A magnetic field in a stationary flow with stretching in a Riemannian manifold fluid

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

Abstract

The problem of the kinematic dynamo at large magnetic Reynolds numbers R m is considered using as an example artificial flow with exponential particle stretching, simulating the stationary stochastic flow of a conducting fluid. The magnetic fields which have a periodic dependence on only one coordinate grow in time exponentially and without bound. Each Fourier harmonic of the deviation from this growing field increases initially rapidly with a rate independent of R m during a time interval t.≈t 0 in R m , and then decays very rapidly.

Keywords

Magnetic Field Reynolds Number Mathematical Application Stationary Flow Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Russ. Acad. Sciences 1981

Authors and Affiliations

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

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