Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion

Abstract

MANY astrophysical magnetic fields are thought to arise by dynamo action due to internal fluid motions, but the natural timescale for magnetic field growth is the diffusion timescale, which in realistic astrophysical applications is very large¹. A fast dynamo is one that operates on the much shorter turnover timescale of the generating fluid flow, and the analytical intractability of smooth flows with diffusion has prompted the use of many ingenious models^2–10, differing from the true problem in having a modified or time-dependent diffusion or singularities in the flow field. Here we adopt a straightforward approach and present numerical computations of linear kinematic dynamos associated with periodic smooth flows, with diffusion explicitly included. Examples of time-varying flows depending on two spatial coordinates give convincing evidence of fast dynamo action for diffusion times up to 10,000 times greater than the turnover time. A three-dimensional steady flow shows similar behaviour, although computations have not beencarried out so far and the asymptotic behaviour is less clear. All these flows have large regions where particle paths are chaotic.