A note on potential energy density in a stratified compressible fluid

Abstract

An exact, local, positive definite expression is obtained for the potential energy density in a wide class of stratified compressible 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 familiar 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.