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Towards an MHD theory for the standoff distance of Earth's bow shock
Author(s) -
Cairns Iver H.,
Grabbe Crockett L.
Publication year - 1994
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/94gl02551
Subject(s) - magnetohydrodynamics , physics , magnetosheath , bow shock (aerodynamics) , mach number , heat capacity ratio , shock (circulatory) , mechanics , isentropic process , shock wave , magnetic field , computational physics , classical mechanics , astrophysics , magnetopause , solar wind , quantum mechanics , medicine
An MHD theory is developed for the standoff distance a s of the bow shock and the thickness Δ ms of the magnetosheath, using the empirical Spreiter et al. relation Δ 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 Δ ms and a s . In general, however, MHD effects produce major differences from previous models, especially at low Alfven ( M A ) and sonic ( M S ) Mach numbers. The magnetic field orientation, M A , M S , and the ratio of specific heats γ are all important variables of the theory. In contrast, the fast mode Mach number need play no direct role. Three principal conclusions are reached. First, the gas‐dynamic and phenomenological models miss important dependances on field orientation and M S and generally provide poor approximations to the MHD results. Second, changes in field orientation and M S are predicted to cause factor of ∼ 4 changes in Δ ms at low M A . These effects should be important when predicting the shock's location or calculating γ from observations. Third, using Spreiter et al.'s value for k in the MHD theory leads to maximum a s values at low M A and nominal M 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 a breakdown in the Spreiter‐like relation at very low M A .