermittency decreases, and the PDF becomes exponential.

Conclusions:

  • The study demonstrates that magnetic field amplification in conductive fluids leads to self-similar statistical behavior under realistic conditions (finite size, diffusion).
  • The findings challenge the notion of ever-increasing intermittency, highlighting a stabilizing effect of diffusion.
  • Parallels are drawn to self-similar phenomena in passive-scalar mixing and map dynamos, suggesting broader applicability.