Local available energetics of multicomponent compressible stratified fluids

TL;DR

This paper generalizes the local available potential energy (APE) theory to multicomponent compressible stratified fluids, providing a simpler, more transparent expression that clarifies the energetics and reference states in fluid dynamics.

Contribution

It introduces a new, simplified expression for APE density in multicomponent compressible fluids, enhancing understanding of fluid energetics and reference state selection.

Findings

Derived a new, simpler APE density expression

Linked APE energetics to Boussinesq and hydrostatic equations

Clarified the physical basis of reference states

Abstract

We extend the local theory of available potential energy (APE) to a general multicomponent compressible stratified fluid, accounting for the effects of diabatic sinks and sources. As for simple compressible fluids, the total potential energy density of a fluid parcel is the sum of its available elastic energy (AEE) and APE density. These respectively represent the adiabatic compression/expansion work needed to bring it from its reference pressure to its actual pressure and the work against buoyancy forces required to move it from its reference state position to its actual position. Our expression for the APE density is new and derived using only elementary manipulations of the equations of motion; it is significantly simpler than existing published expressions, while also being more transparently linked to the relevant form of APE density for the Boussinesq and hydrostatic primitive equations. Our new framework is used to clarify the links between some aspects of the energetics of Boussinesq and real fluids, as well as to shed light on the physical basis underlying the choice of reference state(s) in local APE theory.