2022/12/14 by Jeffrey J. Early, Gerardo Hernández-Dueñas, Early, Jeffrey J. +5
Earth and Planetary Sciences · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Physical sciences #Oceanographic and Atmospheric Processes #Solar and Space Plasma Dynamics #Tropical and Extratropical Cyclones Research
paper · pdf · doi:10.48550/arxiv.2212.07405
openalex publication_date 2022/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 z-η, where z is a fluid parcels height at the current time, and η 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.