Local available energetics of multicomponent compressible stratified fluids

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.

Quantifying mixing and available potential energy in vertically periodic simulations of stratified flows

“…Note that Tailleux (2013 a ) argues for a more general definition of APE, where is replaced by an arbitrary reference state that can depend on a wide range of thermodynamic quantities. This definition is particularly useful for its possible extension to multicomponent, compressible fluids as shown by Tailleux (2018). Defining buoyancy relative to an arbitrary reference state also highlights an inherent ambiguity in calculating APE.…”

A general criterion for the release of background potential energy through double diffusion

“…These equations are presented schematically in figure 1. Although we follow the derivation in Winters et al (1995), these equations may also be derived by volume integrating the local APE budgets derived in Tailleux (2018b). The letter S in equations (2.17)-(2.20) denotes a surface flux, with a superscript adv denoting an advective flux, or diff denoting a diffusive flux.…”

“…A local definition of APE was introduced by Tailleux (2013) and Scotti & White (2014), which was further generalized to include compressibility, a nonlinear equation of state and an arbitrary number of scalar components (Tailleux 2018b). Recently, Tailleux (2018a) derived a new expression for the local APE dissipation rate in a binary compressible fluid with a nonlinear equation of state and showed that in this case the APE dissipation is irreversible.…”

Assessment of algorithms for computing moist available potential energy

“…The idea that simpler alternatives might exist is indeed justified by the fact that some recent APE studies successfully moved away from the use of sorting algorithms by resorting to approaches using probability density functions instead, as in the case of Saenz et al (), itself an extension of Tseng and Ferziger (), although it is unclear how such a method could be applied to a moist atmosphere. Also, it has long been known from the works of Andrews () and Holliday and Mcintyre (), which were recently generalized for multicomponent compressible stratified fluids by Tailleux (), that it is possible to construct a local theory of APE based on an arbitrary reference state defined by a reference pressure p 0 ( z , t ) and specific volume α 0 ( z , t ) in hydrostatic equilibrium. Based on Tailleux () and Novak and Tailleux (), this would lead one to define the APE density for a moist atmosphere as the work that a fluid parcel needs to perform to move from its reference pressure p r to its actual pressure p , namely, where θ l is liquid potential temperature and q T is total water content.…”