V.F. Kamenetsky
Copmuting Center, RAS, Moscow, Russia
Accepted for publication in Planetary and Space Science (1996).
Acknowledgements
This research was partialy supported by the
Bulgarian National Foundation "Scientific Research" under
contracts: NZ 522.
[Abstract] [Introduction] [Mathematical model] [Numerical procedure] [Numerical implementations] [Summary and discussion] [References] [Figures]
Figure 1.
Bow wave and sonic line locations for fixed
magnetopause shape and position and Mach numbers 3.0, 6.0, 12.0,
25.0; the case of rotated equatorial trace with gamma 5/3. A
complete coincidence with the analogical Figure 7 in Stahara et
al., 1977 is observed here.
Figure 2.
Shock wave and embedded shock location for solar
wind flow with Mach number 5 and gamma 5/3 past the rotated
principal meridian of the magnetopause. Sonic lines
are drawn by dashed lines. The position of the embedded shock,
outlined here by condensing of the drawn Mach-number iso- lines, is
in good coincidence with the corresponding result of Spreiter and
Stahara, 1980 (Fig. 4 there).
Figure 3.
Shock, magnetopause and sonic line, obtained in
applying the developed in the present paper grid characteristic
numerical scheme (solid curves). Parameters for the case,
corresponding to curves 1: Mach number 12, gamma 5/3.
Dashed curves present analogical result, obtained for fixed
magnetopause- equatorial trace of Beard's magnetopause.
Figure 4.
Bow wave, magnetopause and sonic line locations for
various supersonic flows past the rotational Stern's, 1985 closed
magnetosphere, making use of its equatorial trace. The upstream
flow parameters are as in Figure 1. The fixed magnetopause,
used in the results of the Figure 1 is drawn here by dashed line.
Figure 5.
Axially symmetric solar wind flow past magnetopause
with inside magnetic pressure, based on the magnetic field
distribution along the principal meridian of the Stern's
magnetopause. Parameters: Mach number 5,gamma 5/3
. The character dimple on the magnetopause
arises almost at the same position, while the subsonic ``pocked''
with Mach number smaller than 1 in the self- consistent case is moved slightly
downstream.
Figure 6.
Result of self-consistent magnetosheath computation
of solar wind flow past a rotational (around the principal meridian
trace) closed Beard's, 1960 magnetosphere. The flow parameters are
as in Figure 5.
Figure 7.
Comparison between magnetopause and bow shock shapes
and positions for the computed flows: with Stern's magnetosphere
model (from Figure 5) - solid lines; with Beard's magnetosphere
magnetic field approach (Figure 6) - dashed lines; and with fixed
Bear's magnetopause - dotted lines.
Figure 8.
a) Pressure distribution line 1, as
derived by Beard's, 1960 approach over the magnetopause shape,
computed self- consistently and shown in Figure 5. Line 2
presents analogical pressure distribution over preliminary fixed
``meridional'' rotational magnetopause
with magnetosheath, shown in Figure 2. Line 3 is the analogical
distribution for the case with Stern's model.
b) The
distributions of the corresponding pressure coefficients .
Figure 9.
Simulation of solar wind flow past an open Stern's
magnetosphere. The picture, presented by solid lines 2
corresponds to parameters' values: C_E*= 0; C_F*=-0.3,
imitating southward IMF; The picture, drawn by
solid lines 1, corresponds to the parameters: C_E*=
0; C_F*= 0.3. The remaining parameters for both
cases are as in Figure 7. Dashed lines present the corresponding
result for the closed magnetosphere.