A Unified Theory of Available PotenUal Energy’

ABSTRACT Traditional derivations of available potential energy in a variety of contexts, involve combining someform of mass conservation together with energy conservation. This raises the questions of why such constructions are required in the first place, and whether there is some general method ofderiving the available potential energyfor an arbitraryfiuid system. By appealing to the underlying Hamiltonian structure of geophysicalfiuid dynamics, it becomes clear why energy conservation is flot enough, and why other conservation laws such as mass conservation needto be incorporated in order to construct an invariant, known as the pseudoenergy, thaï is a positive-definite functional of disturbance quantities. The available potential energy is just the non-kinetic part of the pseudoenergy, the construction of which follows a well defined algorithm. Two notable features of the available potential energy defined thereby are first, that it is a locally defined quantity, and second, that it is inherently definable at finite amplitude (though one may of course always take the small-amplitude limit if this is appropriate). The general theory is made concrete by systematic derivations of available potential energy in a number of different contexts. Ail the well known expressions are recovered, an