Oscillatory α2‐dynamo: numerical investigation

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Abstract
Linear and nonlinear equations describing the generation of a large‐scale magnetic field (α2‐dynamo) in a thin disc of turbulent conducting fluid are derived and discussed. The numerical procedure is based on a finite‐difference implicit scheme for the corresponding nonlinear Cauchy problem with boundary conditions. In addition, the QR‐algorithm for the linear eigenvalue problem is realized.It is demonstrated that the α2‐dynamo is able to generate oscillatory magnetic fields. The periods of oscillation are typically of the order of or less than the diffusion time. These oscillations are suggested to be due to boundary effects. Dependence of the solutions on the generation efficiency and on the distribution of the mean helicity across the disc are discussed in detail.The period of oscillations only slightly depends on the specific form of distribution of the mean helicity across the disc and is determined mainly by the magnitude of the helicity and by the position of the helicity extremum: the nearer this point to the boundary, the greater the oscillation frequency. Nonlinear effects suppress oscillations when the mean helicity attains its maximum at a depth not more than a quarter of the disc thickness, and promote them otherweise.The one‐dimensional system of nonlinear α2‐dynamo equations is reduced to a single nonlinear equation of the Schrödinger type.

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