Local Available Potential Energy Research Articles

On the Local Available Potential Energy Perspective of Baroclinic Wave Development

Abstract Extratropical cyclones convert available potential energy (APE) to kinetic energy. However, our current understanding of APE conversion on synoptic scales is limited, as the well-established Lorenz APE framework is only applicable in a global, volume-integrated sense. Here, we employ a recently developed local APE framework to investigate APE and its tendencies in a highly idealized, dispersive baroclinic wave, which leads to the formation of a primary and a downstream cyclone. By utilizing a Lagrangian approach, we demonstrate that locally the downstream cyclone not only consumes APE but also generates it. Initially, APE is transported from both poleward and equatorward reservoirs into the baroclinic zone, where it is then consumed by the vertical displacement of air parcels associated with the developing cyclone. To a lesser extent, APE is also created within the cyclone when air parcels overshoot their reference state; i.e., air colder than its reference state is lifted and air warmer than its reference state is lowered. The volume integral of the APE tendency is dominated by slow vertical displacements of large air masses, whereas the dry intrusion (DI) and warm conveyor belt (WCB) of the cyclone are responsible for the largest local APE tendencies. Diabatic effects within the DI and WCB contribute to the generation of APE in regions where it is consumed adiabatically, thereby enhancing baroclinic conversion in situ. Our findings provide a comprehensive and mechanistic understanding of the local APE tendency on synoptic scales within an idealized setting and complement existing frameworks explaining the energetics of cyclone intensification.

A Moist Available Potential Energy Budget for an Axisymmetric Tropical Cyclone

Abstract The main energy source for the intensification of a tropical cyclone (TC) is widely accepted to be the transfer of energy from the ocean to the atmosphere via surface fluxes. The pathway through which these surface fluxes lead to an increase in the kinetic energy of the cyclone has typically been interpreted either in terms of total potential energy or dry available potential energy (APE), or through the entropy-based heat engine viewpoint. Here, we use the local theory of APE to construct a budget of moist APE for an idealized axisymmetric simulation of a tropical cyclone. This is the first full budget of local moist APE budget for an atmospheric model. In the local moist APE framework, latent surface heat fluxes are the dominant generator of moist APE, which is then converted into kinetic energy via buoyancy fluxes. In the core region of the TC, the inward transport of APE by the secondary circulation is more important than its local production. The APE viewpoint describes spatially and temporally varying efficiencies; these may be useful in understanding how changes in efficiency influence TC development, and have a maximum that can be linked to the Carnot efficiency featuring in potential intensity theory.

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 it has received very little attention so far. Yet the local APE density framework offers the advantage of providing a positive-definite local form of potential energy, which, like kinetic energy, can be transported, converted, and created or dissipated locally. In contrast to Lorenz’s definition, which relies on the exact from of potential energy, the local APE density 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 nonquadratic 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 density that is easily computable from atmospheric datasets. The advantages of using the local APE density over the classical Lorenz APE are highlighted. The paper also presents the first calculation of the three-dimensional local APE density in observation-based atmospheric data. Finally, it illustrates how the eddy and mean components of the local APE density 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 the Ross Sea, which have suffered from rapid land ice and sea ice loss in recent decades, are particularly susceptible to APE variability.

Local available energetics of multicomponent compressible stratified fluids

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 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 is 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.

On the Minimum Potential Energy State and the Eddy Size–Constrained APE Density

AbstractExactly solving the absolute minimum potential energy state (Lorenz reference state) is a difficult problem because of the nonlinear nature of the equation of state of seawater. This problem has been solved recently but the algorithm comes at a high computational cost. As the first part of this study, the authors develop an algorithm that is ~103–105 times faster, making it useful for energy diagnosis in ocean models. The second part of this study shows that the global patterns of Lorenz available potential energy (APE) density are distinct from those of eddy kinetic energy (EKE). This is because the Lorenz APE density is based on the entire domainwide parcel rearrangement, while mesoscale eddies, if related to baroclinic instability, are typically generated through local parcel rearrangement approximately around the eddy size. Inspired by this contrast, this study develops a locally defined APE framework: the eddy size–constrained APE density based on the strong constraint that the parcel rearrangement/displacement to achieve the minimum potential energy state should not exceed the local eddy size horizontally. This concept typically identifies baroclinically unstable regions. It is shown to be helpful to detect individual eddies/vortices and local EKE patterns, for example, around the Southern Ocean fronts and subtropical western boundary currents. This is consistent with the physical picture that mesoscale eddies are associated with a strong signature in both the velocity field (i.e., EKE) and the stratification (i.e., local APE). The new APE concept may be useful in parameterizing mesoscale eddies in ocean models.

Diagnosing mixing in stratified turbulent flows with a locally defined available potential energy

AbstractA local available potential energy (APE) density useful as suitable diagnostic tool in turbulent stratified flows is considered under the Boussinesq approximation. The local APE is positive, and in the limit of infinitesimal perturbation from an equilibrium state recovers the Lorenz energy cycle definition of APE. In a turbulent stratified flow, the APE can be Reynolds-decomposed into non-trivial mean and turbulent components, which are connected to the mean and turbulent kinetic energy by suitably defined fluxes. We show that the turbulent buoyancy flux $\overline{w'b'}$ and the rate of production of turbulent APE coincide only under very special circumstances. The framework is applied to derive some global bounds on the mixing efficiency of some representative flows.

On the Calculation of Available Potential Energy in Internal Wave Fields

Abstract A comparison of three common formulations for calculating the available potential energy (APE) in internal wave fields is presented. The formulations are the perturbation APE (APE1), the exact local APE (APE2), and its approximation for linear stratification (APE3). The relationship among these formulations is illustrated through a graphical interpretation and a derivation of the energy conservation laws. Numerical simulations are carried out to quantitatively assess the performance of each APE formulation under the influence of different nonlinear and nonhydrostatic effects. The results show that APE2 is the most attractive in evaluating the local APE, especially for nonlinear internal waves, since use of APE2 introduces the smallest errors when computing the energy conservation laws. Larger errors arise when using APE1 because of the large disparity in magnitude between the kinetic energy and APE1. It is shown that the disparity in the tendency of APE1 is compensated by a large flux arising from the reference pressure and density fields. Because the tendency of the kinetic energy is close to that of APE3, computational errors arise when using APE3 only in the presence of nonlinear stratification, and these errors increase for stronger flow nonlinearity.