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

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


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.


Magnetic Field Reynolds Number Mathematical Application Stationary Flow Riemannian Manifold 
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Copyright information

© Russ. Acad. Sciences 1981

Authors and Affiliations

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

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