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Transition to Turbulent Dynamo Saturation.

Kannabiran Seshasayanan1, Basile Gallet2, Alexandros Alexakis1

  • 1Laboratoire de Physique Statistique, École Normale Supérieure, CNRS UMR 8550, Université Paris Diderot, Université Pierre et Marie Curie, 24 rue Lhomond, 75005 Paris, France.

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This summary is machine-generated.

Magnetic energy saturation is viscosity-independent at low magnetic Prandtl numbers (Pm). This study reveals a turbulent scaling regime, crucial for understanding dynamos in astrophysical scenarios, which is missed by current simulations.

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Area of Science:

  • Astrophysical dynamos
  • Magnetohydrodynamics
  • Fluid dynamics

Background:

  • Saturated magnetic energy in dynamo experiments is viscosity-independent.
  • State-of-the-art 3D direct numerical simulations (DNS) show viscosity-dependent magnetic energy.
  • Extrapolation of viscous scaling laws from DNS underestimates magnetic energy for realistic parameters.

Purpose of the Study:

  • Investigate dynamo saturation at very low magnetic Prandtl numbers (Pm).
  • Resolve the discrepancy between experimental and simulation results for magnetic energy scaling.
  • Identify the scaling regime governing dynamo saturation at low Pm.

Main Methods:

  • Developed a reduced model for rapidly rotating flows near the dynamo threshold.
  • Reduced the velocity field to two spatial dimensions and magnetic field to a single Fourier mode.
  • Performed numerical simulations of reduced equations for Pm down to 2×10⁻⁵, a regime inaccessible to 3D DNS.

Main Results:

  • Observed a transition in magnetic energy scaling from a high-Pm viscous regime to a low-Pm turbulent regime.
  • The low-Pm turbulent regime exhibits viscosity independence.
  • The transition to the turbulent saturation regime occurs at Pm≃10⁻³.

Conclusions:

  • The discrepancy in magnetic energy scaling arises from the inability of 3D DNS to reach sufficiently low Pm.
  • A viscosity-independent turbulent scaling regime governs dynamo saturation at low magnetic Prandtl numbers.
  • This low-Pm regime, occurring around Pm≃10⁻³, explains previously overlooked phenomena in dynamo studies.