Coarse-grained local available potential energy
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. A scale decomposition valid generally for filters with both horizontal and vertical support is proposed, and shown to admit a construction in terms of a series of band-passed energies. The physical interpretation of the decomposition is discussed, and 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 three-dimensional Kelvin-Helmholtz instability is provided, including an exact formulation of the scale-dependent instability energy budgets, and the distribution of terms such as cross-scale transfers and APE dissipation in physical space.
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BibTeX
@misc{wenegrat2026coarsegrained,
title = {{Coarse-grained local available potential energy}},
author = {Jacob O. Wenegrat and Tomas Chor and Roy Barkan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.15879},
eprint = {2605.15879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15879},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Coarse-grained local available potential energy
AU - Jacob O. Wenegrat
AU - Tomas Chor
AU - Roy Barkan
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2605.15879
UR - https://arxiv.org/abs/2605.15879
AB - 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. A scale decomposition valid generally for filters with both horizontal and vertical support is proposed, and shown to admit a construction in terms of a series of band-passed energies. The physical interpretation of the decomposition is discussed, and 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 three-dimensional Kelvin-Helmholtz instability is provided, including an exact formulation of the scale-dependent instability energy budgets, and the distribution of terms such as cross-scale transfers and APE dissipation in physical space.
ER -