A three-dimensional analysis of the flow past an open terrestrial magnetopause

We present a three-dimensional analysis covering an investigation of the behavior of the magnetosheath plasma velocity and the magnetic field during the transfer from the magnetosheath to the magnetosphere. Magnetic reconnection is assumed to occur at an arbitrary line parallel to the $y$-axis, located in a region along the magnetopause stretching from the sub-solar point to the north. We do not focus on the process itself, but on its implications for the plasma flow and the magnetic field outside the diffusion region. Viscosity and resistivity are included in the magnetohydrodynamic equation of motion as non-ideal effects. The governing equations are solved approximately using the method of asymptotic expansions, with expansion in orders of large Reynolds and Lundquist numbers. We present two classes of solutions describing the properties north and south of the reconnection line, respectively. Results are presented for two locations of the reconnection line at distances of two and seven Earth radii from the sub-solar point correspondingly. It is shown that the velocity increases faster north of the reconnection line, and that the effect intensifies as the location of the reconnection line moves further away from the sub-solar point. It is also shown for this case, that there is less variation of the magnetic field and an increase in the field strength.