On the Local View of Atmospheric Available Potential Energy

Abstract

The possibility of constructing Lorenz's concept of available potential energy (APE) from a local principle has been known for some time, but has received very little attention so far. Yet, the local APE framework offers the advantage of providing a positive definite local form of potential energy, which like kinetic energy can be transported, converted, and created/dissipated locally. In contrast to Lorenz's definition, which relies on the exact from of potential energy, the local APE theory uses the particular form of potential energy appropriate to the approximations considered. In this paper, this idea is illustrated for the dry hydrostatic primitive equations, whose relevant form of potential energy is the specific enthalpy. The local APE density is non-quadratic in general, but can nevertheless be partitioned exactly into mean and eddy components regardless of the Reynolds averaging operator used. This paper introduces a new form of the local APE that is easily computable from atmospheric datasets. The advantages of using the local APE over the classical Lorenz APE are highlighted. The paper also presents the first calculation of the three-dimensional local APE in observation-based atmospheric data. Finally, it illustrates how the eddy and mean components of the local APE can be used to study regional and temporal variability in the large-scale circulation. It is revealed that advection from high latitudes is necessary to supply APE into the storm track regions, and that Greenland and Ross Sea, which have suffered from rapid land ice and sea ice loss in recent decades, are particularly susceptible to APE variability.

Assessment of algorithms for computing moist available potential energy

“…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. An alternative formulation for APE density in a compressible atmosphere, based on modified potential temperature, has been proposed by Peng et al ().…”

“…Illustrations of how to construct energy budgets in the oceans and dry atmosphere in the case where the reference density profile is defined from a horizontal or isobaric average are discussed by Tailleux () and Novak and Tailleux (), respectively. These recent developments, combined with the physical insights brought about by Emanuel ()'s theoretical expression for MAPE, suggest that a satisfactory theory of available potential energy for a moist atmosphere, which has been lacking so far, might be at hand, provided that one moves away from sorting algorithms altogether, as we hope to demonstrate in subsequent studies.…”

Local available energetics of multicomponent compressible stratified fluids

“…It is easily seen that the APE density for a Boussinesq fluid derived by Holliday & McIntyre (1981) or Tailleux (2013c) can be recovered: 1) by replacing the denominator ρ(η, S, p) in the last term of (2.18) by the constant reference Boussinesq density ρ 00 ; 2) by replacing everywhere the reference pressure p 0 (z) by the Boussinesq pressure p 00 (z) = −ρ 00 g 0 z. As to the APE density for a hydrostatic dry atmosphere discussed by Novak & Tailleux (2018), it is simply recovered from the first term in (2.18) by replacing the upper bound p 0 by the hydrostatic pressure p itself. As a result, Tailleux (2013b)'s arguments may be used to prove the positive definite character of Π, as well as its small amplitude approximation Π 2 ≈ N 2 r (z − z r ) 2 /2, with N 2 r given by…”

“…The most successful attempts, and most clearly related to Lorenz APE theory, are the local frameworks proposed by Andrews (1981) for a simple compressible stratified fluid and by Holliday & McIntyre (1981) for a Boussinesq fluid with a linear equation of state; these attempts, along with other related older formulations, were subsequently unified within the context of Hamiltonian theory by Shepherd (1993). Yet, despite having been established over 35 years ago, it is only relatively recently that local theories of APE have started to receive attention in the context of stratified turbulence (Roullet & Klein 2009;Molemaker & McWilliams 2010;Scotti & White 2014;Winters & Barkan 2013), ocean energetics (Scotti et al 2006;Tailleux 2013b;Roullet et al 2014;Saenz et al 2015;Zemskova et al 2015;MacCready & Giddings 2016), and atmospheric energetics (Kucharski 1997;Kucharski & Thorpe 2000;Peng et al 2015;Novak & Tailleux 2018).…”

The entrainment and energetics of turbulent plumes in a confined space

“…Developments subsequent to Winters et al (1995) that define local budgets of APE (Scotti, Beardsley & Butman 2006;Roullet & Klein 2009;Scotti & White 2014;Novak & Tailleux 2018), following Andrews (1981) and Holliday & Mcintyre (1981), provide the opportunity for establishing a deeper understanding of energetics in the context of plume modelling. However, local APE frameworks for diagnosing stratified turbulence are still being developed and are relatively difficult to apply.…”