Andrievsky A.A., Zheligovsky V.A., Chertovskikh R.A. Kinematic Dynamo by Parity-Antisymmetric Flows

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https://doi.org/10.15688/mpcm.jvolsu.2018.2.7

Aleksandr Andreyevich Andrievsky
Software Architect,
SDC RTSoft Ltd
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Nikitinskaya St., 3 bld. 1, 105037 Moscow, Russian Federation

Vladislav Aleksandrovich Zheligovsky
Doctor of Physical and Mathematical Sciences, Chief Researcher,
Institute of earthquake prediction theory and mathematical geophysics, Russian
Academy of Sciences
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Profsoyuznaya St., 84/32, 117997 Moscow, Russian Federation

Roman Aleksandrovich Chertovskikh
Candidate of Physical and Mathematical Sciences, PhD, Researcher,
Research Center for Systems and Technologies (SYSTEC), University of Porto
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Rua Dr. Roberto Frias, s/n 4200-465 Porto, Portugal;
Senior Researcher, Samara State Aerospace University (National Research University)
Moskovskoe shosse, 34, 443086 Samara, Russian Federation

Abstract. The paper is devoted to mathematical and numerical modelling of kinematic generation of magnetic field, involving large spatial scales, by a small-scale flow of incompressible electrically conducting fluid featuring a mirror antisymmetry. Direct numerical simulation demonstrates that such flows can support a magnetic field generation in presence of two main generation mechanisms, namely, the magnetic alpha-effect and negative eddy diffusivity.

The magnetic field generation can be described as follows:

 

  • α -effect creates large-scale field ⟨h0⟩ of amplitude O(1), oscillating on a time scale O(ε−1).
  • Fluctuations {h0} of this field have an amplitude O(1).
  • Small-scale flow creates {10} with amplitude O(ε).
  • Interaction of this field with small-scale flow creates an electromotive force ⟨v × {h1}⟩ of amplitude O(ε).
  • This electromotive force gives rise to an eddy diffusivity that supports a growth of a mean field ⟨h0⟩ on a time scale O(ε−1).

Here ε is the characteristic spatial scale ratio.

It may be important for applications that the mechanism for generation considered here does work in a wide range of magnetic Prandtl numbers. Numerical simulation for a flow, which velocity has a zero kinetic helicity everywhere in space, shows that the absence of helicity does not affect magnetic field generation.

Key words: magnetohydrodynamics, magnetic field, magnetic α -effect, kinematic dynamo, helicity.

Creative Commons License
Kinematic Dynamo by Parity-Antisymmetric Flows by Andrievsky A.A., Zheligovsky V.A., Chertovskikh R.A. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 2 2018, pp. 83-95

 

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