A UNIFIED THEORY OF AVAILABLE POTENTIAL-ENERGY

Traditional derivations of available potential energy, in a variety of contexts, involve combining some form of mass conservation together w ith energy conservation. This raises the questions of why such constru ctions are required in the first place, and whether there is some gene ral method of deriving the available potential energy for an arbitrary fluid system. By appealing to the underlying Hamiltonian structure of geophysical fluid dynamics, it becomes clear why energy conservation is not enough, and why other conservation laws such as mass conservati on need to be incorporated in order to construct an invariant, known a s the pseudoenergy, that is a positive-definite functional of disturba nce quantities. The available potential energy is just the non-kinetic part of the pseudoenergy, the construction of which follows a well de fined algorithm. Two notable features of the available potential energ y defined thereby are first, that it is a locally defined quantity, an d second, that it is inherently definable at finite amplitude (though one may of course always take the small-amplitude limit if this is app ropriate). The general theory is made concrete by systematic derivatio ns of available potential energy in a number of different contexts. Al l the well known expressions are recovered, and some new expressions a re obtained. The possibility of generalizing the concept of available potential energy to dynamically stable basic flows (as opposed to stat ically stable basic states) is also discussed.