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arXiv · 2605.15879

Coarse-grained local available potential energy

Jacob O. Wenegrat·Tomas Chor·Roy Barkan
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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.

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Jacob O. Wenegrat, Tomas Chor, Roy Barkan. 2026-05-15. Coarse-grained local available potential energy. https://arxiv.org/abs/2605.15879

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