Kinematic dynamo by parity-antisymmetric flows

A. A. Andrievsky ; V. A. Zheltigovskii ; R. A. Chertovskikh

Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 21 (2018) no. 2, pp. 83-95

Résumé

The paper is devoted to mathematical and numerical modelling of kinematic generation of magnetic field, involving large spatial scales, by a small-scale flow of incompressible electrically conducting fluid featuring a mirror antisymmetry. Direct numerical simulation demonstrates that such flows can support a magnetic field generation in presence of two main generation mechanisms, namely, the magnetic alpha-effect and negative eddy diffusivity. The magnetic field generation can be described as follows: $\alpha$-effect creates large-scale field $_0$> of amplitude ${\rm O}(1)$, oscillating on a time scale ${\rm O}(\varepsilon^{-1})$. Fluctuations {h$_0$} of this field have an amplitude ${\rm O}(1)$. Small-scale flow creates {1$_0$} with amplitude ${\rm O}(\varepsilon)$. Interaction of this field with small-scale flow creates an electromotive force $\times${h$_1$}> of amplitude ${\rm O}(\varepsilon)$. This electromotive force gives rise to an eddy diffusivity that supports a growth of a mean field $_0$> on a time scale ${\rm O}(\varepsilon^{-1})$. Here $\varepsilon$ is the characteristic spatial scale ratio. It may be important for applications that the mechanism for generation considered here does work in a wide range of magnetic Prandtl numbers. Numerical simulation for a flow, which velocity has a zero kinetic helicity everywhere in space, shows that the absence of helicity does not affect magnetic field generation.

Détail

Keywords: magnetohydrodynamics, magnetic feld, magnetic $\alpha$-effect, kinematic dynamo, helicity.