Nonlinear dynamos at infinite magnetic Prandtl number

TL;DR

This paper explores nonlinear dynamo behavior at infinite magnetic Prandtl number, showing that magnetic energy concentrates in force-free structures and exhibits chaos at high magnetic Reynolds numbers.

Contribution

It provides the first detailed analysis of nonlinear dynamos in the infinite magnetic Prandtl number limit, revealing structure formation and chaos.

Findings

Magnetic energy concentrates in flat, elongated, force-free structures.

Magnetic energy increases weakly with magnetic Reynolds number.

Structures become unstable and chaotic at high magnetic Reynolds numbers.

Abstract

The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow, and the ABC flow forced at two different scales. The investigation covers roughly three orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration was almost force-free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.