Generation of axisymmetric modes in cylindrical kinematic mean-field dynamos of VKS type

TL;DR

This paper investigates how mean field models can generate axisymmetric magnetic modes in cylindrical dynamos, focusing on the role of the $ ext{ extalpha}$-effect and its distribution, to explain the VKS experiment observations.

Contribution

It identifies necessary properties of the $ ext{ extalpha}$-effect distribution for axisymmetric mode generation in cylindrical mean-field dynamo models.

Findings

Simple $ ext{ extalpha}$-effect distributions require unrealistically large $ ext{ extalpha}$ values.

The study uses two different simulation codes for parametric analysis.

Axisymmetric modes are difficult to produce without extreme $ ext{ extalpha}$-effect parameters.

Abstract

In an attempt to understand why the dominating magnetic field observed in the von-K\'arm\'an-Sodium (VKS) dynamo experiment is axisymmetric, we investigate in the present paper the ability of mean field models to generate axisymmetric eigenmodes in cylindrical geometries. An $\alpha$-effect is added to the induction equation and we identify reasonable and necessary properties of the $\alpha$ distribution so that axisymmetric eigenmodes are generated. The parametric study is done with two different simulation codes. We find that simple distributions of $\alpha$-effect, either concentrated in the disk neighbourhood or occupying the bulk of the flow, require unrealistically large values of the parameter $\alpha$ to explain the VKS observations.