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Optimal Length Scale for a Turbulent Dynamo.

Mira Sadek1,2, Alexandros Alexakis1, Stephan Fauve1

  • 1Laboratoire de Physique Statistique, Ecole Normale Supérieure, CNRS, Université Pierre et Marie Curie, Université Paris Diderot, Paris 75005, France.

Physical Review Letters
|March 5, 2016
PubMed
Summary
This summary is machine-generated.

Discovering an optimal forcing length scale for low Prandtl number dynamo flows significantly cuts energy needs. This finding offers a new strategy for designing efficient turbulent experimental dynamos.

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Area of Science:

  • Plasma Physics
  • Astrophysics
  • Geophysics

Background:

  • Dynamo theory explains magnetic field generation in celestial bodies and planets.
  • Low Prandtl number fluids are crucial in astrophysical and geophysical contexts.
  • Turbulence significantly impacts magnetic field generation, often hindering it.

Purpose of the Study:

  • To identify an optimal forcing length scale for low Prandtl number dynamo flows.
  • To reduce the required energy injection rate for dynamo action.
  • To investigate the effect of forcing wave number on critical magnetic Reynolds number.

Main Methods:

  • Numerical simulations of the induction equation in a periodic box.
  • Utilizing laminar and turbulent ABC flows.
  • Employing a subgrid turbulence model for turbulent flows.
  • Varying the forcing wave number (k_f) to assess its impact.

Main Results:

  • An optimal forcing wave number (k_f L ≃ 4) was identified, minimizing the turbulent critical magnetic Reynolds number (Rm_c^turb).
  • At this optimum, Rm_c^turb is over 10 times smaller than when forced at the largest scales (k_f = 1/L).
  • Turbulent fluctuations hinder dynamo action at large scales, but this effect is suppressed at the optimal forcing scale.

Conclusions:

  • An optimal forcing length scale exists for low Prandtl number dynamo flows.
  • This optimal scale significantly reduces the energy injection rate by up to three orders of magnitude.
  • The findings provide a novel strategy for designing efficient experimental turbulent dynamos.