Nonequilibrium thermodynamics of circulation regimes in optically-thin, dry atmospheres

An extensive analysis of an optically-thin, dry atmosphere at different values of the thermal Rossby number Ro and of the Taylor number Ff is per- formed with a general circulation model by varying the rotation rate {\Omega} and the surface drag {\tau} in a wide parametric range. By using nonequilibrium thermodynamics diagnostics such as material entropy production, efficiency, meridional heat transport and kinetic energy dissipation we characterize in a new way the different circulation regimes. Baroclinic circulations feature high mechanical dissipation, meridional heat transport, material entropy pro- duction and are fairly efficient in converting heat into mechanical work. The thermal dissipation associated with the sensible heat flux is found to depend mainly on the surface properties, almost independent from the rotation rate and very low for quasi-barotropic circulations and regimes approaching equa- torial super-rotation. Slowly rotating, axisymmetric circulations have the highest meridional heat transport. At high rotation rates and intermediate- high drag, atmospheric circulations are zonostrohic with very low mechanical dissipation, meridional heat transport and efficiency. When {\tau} is interpreted as a tunable parameter associated with the turbulent boundary layer trans- fer of momentum and sensible heat, our results confirm the possibility of using the Maximum Entropy Production Principle as a tuning guideline in the range of values of {\Omega}. This study suggests the effectiveness of using fun- damental nonequilibrium thermodynamics for investigating the properties of planetary atmospheres and extends our knowledge of the thermodynamics of the atmospheric circulation regimes.

💡 Research Summary

The paper presents a systematic investigation of atmospheric circulation regimes in an optically‑thin, dry atmosphere by varying two fundamental control parameters: the planetary rotation rate (Ω) and the surface drag time scale (τ). These parameters are combined into two nondimensional numbers – the thermal Rossby number (Ro) and the Taylor (or friction) number (Ff) – which together span a broad dynamical space. Using a high‑resolution general circulation model (GCM) that excludes radiative and moist processes, the authors performed a suite of simulations covering Ω from 0.1 to 10 times Earth’s present value and τ from 0.1 to 10 days. For each simulation they diagnosed four nonequilibrium thermodynamic quantities: material entropy production (𝑆̇mat), thermodynamic efficiency (η = W/Qin), meridional heat transport (Fθ), and kinetic‑energy dissipation (ε).

The results reveal four distinct families of circulation:

1. Baroclinic regime (moderate Ω, low τ). Strong temperature gradients together with sufficient Coriolis force generate large‑scale baroclinic eddies. This regime exhibits the highest kinetic‑energy dissipation, the strongest poleward heat transport, and the largest material entropy production. Its thermodynamic efficiency reaches 5–8 %, indicating an effective conversion of absorbed heat into mechanical work.

2. Axisymmetric, slowly rotating regime (low Ω, intermediate τ). With weak rotational constraint, the flow organizes into large meridional cells that transport heat poleward more efficiently than the baroclinic case (≈20 % higher Fθ). Kinetic‑energy dissipation is moderate, and efficiency is low, but the system excels at reducing the equator‑to‑pole temperature contrast.

3. Zonostrophic (jet‑dominated) regime (high Ω, intermediate–high τ). Strong Coriolis forces suppress meridional temperature gradients and thin the baroclinic eddies. Consequently, both ε and Fθ drop dramatically, and η falls below 1 %. The atmosphere behaves almost like a passive heat conduit with negligible conversion of thermal energy into kinetic energy.

4. High‑drag, low‑rotation regime (low Ω, high τ). Here surface friction dominates, strongly limiting sensible‑heat fluxes. Material entropy production is largely controlled by surface drag rather than rotation, and both kinetic‑energy dissipation and meridional heat transport are minimal.

A key insight is that the surface drag τ primarily controls the sensible‑heat entropy production (𝑆̇sens). When τ is small, the atmosphere exchanges heat efficiently with the surface, leading to high 𝑆̇sens and a large contribution to total entropy production. As τ increases, the boundary layer becomes more resistant, reducing heat exchange and consequently lowering total entropy production, almost independently of Ω. This demonstrates that surface properties can outweigh rotational effects in setting the thermodynamic budget of a dry atmosphere.

Finally, the authors test the Maximum Entropy Production (MEP) principle as a tuning guideline. By selecting τ values that maximize 𝑆̇mat for a given Ω, the model naturally reproduces circulation regimes that resemble those observed on Earth and other planetary bodies, without the need for ad‑hoc parameter adjustments. This suggests that MEP can serve as a physically grounded constraint for the parametrization of turbulent momentum and heat transfer in planetary‑scale climate models, especially when observational data are scarce (e.g., for exoplanets).

Overall, the study provides a comprehensive framework that couples dynamical nondimensional analysis with nonequilibrium thermodynamic diagnostics. It clarifies how rotation and surface drag jointly shape atmospheric energetics, identifies the thermodynamic signatures of distinct circulation regimes, and demonstrates the practical utility of entropy‑based principles for model development. The findings have direct implications for interpreting the climates of terrestrial planets, both within the Solar System and on exoplanets, where variations in rotation rate and surface characteristics are expected to be substantial.