Available Potential Energy in density coordinates

Alain Colin de Verdière, Thierry Huck, Souren Pogossian, Michel Ollitrault
Laboratoire d’Océanographie Physique et Spatiale, Université de Bretagne Occidentale, Brest, France

Journal of Physical Oceanography
https://doi.org/10.1175/JPO-D-17-0272.1
Published Online: 16 July 2018 


Abstract

The vertically integrated potential energy of an incompressible stratified fluid formulated in density coordinates can be simply written as a weighted vertical sum of the squares of the vertical displacements of density surfaces, a general expression valid for arbitrary displacements. The sum of this form of potential energy and kinetic energy is then a conserved quantity for the multi-layer shallow water model. The formulation in density coordinates is a natural one to find the Lorenz reference state of available potential energy. We describe the method to compute the available potential energy (APE) of an ocean state and provide two applications. The first is the classical double gyre, wind-driven circulation simulated by a shallow water model at high resolution. We show that the eddy kinetic and eddy potential energies are localized in regions of large gradient of mean APE. These large gradients surround an APE minimum found between the two gyres. The second is the time mean World Ocean Circulation reconstructed from hydrography (the World Ocean Atlas) and reference velocities at 1000 db from the Argo float program to obtain an absolute circulation. The total available potential energy exceeds the total mean kinetic energy of the World Ocean by three orders of magnitude pointing out the very small Burger number of the circulation. Four examples of the Gulf Stream, the Kuroshio, the Agulhas Retroflection and the Confluence regions confirm the shallow water model results that large gradients of mean available potential energy can be used as predictors for the presence of high eddy kinetic energy (obtained here from Satellite Altimetry).

Corresponding author address: A. Colin de Verdière, Laboratoire d’Océanographie Physique et Spatiale, IUEM Technopole Brest Iroise, Batiment D, rue Dumont d’Urville, 29280, Plouzané, France. E-mail: acolindv@univ-brest.fr