Dissipative structures in a nonlinear dynamo

TL;DR

This paper investigates the structure and scaling laws of magnetic fields generated by a nonlinear dynamo in magnetohydrodynamics, revealing cigar-like dissipative regions and their dependence on diffusivity.

Contribution

It provides new numerical scaling laws for energy and dissipation in the Archontis dynamo, along with rigorous results on solution existence and detailed analysis of dissipative structures.

Findings

Dissipation concentrates in cigar-like structures along separatrices.

Scaling laws show dissipation regions scale with the square root of diffusivity.

Symmetries influence the structure of the magnetic field and flow.

Abstract

This paper considers magnetic field generation by a fluid flow in a system referred to as the Archontis dynamo: a steady nonlinear magnetohydrodynamic (MHD) state is driven by a prescribed body force. The field and flow become almost equal and dissipation is concentrated in cigar-like structures centred on straight-line separatrices. Numerical scaling laws for energy and dissipation are given that extend previous calculations to smaller diffusivities. The symmetries of the dynamo are set out, together with their implications for the structure of field and flow along the separatrices. The scaling of the cigar-like dissipative regions, as the square root of the diffusivities, is explained by approximations near the separatrices. Rigorous results on the existence and smoothness of solutions to the steady, forced MHD equations are given.