Tellus (198 l), 33,505-508 SHORT CONTRIBUTION

In this paper the known property of the “quasi-geostrophic ” form of the adiabatic equation to conserve rather than convert mean total poten-tial energy (TPE) or available potential energy (APE) is analysed by tracing the contributions to the conversion to kinetic energy (KE), made by individual terms of the adiabatic equation. The approach and notation of a previous paper (Burger and Riphagen, 1979, hereafter referred to as BR1) are used, and that paper’s final example is amplified. Application of the same approach to the Lorenz (1955) form of APE then demonstrates the analytical mechanism which enables an acceptable energy behaviour to be obtained in this context. As was shown in eq. (5.2) of BR1, for a scalar E, where the integration is over the mass of the atmosphere. The rate of change of mean TPE (for a quasi-hydrostatic atmosphere) may now be ex-pressed as =J (-q a at Also, for any suitably well-behaved scalar A, the Gauss divergence theorem with the kinematic boundary condition that the component of velocity normal to the surface of the earth must vanish, gives [See eq. (5.4) of BR1.1 In what follows we shall apply the simpler boundary condition o = 0 at p = po = constant, on a level earth, in which case the first two (divergence) terms of (2) vanish separately under integration, and thus also its last term and that of (1). The energy conversion is therefore completely characterized by the expression acp TI&, and can thus be straightforwardly evaluated from the thermodynamic equation. For an atmosphere which is quasi-hydrostatic, adiabatic, frictionless quasi-geostrophic (Ro < l), stratified, of limited static stabikity and of moderat