Quasi-two-dimensional fast kinematic dynamo instabilities of chaotic fluid flows

Abstract

This paper tests previous heuristically derived general theoretical results for the fast kinematic dynamo instability of a smooth, chaotic flow by comparison of the theoretical results with numerical computations on a particular class of model flows. The class of chaotic flows studied allows very efficient high resolution computation. It is shown that 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 Rm. The initial exponential growth rate of moments of the magnetic field, the long time dynamo growth rate, and multifractal dimension spectra of the magnetic fields are calculated from theory using the numerically determined finite time Lyapunov exponent probability distribution of the flow and the cancellation exponent. All these results are numerically tested by generating a quasi-two-dimensional dynamo at magnetic Reynolds number Rm of order up to 105.