FRACTAL DIMENSIONS OF FAST DYNAMO MAGNETIC-FIELDS

Recent studies of the fast kinematic dynamo find that, without diffusion, the magnetic flux tends to concentrate on a fractal set and generally exhibits an arbitrarily fine-scaled alternation in the orientation of the magnetic field. The presence of small magnetic diffusivity in conjunction with this arbitrarily fine-scaled alternation in the magnetic field orientation radically changes the small scale spatial structure of the field. Motivated by this consideration, we study the multifractal dimension spectra associated with fast dynamo magnetic fields both with and without diffusion. These spectra are shown to be different in the two cases. In addition, using a partition function technique, we obtain results giving the dimension spectra in terms of the distribution of finite time Lyapunov exponents. Numerical experiments illustrating and testing these results are presented.