We have seen that the relative movement of a conducting body and a magnetic field can lead to the dissipation of energy. This has been used by engineers for over a century to dampen unwanted motion. Indeed, as far back as 1873 we find Maxwell noting: ‘A metallic circuit, called a damper, is sometimes placed near a magnet for the express purpose of damping or deadening its vibrations.’ Maxwell was talking about a magnetic field moving through a stationary conductor. We are interested in a moving conductor in a stationary field, but of course, this is really the same thing. We have already touched upon magnetic damping in Chapter 5, and we discussed some of its consequences in Chapter 6. In particular, we saw that the intense magnetic field in a sunspot locally deadens the convective motions in the outer layer of the sun, thus cooling the spot and giving it a dark appearance. Here we make the jump from sunspots to steelmaking, and describe how magnetic fields are used in certain casting operations to suppress unwanted motion.

There has been a myriad of papers on this topic and at times one is reminded of Rayleigh's indigestion. Here we focus on the unifying themes.

Turbulence is not an easy subject. Our understanding of it is limited, and those bits we do understand are arrived at through detailed and difficult calculation. G K Batchelor gave some hint of the difficulties when, in 1953, he wrote:

Little has changed since 1953. Nevertheless, it is hard to avoid the subject of turbulence in MHD, since the Reynolds number, even in metallurgical MHD, is invariably very high. So at some point we simply have to bite the bullet and do what we can. This chapter is intended as an introduction to the subject, providing a springboard for those who wish to take it up seriously. In order not to demotivate the novice, we have tried to keep the mathematical difficulties to a minimum. Consequently, only schematic outlines are given of certain standard derivations and proofs. For example, deriving the standard form for second- and third-order velocity correlation tensors in isotropic turbulence can be hard work. Such derivations are well documented elsewhere and so there seems little point in giving a blow-by-blow description here.

The amount of energy required to reduce alumina to aluminium in electrolysis cells is staggering. In North America, for example, around 2% of all generated electricity is used to produce aluminium. Worldwide, around 2×1010kg of aluminium are produced annually, and this requires in excess of 1011 kWh p.a. The corresponding electricity bill is around £1010 p.a.! Yet much of this energy (around one half) is wasted in the form of I2R heating of the electrolyte used to dissolve the alumina. Needless to say, strenuous efforts have been made to reduce these losses, mostly centred around minimising the volume of electrolyte. However, the aluminium industry is faced with a fundamental problem. When the volume of electrolyte is reduced below some critical threshold, the reduction cell becomes unstable. It is this instability, which is driven by MHD forces, which is the subject of this chapter.

Interfacial Waves in Aluminium Reduction Cells

Early attempts to produce aluminium by electrolysis

It is not an easy matter to produce aluminium from mineral deposits. The first serious attempt to isolate elemental aluminium was that of Humphrey Davy, Faraday's mentor at the Royal Institution. (In fact, Davy's preferred spelling – aluminum – is still used today in North America.) In 1809 he passed an electric current through fused compounds of aluminium and into a substrate of iron.

A high-frequency induction coil can be used to heat, levitate and stir liquid metal. This has given rise to a number of metallurgical processes, some old (such as induction furnaces) and some new. In this chapter, we shall discuss five.

1. (i) Induction furnaces. These have remained virtually unchanged for the best part of a century, yet we are still unable to calculate reliably the stirring velocity within a furnace!

2. (ii) Cold crucible melting. This is an ingenious process which combines the functions of an induction melter and a continuous caster, all in one device.

3. (iii) Levitation melting. This is now routinely used in the laboratory to melt small specimens of highly reactive metals. Unfortunately, if the levitated drop becomes too large, it tends to drip.

4. (iv) The electromagnetic valve. This provides a non-contact means of modulating and shaping a liquid-metal jet. It is a sort of levitation melter in which the metal is allowed to leak out of the bottom.

5. (v) Electromagnetic casting. Some aluminium producers have replaced the casting mould in a continuous caster by a high-frequency induction coil. Thus, the melt pool is supported by magnetic pressure rather than by mechanical means. It is extraordinary that large ingots, which may be a metre wide and ten metres long, can be formed by pouring the liquid metal into free space and soaking it with water jets!

This chapter is a short introduction to the use of models in atmospheric research and forecasting. In Section 8.1 we explain how a hierarchy of models – simple, intermediate and complex – can be used for gaining understanding of atmospheric behaviour and interpreting atmospheric data. In Section 8.2 we give brief details of the numerical methods used in the more complex theoretical models, while in Section 8.3 we outline the use of these models for forecasting and other purposes. In Section 8.4 we describe an example of a class of laboratory models of the atmosphere. Finally, in Section 8.5, we give some examples of atmospheric phenomena that arise from interactions between basic physical processes and that can be elucidated only with the aid of models of intermediate complexity.

The hierarchy of models

The basic philosophy of atmospheric modelling was outlined in Section 1.2. It was mentioned there that a hierarchy of models, from simple to complex, must be used for understanding and predicting atmospheric behaviour; this hierarchy is illustrated in Figure 8.1. The simple models (‘back-of-the-envelope’ or ‘toy’ models) involve a minimum number of physical components and are described by straightforward mathematical equations that can usually be solved analytically. These models provide basic physical intuition: most of the models considered earlier in this book are of this type. The intermediate models involve a small number of physical components but usually require a computer for solution of the mathematical equations.

In this chapter we show how basic thermodynamic concepts can be applied to the atmosphere. We first note in Section 2.1 that the atmosphere behaves as an ideal gas. Some basic information on the various gases comprising the atmosphere is presented in Section 2.2. The fact that the atmosphere is fairly close to being in hydrostatic balance is used in Section 2.3 to develop some very simple ideas about the vertical structure of the atmosphere. An important quantity related to entropy, the potential temperature, is discussed in Section 2.4. The concept of an air parcel is introduced in Section 2.5 and is used to develop ideas about atmospheric stability and buoyancy oscillations. A brief introduction to the concept of available potential energy is given in Section 2.6.

The rest of the chapter is devoted to the implications of water vapour in the air. Section 2.7 recalls the basic thermodynamics of phase changes and introduces several measures of atmospheric water vapour content. These ideas are exploited in Section 2.8, in which some effects of the release of latent heat are investigated in a calculation of the saturated adiabatic lapse rate, which gives information on the stability of a moist atmosphere. The tephigram, a graphical method of representing the vertical structure of temperature and moisture and calculating useful physical results, is introduced in Section 2.9. Finally, some of the basic physics of the formation of cloud droplets by condensation of water vapour is considered in Section 2.10.

This chapter gives a quick sketch of some of the material to be covered in this book. We start in Section 1.1 with an outline of some of the more important physical processes that occur in the Earth's atmosphere. To interpret atmospheric observations we need to develop physical and mathematical models; they are briefly discussed in Section 1.2. In Section 1.3 two simple models are introduced; the second of these is a very basic representation of the greenhouse effect, which can be adapted to give some insight into aspects of global warming. In Section 1.4 we present a selection of observations of atmospheric processes, together with simple physical explanations for some of them. In Section 1.5 we briefly mention some ideas on weather and climate.

The atmosphere as a physical system

The Earth's atmosphere is a natural laboratory, in which a wide variety of physical processes takes place. The purpose of this book is to show how basic physical principles can help us model, interpret and predict some of these processes. This section presents a brief overview of the physics involved.

The atmosphere consists of a mixture of ideal gases: although molecular nitrogen and molecular oxygen predominate by volume, the minor constituents carbon dioxide, ozone and water vapour play crucial roles. The forcing of the atmosphere is primarily from the Sun, though interactions with the land and the ocean are also important.

In keeping with the emphasis on atmospheric physics in this book, the purpose of the present chapter is to illustrate the use of basic physical principles in the study of some aspects of atmospheric chemistry, rather than to provide a comprehensive treatment of atmospheric chemistry as a whole. We therefore focus on stratospheric chemistry, which provides some simple yet important applications of the basic principles and also some examples of interactions between chemistry and dynamics.

In Section 6.1 we outline some of the basic thermodynamics of chemical reactions, while in Section 6.2 we introduce some elementary aspects of chemical kinetics, including the concepts of reaction rates and chemical lifetimes. In Section 6.3 we focus on bimolecular reactions and show how physical reasoning can give an expression for the reaction rate. The process of photodissociation is introduced in Section 6.4. Once these basic ideas have been established, we apply them to stratospheric ozone in Section 6.5, first describing the Chapman theory (which involves oxygen compounds only) and then introducing the effects of catalytic cycles. The principles of chemical transport by atmospheric flows are discussed in Section 6.6, with a qualitative description of the main global-scale meridional transport structures in the middle atmosphere. Finally, in Section 6.7, we bring several of these ideas together in a general description of the processes implicated in the formation of the Antarctic ozone hole.