6 - Dynamics at Moderate to High Magnetic Reynolds' Number

Summary

…and to those philosophers who pursue the inquiry (of induction) zealously yet continuously, combining experiment with analogy, suspicious of their preconceived notions, paying more respect to the fact than a theory, not too hasty to generalise, and above all things, willing at every step to cross-examine their own opinions, both by reasoning and experiment, no branch of knowledge can afford so fine and ready a field for discovery as this.

Faraday (1837)

When R_m is high there is a strong influence of u on B, and so we obtain a two-way coupling between the velocity and magnetic fields. The tendency for B to be advected by u, which follows directly from Faraday's law of induction, results in a completely new phenomenon, the Alfvèn wave. It also underpins existing explanations for the origin of the earth's magnetic field and of the solar field. We discuss both of these topics below. First, however, it may be useful to comment on the organisation of this chapter.

The subject of high-R_m MHD is vast, and clearly we cannot begin to give a comprehensive coverage in only one chapter. There are many aspects to this subject, each of which could, and indeed has, filled text-books and monographs. Our aim here is merely to provide the beginner with a glimpse of some of the issues involved, offering a stepping-stone to more serious study. The subject naturally falls into three or four main categories. There is the ability of magnetic fields to support inertial waves, both Alfvèn waves and magnetostrophic waves.