Supplemental reading:

Holton (1979), sections 7.1–7.4

Houghton (1977), sections 8.1–8.3

Lindzen (1973)

Atmospheric waves (eddies) are important in their own right as major components of the total circulation. They are also major transporters of energy and momentum. For a medium to propagate a disturbance as a wave there must be a restoring ‘force', and in the atmosphere, this arises, primarily, from two sources: conservation of potential temperature in the presence of positive static stability and from the conservation of potential vorticity in the presence of a mean gradient of potential vorticity. The latter will be treated later; it leads to what are known as Rossby waves. The former leads to internal gravity waves (and surface gravity waves as well). Internal gravity waves are simpler to understand and clearly manifest the various ways in which waves interact with the mean state. For reasons which will soon become clear internal gravity waves are not a dominant part of the midlatitude tropospheric circulation (though they are important). None the less, we will study them in some detail – as prototype atmospheric waves. As a bonus, the theory we develop will be sufficient to allow us to understand atmospheric tides, upper atmosphere turbulence, and the quasi-biennial oscillation of the stratosphere. We will also use our results to speculate on the circulation of Venus. The mathematical apparatus needed will, with one exception, not go beyond understanding the simple harmonic oscillator equation. The exception is that I will use elementary WKB theory (without turning points). Try to familiarize yourself with this device, though it will be briefly sketched in Chapter 10.