| We present a theory of available energy for symmetric circulations of a rotating, stratified fluid. The theory is a generalization of the classical theory of available potential energy (APE), in that it accounts for both the momentum and the thermal constraints on the circulation. The generalization relies on the Hamiltonian structure of the conservative dynamics, although (as with classical APE) it still defines the energetics in a non-conservative framework.;The theory is then applied in the context of the primitive equations in spherical coordinates, to diagnose the available energy of the residual mean meridional circulation of the middle atmosphere. Both simulated fields from the Canadian Middle Atmosphere Model and the ERA-40 re-analysis data are used for diagnostic comparison.;With the non-resting reference state constructed using the radiative equilibrium temperature the available energy diagnostic robustly identifies the circulation as being thermally damped and mechanically forced, in both the stratosphere and mesosphere, which agrees with its causality. The boundary flux term and the thermal forcing are both negative, with the mechanical forcing, due to deposition of momentum by the waves breaking in-situ, being identified as the driving agent; this agrees with the gyroscopic pumping mechanism as the driving process of the middle atmosphere meridional circulation.;In contrast, with the resting (Lorenz-like) reference state the thermal forcing is seen as driving the circulation in the stratosphere (along with the boundary flux), with mechanical forcing being identified as a damping. In the mesosphere the diagnostic with the resting reference state does not encounter a causality problem, with the thermal forcing being identified as damping, and the mechanical forcing along with the boundary flux being the driving agent. However, the circulation is diagnosed as being less strongly forced compared to the non-resting reference state.;The energy budget is derived for the circulation transverse to a given balanced reference flow. For a simple example, it is shown that by including momentum constraints, the available energy of the transverse circulation to a symmetrically stable flow is zero, while the energetics of a mechanically driven symmetric circulation properly reflect its causality. |
