A theory of available potential energy (APE) for symmetric circulations which includes momentum constraints is presented. The theory is a generalization of the classical theory of APE, which includes only thermal constraints on the circulation.

Accounting for momentum constraints is important in various contexts, including the middle atmosphere circulation, which is mechanically driven and thermally damped. The classical theory of APE applied in such a context may fail to describe the correct causality of the circulation.

The generalization relies on the Hamiltonian structure of the (conservative) dynamics, is exact at finite amplitude, and has a local form.

We apply the theory for the case of the f-plane Boussinesq equations. It is shown that by including momentum constraints, the APE of a symmetrically stable flow is zero, while the energetics of a mechanically driven symmetric circulation properly reflect its causality.