Abstract
All known fast dynamos where diffusion has been explicitly included exhibit eigenfunctions with fine structures whose characteristic sizes apparently scale as R −1/2m , where R m is the magnetic Reynolds number. Results for a number of such calculations are summarised, including cases with and without stagnation points, in Cartesian and spherical geometries. In all cases there is agreement with the conclusion of Moffatt and Proctor (1985) that fast dynamos can only occur where such fine structures are present. However, the fraction of space occupied by these structures tends to zero as R m →∞, and the associated Lorentz force becomes infinite. There are thus paradoxes in considering the kinematic problem in this limit, and an astrophysically meaningful calculation must embody the back reaction of the magnetic field on the flow dynamics.
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© 1995 Springer-Verlag Berlin Heidelberg
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Galloway, D.J., Hollerbach, R., Proctor, M.R.E. (1995). Fine structure in fast dynamo computations. In: Meneguzzi, M., Pouquet, A., Sulem, PL. (eds) Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence. Lecture Notes in Physics, vol 462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102432
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DOI: https://doi.org/10.1007/BFb0102432
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