Nearly incompressible magnetohydrodynamics at low Mach number
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 lowest-order behavior is that of incompressible magnetohydrodynamics, associated with order Mach number-squared ''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 Alfven 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.
- Research Organization:
- Bartol Research Institute, University of Delaware, Newark, Delaware 19716
- OSTI ID:
- 6937017
- Journal Information:
- Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 31:12; ISSN PFLDA
- Country of Publication:
- United States
- Language:
- English
Similar Records
INHOMOGENEOUS NEARLY INCOMPRESSIBLE DESCRIPTION OF MAGNETOHYDRODYNAMIC TURBULENCE
Nearly incompressible fluids: Hydrodynamics and large scale inhomogeneity
Related Subjects
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ASYMPTOTIC SOLUTIONS
COMPRESSIBLE FLOW
FLOW MODELS
FLUID FLOW
FLUID MECHANICS
HYDRODYNAMICS
INCOMPRESSIBLE FLOW
MACH NUMBER
MAGNETOHYDRODYNAMICS
MATHEMATICAL MODELS
MECHANICS
TURBULENCE
VELOCITY