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

Abstract

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.

Accurate computation of moist available potential energy with the Munkres algorithm

“…We thank a reviewer for bringing to our attention the recent work of Su and Ingersoll (), which discusses an exact algorithm that they find runs faster than the Munkres algorithm for 3D grids with few distinct pressure levels. It may be possible to use a similar approach to speed up the exact calculation of MAPE for 2D or 3D domains in the atmosphere.…”

Large‐Scale Fresh and Salt Water Exchanges in the Indian Ocean

“…One possible reason for this is due to the fact that a key source of eddies is from the background potential energy. Wind‐driven Ekman pumping and suction can change isopycnal slope and background potential energy, which can change eddy magnitude (Su et al, ; Su & Ingersoll, ). This process provides a valid mechanism for a decadal increase in eddy magnitude and the eddy component of transport in this region.…”

Dynamics of Mesoscale Eddies Interacting With a Western Boundary Current Flowing by a Gap

“…The latitude of the Luzon Strait is coincident with the belt of the highest mesoscale eddy activity in the northwestern Pacific Ocean (Chelton et al, 2011;Qiu & Chen, 2010), with the eddy horizontal scales on the order of one or a few deformation radii of the first baroclinic mode. These eddies carry high available potential energy density (Su & Ingersoll, 2016) and displace the isopycnal of the gyre boundary significantly through the so-called residual-mean dynamics (Su et al, 2014). Early studies suggest no connection between the eddies on the different sides of the Luzon Straits (Li et al, 2004;Li et al, 2007;Wang et al, 2005).…”