Revisiting the ABC flow dynamo

TL;DR

This paper studies the dynamo properties of the classical ABC flow at high magnetic Reynolds numbers, revealing complex eigenvalue behaviors and showing that the flow's fast dynamo nature is not yet confirmed at Rm=25000.

Contribution

It provides a detailed analysis of the eigenvalue spectrum of the ABC flow dynamo, identifying key transitions and demonstrating the ongoing variation of growth rates at high Rm.

Findings

Two eigenvalue crossings identified in growth rate.

Dominant eigenvalue becomes real at a finite parameter.

At Rm=25000, the flow still does not exhibit asymptotic fast dynamo behavior.

Abstract

The ABC flow is a prototype for fast dynamo action, essential to the origin of magnetic field in large astrophysical objects. Probably the most studied configuration is the classical 1:1:1 flow. We investigate its dynamo properties varying the magnetic Reynolds number Rm. We identify two kinks in the growth rate, which correspond respectively to an eigenvalue crossing and to an eigenvalue coalescence. The dominant eigenvalue becomes purely real for a finite value of the control parameter. Finally we show that even for Rm = 25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its still varies very significantly with the controlling parameter. Even at these very large values of Rm the fast dynamo property of this flow cannot yet be established.