Towards an MHD theory for the standoff distance of Earth's bow shock

Details Towards an MHD theory for the standoff distance of Earth's bow shock Towards an MHD theory for the standoff distance of Earth's bow shock

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994georl..21.2781c&link_type=abstract

Geophysical Research Letters (ISSN 0094-8276), vol. 21, no. 25, p. 2781-2784

Mathematics

Logic

27

Geomagnetism, Magnetic Field Configurations, Magnetohydrodynamic Flow, Magnetohydrodynamics, Magnetosheath, Mathematical Models, Shock Waves, Computerized Simulation, Gas Dynamics, Planetary Magnetic Fields, Quadratic Equations

Scientific paper

An MHD theory is developed for the stand-off distance a(sub s) of the bow shock and the thickness delta(sub ms) of the magnetosheath, using the empirical Spreiter et al. relation delta(sub ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for delta(sub ms) and a(sub s). In general, however, MHD effects produce major differences from previous models, especially at low Alfven (M(sub A)) and sonic (M(sub S)) Mach numbers. The magnetic field orientation, M(sub A), M(sub S) and the ratio of specific heats gamma are all important variables of the theory. Three principal conclusions are reached. First, the gasdynamic and phenomenological models miss important dependances on field orientation and M(sub S) and generally provide poor approximations to the MHD results. Second, changes in field orientation and M(sub S) are predicted to cause factor of approximately 4 changes in delta(sub ms) at low M(sub A). Third, using Spreiter et al.'s value for k in the MHD theory leads to maximum a(sub s) values at low M(sub A) and nominal M(sub S) that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or breakdown in the Spreiter-like relation at very low M(sub A).

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