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

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/R m = 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 R m = 104 case should persist as R m → ∞.