# Eddy-mixing entropy as a measure of turbulent disorder in barotropic ocean jets

## TL;DR

This paper investigates eddy-mixing entropy in a barotropic ocean model, revealing its role in understanding turbulence stages and the influence of forcing and dissipation, with implications for ocean circulation and climate modeling.

## Contribution

It introduces eddy-mixing entropy as a diagnostic tool for turbulence stages and explores the maximum entropy principle in a forced-dissipative geophysical flow.

## Key findings

- Eddy-mixing entropy tracks turbulence lifecycle stages.
- Maximum entropy principle influences flow statistics.
- Discussions on limitations of mean-field approximations.

## Abstract

Understanding the statistics of ocean geostrophic turbulence is of utmost importance in understanding its interactions with the global ocean circulation and the climate system as a whole. Here, a study of eddy-mixing entropy in a forced-dissipative barotropic ocean model is presented. Entropy is a concept of fundamental importance in statistical physics and information theory; motivated by equilibrium statistical mechanics theories of ideal geophysical fluids, we consider the effect of forcing and dissipation on eddy-mixing entropy, both analytically and numerically. By diagnosing the time evolution of eddy-mixing entropy it is shown that the entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability, formation of large scale structures and steady state fluctuations. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced-dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance entropy and statistical mechanics in the study of geostrophic turbulence.