Journal of Fluid Mechanics

A fast kinematic dynamo in two-dimensional time-dependent flows

Niels F.  Otani 
School of Electrical Engineering, Cornell University, Ithaca, NY 14853, USA

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A time-continuous, constant-resistivity version of the fast dynamo model introduced by Bayly & Childress (1988) is studied numerically. The expected dynamo mechanism in this context is described and is shown to be operative in the simulations. Exponential growth of the fastest growing mode is observed, with the growth rate for the smallest resistivity attempted (1/Rm = 10-4) agreeing well with the Bayly–Childress model. It is argued, based on the long- and short-wavelength behaviour of the mode for different resistivities, that the growth rates obtained for the Rm = 104 case should persist as Rm [rightward arrow] [infty infinity].

(Published Online April 26 2006)
(Received November 10 1992)
(Revised February 10 1993)