Journal Article

Newtonian non-linear hydrodynamics and magnetohydrodynamics

Nicolaos K. Spyrou and Christos G. Tsagas

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 388, issue 1, pages 187-196
Published in print July 2008 | ISSN: 0035-8711
Published online July 2008 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.13309.x
Newtonian non-linear hydrodynamics and magnetohydrodynamics

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We use covariant techniques to study the non-linear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous magnetized environments. The non-linear electrodynamic formulae are derived and successively applied to electrically resistive and to highly conductive fluids. By nature, the covariant equations isolate the magnetic effects on the kinematics and the dynamics of the medium, combining mathematical transparency and physical clarity. Employing the Newtonian analogue of the relativistic 1 + 3 covariant treatment also facilitates the direct comparison with the earlier relativistic studies and helps to identify the differences in an unambiguous way. The purpose of this work is to set the framework and take a first step towards the detailed analytical study of complex non-linear systems, like non-relativistic astrophysical plasmas and collapsing protogalactic clouds.

Keywords: hydrodynamics; MHD

Journal Article.  7418 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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