QUASI-2-DIMENSIONAL FAST KINEMATIC DYNAMO INSTABILITIES OF CHAOTIC FLUID-FLOWS

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.