Newtonian nonlinear hydrodynamics and magnetohydrodynamics

Abstract

We use covariant methods to analyse the nonlinear 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 magnetised environments. The nonlinear 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 nonlinear systems, like non-relativistic astrophysical plasmas and collapsing protogalactic clouds.

Typos corrected, references added and updated (MNRAS in press)

References in corpus (17)

• Unified Schemes for Radio-Loud Active Galactic Nuclei
• The Magnetized Universe
• Relativistic cosmology and large-scale structure
• Generalized Ohm's law for relativistic plasmas
• Cosmology with inhomogeneous magnetic fields
• A Gauge-invariant Analysis of Magnetic Fields in General Relativistic Cosmology
• Magnetized cosmological perturbations
• Gauge-invariant magnetic perturbations in perfect-fluid cosmologies
• Cosmological perturbations on a magnetised Bianchi I background
• Covariant analysis of Newtonian multi-fluid models for neutron stars: I Milne-Cartan structure and variational formulation
• Magnetic tension and the geometry of the universe
• Magnetic field amplification in CDM anisotropic collapse
• Covariant analysis of Newtonian multi-fluid models for neutron stars: II Stress - energy tensors and virial theorems
• Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: Dynamical equivalence and consequences
• Magnetic tension and gravitational collapse
• Galaxy formation and cosmic-ray acceleration in a magnetized universe
• Covariant approach to the conformal dynamical equivalence in astrophysics

Cited by in corpus (5)

• Relativistic cosmology and large-scale structure
• Raychaudhuri's equation and aspects of relativistic charged collapse
• Vorticity production and survival in viscous and magnetized cosmologies
• Large-scale peculiar velocity fields: Newtonian vs relativistic treatment
• Magnetised cosmological perturbations in the post-recombination era