Exact expressions for available potential energy and available potential vorticity
Abstract
Exact analytical expressions for available potential energy density (APE) and available potential vorticity (APV) are derived from first principles. These APE and APV expressions align with previously known quantities found using perturbation expansions in Holliday & McIntyre (1981) and Wagner & Young (2015), respectively. The key is to recast the equations of motion and their conservation laws in terms of the coordinate label , where z is a fluid parcels height at the current time, and is the isopycnal deviation from the parcels current height after adiabatic rearrangement of all parcels into the no-motion state. In addition to their intuitive appeal and simplicity, the new APE and APV expressions are easily implemented in numerical computations of Boussinesq dynamics with non-constant stratification.
Keywords
Cite
@article{arxiv.2212.07405,
title = {Exact expressions for available potential energy and available potential vorticity},
author = {Jeffrey J. Early and Gerardo Hernández-Dueñas and Leslie M. Smith and M. -Pascale Lelong},
journal= {arXiv preprint arXiv:2212.07405},
year = {2022}
}