Other
Scientific paper
Oct 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt.........4n&link_type=abstract
Thesis (PHD). NEW YORK UNIVERSITY , Source DAI-B 58/04, p. 1917, Oct 1997, 130 pages.
Other
Turbulence, Beltrami Waves, Galactic Magnetic Fields
Scientific paper
This study is devoted to the investigation of multiple velocity modes in fast dynamos of the pulsed-wave type. In particular we are concerned with the role of the small-scale vortical structures of turbulence on the growth of magnetic energy and the relative size of the mean field developed once dynamical saturation sets in. The work is in two related but distinct parts. In the first we extend a kinematic dynamo model of Soward based upon the asymptotics of a large stretch limit to velocity waves with several distinct wavenumbers. Since the main ideas emerge by considering just two Beltrami waves, one having wavenumber 1 and the other having wavenumber n ≫ 1 and amplitude a ≪ 1, we concentrate first on this case. In the asymptotics for large stretch the time length α of each pulse is long, α ≫ 1, the small parameter being in effect the ratio of the dominate wavelength to the typical particle excursion associated with a pulse. The action of the flow is reduced to a map acting on the set of all possible magnetic fields, and measuring the magnetic field at the end of each pulse. The map is iterated until an eigenfunction emerges and the corresponding eigenvalue is computed. In the limit of a perfect conductor, the classical eigenfunction is lost but the magnetic field is still treated in a formal way as in classical perturbation of spectra. Based on physical arguments related to the cut-off length under which all small scales are destroyed by diffusion, we obtain for the multiple wave case asymptotic estimates for induced transformations of the Fourier coefficients of the magnetic field. We then obtain an expression for the growth rate of the dynamo in the perfectly conducting limit. We find that the effect of multiple waves on the growing rate is small in the parameter range studied, but that there are substantial effects on the form of the small-scale magnetic structure. In the second part the same type of kinematic flow is analyzed numerically and growth estimates are checked to be within the bounds prescribed. Estimates for the small scale magnetic structure are given both in terms of spectrum and relative to mean field magnitude. We then consider a numerical model of the full MHD dynamo problem, using the same type or flow. We consider two cases, one where the higher velocity modes participate in the dynamo but are unforced, another where all modes are forced. (The viscous Reynolds number is taken as O(1).) The observation is that the differences between unsustained high modes and an absence of high velocity modes are minimal, but the presence of a forcing of the high velocity modes significantly affects the relative magnitudes of the mean field and mean square field during the saturation phase. This important effect can lead to the enhanced mean field observed in galactic magnetic fields, as a kind of inverse magnetic cascade induced by the small turbulent eddies.
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