5 - MHD Waves and Discontinuities

Summary

This chapter starts by distinguishing between the primitive and conservative equations of MHD in 1-D, emphasising that the former deal only with continuous flow, whereas the latter admit flow discontinuities. The first application is to MHD waves including Alfvén, slow, fast, and magneto-acoustical waves. An intuitive analogy is given describing what one might experience in an MHD atmosphere when a “thunder clap” occurs. The MHD Rankine–Hugoniot jump conditions for MHD are introduced and solved (using difference theory) revealing tangential/contact/rotational discontinuities and, most importantly, shock waves including slow, intermediate, and fast shocks. In the context of the not strictly hyperbolic nature of the MHD equations, both the entropy and evolutionary conditions are used to determine the physicality and uniqueness of the shock solution. Finally, discussion of MHD shocks includes the special cases of switch-on/off shocks and Euler shocks.