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.
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© 1981 Russ. Acad. Sciences
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Arnold, V.I. (1981). A magnetic field in a stationary flow with stretching in a Riemannian manifold fluid. In: Givental, A., Khesin, B., Varchenko, A., Vassiliev, V., Viro, O. (eds) Vladimir I. Arnold - Collected Works. Vladimir I. Arnold - Collected Works, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31031-7_34
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DOI: https://doi.org/10.1007/978-3-642-31031-7_34
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31030-0
Online ISBN: 978-3-642-31031-7
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