Some remarks on the antidynamo theorem

  • Vladimir I. Arnold
Part of the Vladimir I. Arnold - Collected Works book series (ARNOLD, volume 2)


1. Of particular interest in the consideration of a magnetic field In a specified flow of a conducting fluid is the problem of the enhancement or maintenance of the initial magnetic field (kinematic dynamo). Steady-state fields (the maintenance case) usually arise with an increase in the magnetic Reynolds number, when the exponential attenuation changes to an exponential growth, which ls finally limited by the nonlinearlty arising because of the effect of the field on the motion. We shall indicate another type of steady-state magnetic field, which exists for any magnetic Reynolds number. The simplest example of such a field is a nonzero averaged field in infinite space.


Magnetic Field Reynolds Number Mathematical Application Mathematical Method Exponential Growth 
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Copyright information

© Izd. Moscow State Univ. 1982

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.HeidelbergGermany

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