Linear dynamo simulations with time-dependent helical flows

J. Leorat

Directeur de recherches au CNRS, URA 173 (CNRS) and Observatoire de Paris-Meudon, 92195 Meudon, France

Abstract
The dynamo effect in cylindrical geometry is studied with the help of numerical simulations. Time-dependent flows in the kinematic dynamo problem model the turbulence expected for realistic flows. The cylindrical conducting flow is surrounded by an insulator, and periodic solutions along the axial direction are looked for. Radial derivatives are computed with a high-order, compact, finite difference scheme, and a Fourier spectral method is used for the azimuthal and axial coordinates. In Order to compare with previous results of Lupian and Shukurov [8] obtained with infinitely conducting boundaries, the study considers first a peculiar steady helical flow geometry, and a critical magnetic Reynolds number of about 30 is found for this velocity field. At a given magnetic Reynolds number above critical, the unstable magnetic modes lie in a band of wave numbers varying with the geometry of the flow. The relation between the preferred modes and the flow configuration is discussed. Are the differences between the results of [81 and the numerical simulations related to the nature of the boundaries? The explanation of this question would help to select more efficient flows, not subject to the constraints of helical symmetry, which may be simulated with the same code. The turbulent fluctuations of the flow configuration are simulated using a simple time periodic modulation. The helical dynamo proves to withstand successfully relatively large variations of its parameters. Figs 3, Refs 10.