Magnetohydrodynamic equations under anisotropic conditions

Abstract

Scaling analysis is used to derive approximations of magnetohydrodynamics with self-consistent leading-order dynamics under general conditions of anisotropy. Both incompressible and weakly compressible limits are considered. The horizontal magnetic and velocity fields obey dynamics given by a reduced closed set of equations, but the vertical components have different decoupled dynamics in the different regimes. Conservation laws are also discussed. It is shown that the reduced equations are not self-consistent unless either the ratio of vertical to horizontal length scales is large or the fluid is gravitationally stratified and the ratio of length scales is small. New equations are derived for a rotating stratified plasma, which are an extension of the quasigeostrophic equations of neutral fluids.

Reduced magnetohydrodynamics and parallel spectral transfer

“…However, as noted by Kinney and McWilliams, 27 it is not a cascade in the traditional sense since Eq. ͑17͒ depends upon the ͑mode-independent͒ amplitude B 0 .…”

Scaling of Anisotropy in Hydromagnetic Turbulence

“…1 and 3) that saturation of anisotropy occurs at low b͞B, as one would expect (see discussion above) when resonant spectral transfer is dominant. As yet, computations have not fully explored the weak and strong B 0 limits, but a possible basis for understanding the transition between such regimes has been discussed recently [11]. For the parameters explored in the simulations here, however, it appears that the use of reduced MHD, an entirely "zero frequency" description, is justified.…”

“…In particular, an angular measure of the anisotropy of the spectrum varies linearly with field strength over a useful range of applied field magnitudes. A simple argument, based upon the physics of reduced MHD [9][10][11], explains this scaling property as well as its saturation.Within the MHD framework, anisotropy associated with a (uniform) dc magnetic field ͑B 0 ͒ may take a number of forms [12][13][14]. Here we are concerned specifically with dynamical development of spectral anisotropy due to asymmetry of nonlinear spectral transfer relative to the mean field direction [14,15].…”

“…In particular, an angular measure of the anisotropy of the spectrum varies linearly with field strength over a useful range of applied field magnitudes. A simple argument, based upon the physics of reduced MHD [9][10][11], explains this scaling property as well as its saturation.…”

Reduced MHD in Astrophysical Applications: Two-dimensional or Three-dimensional?

“…Investigations of the turbulence properties of RMHD have also been carried out (e.g., Dahlburg et al 1985;Kinney & McWilliams 1997;Dmitruk et al 2003;Oughton et al 2004;Rappazzo et al 2010Rappazzo et al , 2012.…”