Simulations of small-scale turbulent dynamo.pdf

a r X i v : a s t r o - p h / 0 3 1 2 0 4 6 v 3 1 6 J a n 2 0 0 5 ASTROPHYSICAL JOURNAL 612, 276 (2004) [e-print astro-ph/0312046] Preprint typeset using LATEX style emulateapj v. 11/12/01 SIMULATIONS OF THE SMALL-SCALE TURBULENT DYNAMO ALEXANDER A. SCHEKOCHIHIN, 1 STEVEN C. COWLEY, 2 SAMUEL F. TAYLOR 3 Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Rd., London SW7 2BW, UK JASON L. MARON 4 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, Iowa City, IA 52242 AND JAMES C. MCWILLIAMS Department of Atmospheric Sciences, UCLA, Los Angeles, CA 90095-1565 February 2, 2008 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