The previous section showed that a fixed observer relatively close to the solar equatorial plane will observe successive fast and slow solar wind streams during much of the solar cycle. What interactions are there between these streams? Obviously, there must be interactions because plasma from the fast stream will catch up with and overtake plasma from the slow stream. Figure 11.8 [Hundhausen, 1972] shows the qualitative predictions of this scenario: formation of a compression region in the rear of the slow stream, the likely formation of a shock emanating from the compression region (most likely two, as discuseed below), and a rarefaction region at the rear of the fast steam, all with characteristic variations in the plasma and field variables. Intuitively it can be seen that these interaction regions will have spiral shapes that may wrap multiple times around the Sun. These regions are called ``co-rotating interaction regions'' or CIRs since they corotate with the Sun.
Figure 11.8: Schematic illustration of a fast stream interacting with a slow stream
[Hundhausen, 1972].
Co-rotating interaction regions are not always bounded by shocks. The reason is that shock formation occurs due to the nonlinear steepening of waves, thereby requiring several nonlinear steepening times to elapse before a shock is formed. Since most CIRs do not have shocks at 1 AU but have steepened into shocks by 2 AU, empirically the nonlinear steepening time must be of order 4 days. (Exercise: why?) The reason why two shocks are eventually formed at a CIR is due to symmetry about the pressure enhancement caused by compression and entraining of the slow wind ahead of the fast stream (Figure 11.9 [Gosling, 1996]): shocks are driven away from the pressure increase in both directions, resulting in a so-called ``Forward-Reverse shock pair'' in which the forward shock propagates away from the Sun while the reverse shock propagates towards the Sun but is carried out with the solar wind flow.
Figure 11.9: Superposed-epoch analysis of the plasma parameters for CIRs [Gosling et al.,
1996]. Note the well defined
pressure pulse and compression region in the modified portion of the slow stream.
Figure 11.10 [Hundhausen, 1973; Gosling, 1996] displays the results of 1-D MHD simulations
of this process. Note the formation of a pressure increase with drives forward and reverse
shocks with the formation of a characteristic two step increase in the flow speed with a
subsequent slow fall-off to the slow speed (in the rarefaction region). At first
sight this two-step profile is inconsistent with both the forward and reverse shock being
fast mode shocks. However, this is a reference frame effect: in the frame of
the reverse shock the upstream speed (undisturbed fast stream at later times) is greater than
the downstream speed (earlier times). In fact, the Rankine-Hugoniot conditions for
mass flux across the shock in the shock frame (equation 4.17) can be used with the observed
upstream and downstream flow speeds to calculate the shock speed 
; i.e.,
Figure 11.10: Evolution towards a CIR state of a high temperature region imposed at the
inner boundary of the
solar wind [Hundhausen, 1973]. Note the development of shocks, a pressure pulse, and
the characteristic two-step increase and decay of the solar wind speed. Yes there is one
Figure 11.11 [Smith, 1985] shows the observed evolution of a CIR from 1 AU to 4.2 AU. Note the evidence for magnetic field and plasma compression at 1 AU, but an absence of shocks there, which had evolved to a good example of a forward-reverse shock pair and CIR by 4.2 AU.
Figure 11.11: Figure from Smith [1985] described in the text.
These and similar events can be compared with the results of MHD simulations: Figure 11.12 [Gosling et al., 1976; Pizzo, 1985] illustrates the very good agreement between observation and theory available using only MHD.
Figure 11.12: The top panel shows the plasma density profiles observed by IMP 7 near 1 AU and by
Pioneer 10 near 4.5 AU. The bottom panel compares the measured Pioneer 10 density structure
with that predicted by a 1-D MHD code using the IMP 7 data as input. Very good agreement
is evident [Gosling et al., 1976].
Figure 11.13 illustrates the winding up of CIRs (and the Archimedean spiral) at large heliocentric distances, where they are clearly likely to have important effects on the plasma.
Figure 11.13: MHD simulation of (1) high speed streams which cause the development
of CIR structure and (2) the propagation of transient shocks which also modify
the CIR structure (bottom two panels particularly) [Akasofu and Hakamada, 1983].
The shock waves and associated structures of CIRs are important in numerous ancillary ways in the solar wind. For instance, CIRs dissipate the energy in fast streams by slowing and heating the plasma, while the magnetic compression regions and turbulence associated with shocks can scatter cosmic rays. Moreover, particles can be accelerated at the CIR shocks. The shocks and most of the plasma structure of CIRs are merged together and primarily smoothed out beyond about 20 AU. Only the magnetic compression regions tend to persist into the outer heliosphere beyond 20 AU. These effects are discussed more in Lectures 12 and 20.