Toward the analogue of thermally generated electromagnetic fields

TL;DR

This paper explores the analogy between magnetic and vorticity fields in fluids considering dissipation and sources, introducing a new parameter to classify behaviors and analyzing the extent of their similarity through numerical simulations.

Contribution

It introduces a new dimensionless number S_M to better classify magnetized fluid behavior and investigates the analogy between magnetic and vorticity fields beyond ideal conditions.

Findings

Existence of a range of Prandtl numbers where the fields remain analogous

Introduction of the S_M number for classifying magnetized fluid behavior

Numerical simulations highlight the limits of the magnetic-vorticity analogy

Abstract

Magnetic and vorticity fields evolution equations are known to obey the same equation when effects of dissipation and sources terms are negligible. We investigate the analogy between the two fields for non-vanishing dissipation and sources. In addition to the Reynolds (Re)and Prandtl (Pr_M) numbers, we define a new number (S_M) that is given by the ratio of the diffusive term to the Biermann battery term and which allows for a different classification of magnetised fluid behaviour. Numerical simulations of the two fields are then carried out given a parameter space made of Reynolds, Prandtl and Source numbers. We find it appropriate to present and discuss the findings against Prandtl numbers given that these provide the link between viscous and magnetic diffusion. Our simulations indicate that there exists a range of Prandtl numbers for which the fields remain analogues which raises the important question of how far the analogy goes.