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Title:
Magnetic field evolution in simulations with Euler potentials
Authors:
Brandenburg, Axel
Affiliation:
AA(NORDITA, AlbaNova University Center, Roslagstullsbacken 23, SE 10691 Stockholm, Sweden; Department of Astronomy, AlbaNova University Center, Stockholm University, SE 10691 Stockholm, Sweden)
Publication:
Monthly Notices of the Royal Astronomical Society, Volume 401, Issue 1, pp. 347-354. (MNRAS Homepage)
Publication Date:
01/2010
Origin:
WILEY
Astronomy Keywords:
hydrodynamics, magnetic fields, MHD, turbulence
DOI:
10.1111/j.1365-2966.2009.15640.x
Bibliographic Code:
2010MNRAS.401..347B

Abstract

Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation.
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