A scaling theory for the macroturbulence of weakly supercritical planetary atmospheres

Abstract

A theory for the general circulation of the atmosphere must be based on a theory of its macroturbulence. A central component is the near-surface eddy heat flux, which is closely tied to the mass transport of the surface branch of the circulation. Existing scaling theories are largely formulated within the two-layer quasi-geostrophic framework, which assumes supercritical states and an inverse cascade of kinetic energy---conditions that are frequently not satisfied in planetary atmospheres, including Earth's. Nevertheless, such theories have shown some empirical success, including that the Rhines scale is associated with the mixing length even in the absence of any inverse energy cascade. Here, we analyze hundreds of idealized, dry general circulation model simulations spanning wide ranges of rotation rates, meridional temperature gradients, vertical stratification, and seasonality. Most simulations reside in the marginally critical regime where strongly nonlinear scaling theories fail. We propose a new theory that captures both domain-averaged and local eddy heat flux behavior across all simulations. The theory uses scaling arguments for the zonal momentum balance and accounts for kinematic effects on eddy mixing. The scaling depends on a non-dimensional thermal Rossby number and implicitly accounts for the role of nonlinear eddy momentum fluxes across jets. We demonstrate the skill of the proposed scaling in explaining global near-surface temperature distributions across a wide range of climate states in a simple energy balance model. Implications for general circulation theory and extending the scalings to moist atmospheres are discussed.

MONKI: a three-dimensional Monte Carlo simulator for transfer of polarised light in planetary atmospheres
Victor J. H. Trees, Ping Wang, Job I. Wiltink +4
Geoscientific Model Development12 Oct 2026Peer-reviewedCC BY 4.0Climate scienceCrossref
Scaling methodology for supercritical CO2 extraction process: applicability of the solvent-to-feed mass ratio criterion under different flow directions and extraction basket geometries
Adil Mouahid, Cyrielle Girard, Lucero Benitez +8
Chemical Engineering Research and Design1 Sep 2026Peer-reviewedCC BYFull textEcology Environmental science & pollutionHAL
A High-Density Supercritical Fluid of H2.
Atsuko Nakayama, Naoto Fujii, Koji Hirama +7
The journal of physical chemistry letters1 Oct 2026Peer-reviewedCC BY-NC-NDFull textGeophysics & seismologyEurope PMC
Van der Waals interactions in supercritical water under Earth's mantle conditions
Jiajia Huang, Rui Hou, Ding Pan
arXiv16 Sep 2026PreprintarXiv licenceFull textGeophysics & seismology Computational physicsarXiv
The diversity of planetary climates in the Solar System as a basis for reflection and work on the study of exoplanet climates
Olivier Planchon
HAL18 Sep 2026PreprintCC BY 4.0Full textPlanetary science & exoplanets General earth scienceHAL

Cite

BibTeX RIS

BibTeX

@misc{eusebi2026scaling,
  title = {{A scaling theory for the macroturbulence of weakly supercritical planetary atmospheres}},
  author = {Ryan Eusebi and Tapio Schneider and Andy Thompson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06787},
  eprint = {2609.06787},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06787},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - A scaling theory for the macroturbulence of weakly supercritical planetary atmospheres
AU  - Ryan Eusebi
AU  - Tapio Schneider
AU  - Andy Thompson
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06787
UR  - https://arxiv.org/abs/2609.06787
AB  - A theory for the general circulation of the atmosphere must be based on a theory of its macroturbulence. A central component is the near-surface eddy heat flux, which is closely tied to the mass transport of the surface branch of the circulation. Existing scaling theories are largely formulated within the two-layer quasi-geostrophic framework, which assumes supercritical states and an inverse cascade of kinetic energy---conditions that are frequently not satisfied in planetary atmospheres, including Earth's. Nevertheless, such theories have shown some empirical success, including that the Rhines scale is associated with the mixing length even in the absence of any inverse energy cascade. Here, we analyze hundreds of idealized, dry general circulation model simulations spanning wide ranges of rotation rates, meridional temperature gradients, vertical stratification, and seasonality. Most simulations reside in the marginally critical regime where strongly nonlinear scaling theories fail. We propose a new theory that captures both domain-averaged and local eddy heat flux behavior across all simulations. The theory uses scaling arguments for the zonal momentum balance and accounts for kinematic effects on eddy mixing. The scaling depends on a non-dimensional thermal Rossby number and implicitly accounts for the role of nonlinear eddy momentum fluxes across jets. We demonstrate the skill of the proposed scaling in explaining global near-surface temperature distributions across a wide range of climate states in a simple energy balance model. Implications for general circulation theory and extending the scalings to moist atmospheres are discussed.
ER  -

Abstract

Related

Cite