Coarse-grained local available potential energy

TL;DR

This paper introduces a framework for analyzing local available potential energy (APE) across multiple scales in stratified flows using coarse-graining, enabling a comprehensive view of energy conversions.

Contribution

It develops evolution equations for local APE at different scales, including cross-scale fluxes, and demonstrates the approach with a Kelvin-Helmholtz instability simulation.

Findings

Derived scale-specific APE evolution equations.

Identified cross-scale APE flux terms.

Applied framework to 2D Kelvin-Helmholtz instability.

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.