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Title:
Simulations of the Small-Scale Turbulent Dynamo
Authors:
Schekochihin, Alexander A.; Cowley, Steven C.; Taylor, Samuel F.; Maron, Jason L.; McWilliams, James C.
Affiliation:
AA(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, UK; Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK ), AB(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, UK; Also at the Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547.), AC(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, UK), AD(Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627; and Center for Magnetic Reconnection Studies, Department of Physics and Astronomy, University of Iowa, 203 Van Allen Hall, Iowa City, IA 52242), AE(Department of Atmospheric Sciences, UCLA, Los Angeles, CA 90095-1565)
Publication:
The Astrophysical Journal, Volume 612, Issue 1, pp. 276-307. (ApJ Homepage)
Publication Date:
09/2004
Origin:
UCP
Astronomy Keywords:
Magnetic Fields, Methods: Numerical, Magnetohydrodynamics: MHD, Plasmas, Turbulence
DOI:
10.1086/422547
Bibliographic Code:
2004ApJ...612..276S

Abstract

We report the results of an extensive numerical study of the small-scale turbulent dynamo. The primary focus is on the case of large magnetic Prandtl numbers Prm, which is relevant for hot low-density astrophysical plasmas. A Prm parameter scan is given for the model case of viscosity-dominated (low Reynolds number) turbulence. We concentrate on three topics: magnetic energy spectra and saturation levels, the structure of the magnetic field lines, and intermittency of the field strength distribution. The main results are as follows: (1) the folded structure of the field (direction reversals at the resistive scale, field lines curved at the scale of the flow) persists from the kinematic to the nonlinear regime; (2) the field distribution is self-similar and appears to be lognormal during the kinematic regime and exponential in the saturated state; and (3) the bulk of the magnetic energy is at the resistive scale in the kinematic regime and remains there after saturation, although the magnetic energy spectrum becomes much shallower. We propose an analytical model of saturation based on the idea of partial two-dimensionalization of the velocity gradients with respect to the local direction of the magnetic folds. The model-predicted saturated spectra are in excellent agreement with numerical results. Comparisons with large-Re, moderate-Prm runs are carried out to confirm the relevance of these results and to test heuristic scenarios of dynamo saturation. New features at large Re are elongation of the folds in the nonlinear regime from the viscous scale to the box scale and the presence of an intermediate nonlinear stage of slower than exponential magnetic energy growth accompanied by an increase of the resistive scale and partial suppression of the kinetic energy spectrum in the inertial range. Numerical results for the saturated state do not support scale-by-scale equipartition between magnetic and kinetic energies, with a definite excess of magnetic energy at small scales. A physical picture of the saturated state is proposed.
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