Simulations of the Small‐Scale Turbulent Dynamo

  • Schekochihin A
  • Cowley S
  • Taylor S
  • et al.
379Citations
Citations of this article
103Readers
Mendeley users who have this article in their library.

Abstract

We report an extensive numerical study of the small-scale turbulent dynamo at large magnetic Prandtl numbers Pm. A Pm scan is given for the model case of low-Reynolds-number turbulence. We concentrate on three topics: magnetic-energy spectra and saturation levels, the structure of the field lines, and the field-strength distribution. The main results are (1) the folded structure (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 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 spectra are in excellent agreement with numerical results. Comparisons with large-Re, moderate-Pm runs are carried out to confirm the relevance of these results. 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.

Cite

CITATION STYLE

APA

Schekochihin, A. A., Cowley, S. C., Taylor, S. F., Maron, J. L., & McWilliams, J. C. (2004). Simulations of the Small‐Scale Turbulent Dynamo. The Astrophysical Journal, 612(1), 276–307. https://doi.org/10.1086/422547

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free