Andrews, D. G., 1981: A note on potential energy density in a stratified compressible fluid. Journal of Fluid Mechanics, 107, 227-236.

Abstract: An exact, local, positive definite expression is obtained for the potential energy density in a wide class of stratified compresible fluids. This expression is an extension of that derived for incompressible stratified fluids in the preceding paper by Holliday & McIntyre (1981), and also represents a finite-amplitude analogue of the disturbance potential energy density that is famiiar in small-amplitude theory. Its volume integral reduces to Lorenz' (1955) available potential energy under suitable choice of a hydrostatic reference state, provided that the fluid is contained within a fixed volume enclosed by rigid impermeable boundaries.