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α effect in three-dimensional vortex of conducting rotating liquid.

L L Ogorodnikov1, S S Vergeles1

  • 1<a href="https://ror.org/00z65ng94">Landau Institute for Theoretical Physics</a>, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and <a href="https://ror.org/055f7t516">National Research University Higher School of Economics</a>, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia.

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This study analyzes helical turbulent flow statistics in rotating fluids. We found the alpha-effect

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Area of Science:

  • Fluid dynamics
  • Magnetohydrodynamics
  • Turbulence theory

Background:

  • Investigating helical turbulent pulsations within a rotating fluid's large-scale vortex.
  • Considering helical flow generated by a statistically axially symmetric random force with broken mirror symmetry.

Purpose of the Study:

  • To analytically calculate velocity-vorticity mean, magnitude, and anisotropy.
  • To examine the alpha-effect in electrically conducting liquids.
  • To determine the influence of Rossby (Ro) and magnetic Prandtl (Pr_m) numbers on the alpha-effect.

Main Methods:

  • Analytical calculation of one-point statistics for helical turbulent pulsations.
  • Analysis of the alpha-effect in a rotating fluid system.
  • Investigating the dependence of alpha-matrix elements on Ro and Pr_m numbers.

Main Results:

  • The velocity-vorticity mean, its magnitude, and anisotropy were analytically calculated.
  • The alpha-effect in electrically conducting liquids was examined.
  • Alpha-matrix elements show strong dependence on the relation between Rossby and magnetic Prandtl numbers (Ro << 1, Pr_m << 1).

Conclusions:

  • A criterion was established for when the alpha-effect induces instability in large-scale magnetic fields.
  • The findings are crucial for understanding turbulence and magnetic field generation in rotating systems.
  • The study highlights the critical role of fluid properties and rotation in magnetohydrodynamic phenomena.