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

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.