This paper tests previous heuristically derived general theoretical re
sults for the fast kinematic dynamo instability of a smooth, chaotic f
low by comparison of the theoretical results with numerical computatio
ns on a particular class of model flows. The class of chaotic hows stu
died allows very efficient high resolution computation. It is shown th
at an initial spatially uniform magnetic field undergoes two phases of
growth, one before and one after the diffusion scale has been reached
. Fast dynamo action is obtained for large magnetic Reynolds number R(
m). The initial exponential growth rate of moments of the magnetic fie
ld, the long time dynamo growth rate, and multifractal dimension spect
ra of the magnetic fields are calculated from theory using the numeric
ally determined finite time Lyapunov exponent probability distribution
of the flow and the cancellation exponent. All these results are nume
rically tested by generating a quasi-two-dimensional dynamo at magneti
c Reynolds number R(m) of order up to 10(5). (C) 1996 American Institu
te of Physics.