Temporal evolution of the solar wind and the formation of a standing shock
The temporal evolution of the solar wind from one steady state to another is explored when momentum deposition produces multiple critical points in the flow. It is shown that the wind always evolves in time to a new steady state compatible with the solution of the steady state equation of motion. However, for the same initial state and identical asymptotic momentum deposition rate, the temporal evolution pattern of the wind depends on the detailed time history of momentum addition and is therefore not unique. This feature plays an important role in the particular case when multiple (three in this study) steady states exist for identical boundary conditions; each one of these solutions is thus shown to be physically accessible. The details of the temporal evolution pattern of the wind reveal the formation of a shock discontinuity whenever the flow becomes supersonic at a critical point upstream from the initial critical point. If the flow remains supersonic at that inner critical point, the shock can become a standing one, depending on the strength and the temporal history of momentum addition. The results of this study indicate that the time scale required for the solar wind to evolve between steady states is of the order of 30-60 hours. Furthermore, the results also reveal the interesting and novel phenomenon that a standing shock is likely to develop in the inner solar wind flow within this time frame, in particular, in coronal hole regions with rapidly diverging geometries.