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Low Mach number predictions in an extended axially symmetric MHD theory of the magnetosheath
Author(s) -
Grabbe Crockett L.
Publication year - 1997
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 - 10.1029/97gl02584
Subject(s) - magnetosheath , magnetopause , physics , bow shock (aerodynamics) , magnetohydrodynamics , mach number , magnetosphere , solar wind , mechanics , shock wave , geophysics , plasma , quantum mechanics
A recent axisymmetric magnetohydrodynamic (MHD) model for the Earth's magnetosheath near the Sun‐Earth line, with boundary conditions given by Rankine‐Hugoniot (RH) equations at the bow shock and the Chapman‐Ferraro (CF) condition at the magnetopause, is extended by including smaller terms in the CF condition that become important at low Mach numbers. Three conclusions are predicted for the magnetosheath. (1) The magnetosheath thickness Δ ms decreases with decreasing Alfven Mach number M A for M A > M * (in which only the “gasdynamic” root of the RH equations for the bow shock boundary is physical), where M * ∼ 2 is the root‐transition value for the RH equations at which all 3 roots coalesce. When M A < M * switch‐on shock roots (purely MHD) are also physical, and Δ ms associated with those roots shows a rapid increase to a large value, followed by a rapid decrease back to a very small value as the decreasing M A approaches 1. Thus Δ ms associated with these switch‐on roots may give more distant bow shocks, and may rapidly vary with small M A changes. (2) Δ ms is very sensitive to the value for the CF constant k CF at the magnetopause. For larger M A and sonic Mach numbers M s the ratio of Δ ms to the geocentric radial distance a mp of the magnetopause varies from 0.44 for 90% coupling efficiency of the solar wind momentum density to the magnetopause down to 0.18 for 60% coupling efficiency. This suggests a balance between the solar wind coupling efficiency to the magnetopause and the thickness of the magnetosheath, in which an increase (decrease) in the coupling efficiency increases (decreases) the thickness of the magnetosheath to counter that efficiency by moving the bow shock further upstream (downstream), hence minimizing the variation in time of that coupling efficiency. (3) The linear relation between Δ ms and the density ratio ρ sw /ρ bs observed in simulations breaks down for M A or M s ≲ 2. The slope steadily drops as M s → 1, but increases as M A → 1.