APE dissipation is a form of Joule heating. It is irreversible, not reversible

TL;DR

This paper demonstrates that Available Potential Energy (APE) dissipation is fundamentally a form of Joule heating, which is irreversible and increases background gravitational potential energy by expanding fluid parcels, challenging previous paradigms.

Contribution

The paper proves from first principles that APE dissipation is a form of Joule heating, clarifying its irreversibility and energy transfer mechanisms in stratified fluids.

Findings

APE dissipation is equivalent to Joule heating.

APE dissipation irreversibly increases background GPE.

Turbulent mixing homogenizes conserved variables.

Abstract

Available Potential Energy (APE) dissipation plays a central role in the description of mixing in turbulent stratified fluids. The dominant paradigm is that it converts APE into background gravitational potential energy ${\rm GPE}_r$, and that the APE thus converted can be infinitely recycled back into APE by external buoyancy fluxes such as high-latitude cooling in the oceans. In this paper, we argue that such a paradigm is unphysical, because its corollary is that APE dissipation is neither truly dissipative nor irreversible, while also violating energy conservation in more subtle ways. In this paper, we prove from first principles that in reality, APE dissipation is a form of Joule heating, which --- like viscous dissipation --- can only increase ${\rm GPE}_r$ via locally expanding the fluid parcels, a tiny effect. ${\rm GPE}_r$ thus primarily increases at the expense of the exergy of the stratification, a subcomponent of the background internal energy, regardless of whether the flow is laminar or turbulent. The results greatly clarify the energetics of mechanically- and buoyancy-driven circulations. As a side benefit, our results yield a new physical principle justifying why turbulent mixing tends to homogenise the fluid's materially conserved variables rather than relax the fluid towards thermodynamic equilibrium.