English

Coarse-grained local available potential energy

Fluid Dynamics 2026-05-18 v1 Atmospheric and Oceanic Physics

Abstract

The available potential energy (APE) of a fluid can be defined locally in space, providing useful insights into both the energetics and dynamics of stratified flows ranging from three-dimensional turbulence to planetary scale circulations. Here we develop a framework for considering the multi-scale evolution of the local APE using a spatial filtering, or coarse-graining, approach. Evolution equations for the APE at scales larger, and smaller, than the filtering scale are derived -- including the cross-scale APE flux term. These results can be paired with existing frameworks for coarse-grained kinetic energy, offering the potential for examining a complete energy cycle that accounts for conversions between both spatial scales and energy reservoirs. An illustrative example of the application of this approach to a simulation of two-dimensional Kelvin-Helmholtz instability is provided.

Keywords

Cite

@article{arxiv.2605.15879,
  title  = {Coarse-grained local available potential energy},
  author = {Jacob O. Wenegrat and Tomas Chor and Roy Barkan},
  journal= {arXiv preprint arXiv:2605.15879},
  year   = {2026}
}