Toward the analogue of a thermally generated electromagnetic field

Abstract

The evolution equations for magnetic and vorticity fields are known to display the same pattern when dissipation and sources terms are neglected. We investigate the analogy between the two fields for non-vanishing dissipation and sources. In addition to the magnetic Reynolds (ReM) and Prandtl (PrM) numbers, we define a new number (SM) that is given by the ratio of the diffusive term to the Biermann battery term and which allows for a different classification of magnetized fluid behavior. 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 and also raises the prospect of a theory of analogue magnetism.