1. Comprehensive accounts of the principles of fluid dynamics are given in many texts, such as that of Batchelor (1967). Careful discussions of the dynamical and geometric arguments involved in the derivation of the primitive equations are given by Phillips (1973) and Gill (1982), Section 4.12. Hoskins et al. (1985) present a historical account of the use of Ertel's potential vorticity in meteorology, and mention several modern applications. The derivation of the kinematic boundary condition at a material surface is explained by Batchelor (1967), p. 73.
2. Formal derivations of the quasi-geostrophic equations on a beta-plane are given for example by Pedlosky (1979) and Gill (1982). The omega equation is discussed by Hoskins, Dragici and Davies (1978).
3. The transformation [Eq. (3.5.1)] leading to the TEM equations [Eqs. (3.5.2)] was introduced by Andrews and McIntyre (1976a, 1978a) and Boyd (1976). Alternative definitions of the residual circulation are given by Andrews and McIntyre (1978a) and Holton (1981). The identity of Eq. (3.5.10) is due to Bretherton (1966a).
4. The significance of conservation laws such as Eq. (3.6.2) is discussed by McIntyre (1980a, 1981). Successive generalizations of the original Charney-Drazin nonacceleration theorem were derived by Dickinson (1969), Holton (1974, 1975), Boyd (1976), and Andrews and McIntyre (1976a, 1978a).
5. Finite-amplitude versions of the generalized Eliassen-Palm theorem are discussed by Edmon et al. (1980), Andrews (1983) and Killworth and McIntyre (1985). The GLM theory is described in detail by Andrews and McIntyre (1987b,c); a useful introductory survey is that of McIntyre (1980a). Modified versions of this theory are outlined by McIntyre (1980a,b). For the relationship between the “form drag” and the EP flux see Bretherton (1969) and Andrews and McIntyre (1976a).