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

Exactly 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 ~10^3–10^5 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.