Nearly incompressible magnetohydrodynamics at low Mach number
Abstract
The dynamics of a compressible magnetofluid plasma with a polytropic equation of state are considered in the limit of low plasma frame acoustic Mach number. The relationship between the equations describing the low Mach number flow and the equations of idealized incompressible magnetohydrodynamics is investigated using a multiple time scale asymptotic expansion procedure, which is justified by appealing to several rigorous theorems concerning both hydrodynamics and magnetohydrodynamics. When appropriate assumptions are adopted concerning the degree of departure from incompressibility, the lowestorder behavior is that of incompressible magnetohydrodynamics, associated with order Mach numbersquared ``pseudosound'' density fluctuations. The first corrections to incompressible flow take the form of magnetoacoustic fluctuations, with associated pressure fluctuations at the same order as the pseudosound pressure. Resumming the asymptotic series gives rise to a simple set of equations that describes ``nearly incompressible magnetohydrodynamics.'' The theory provides a justification for the turbulent density spectrum theory of Montgomery, Brown, and Matthaeus [J. Geophys. Res. 92, 282 (1987)] and clarifies several issues pertaining to Alfvén wave turbulence in the solar wind. The nearly incompressible description may also be useful in other theoretical contexts, particularly in extensions of incompressible magnetohydrodynamic turbulence theory, since it is expected to be valid for finite times (until possible shock structures form) when the global Mach number is sufficiently small.
 Publication:

Physics of Fluids
 Pub Date:
 December 1988
 DOI:
 10.1063/1.866880
 Bibcode:
 1988PhFl...31.3634M
 Keywords:

 Incompressible Flow;
 Magnetohydrodynamic Flow;
 Solar Wind;
 Space Plasmas;
 Asymptotic Methods;
 Comparison;
 Compressible Flow;
 Turbulent Flow;
 Plasma Physics