Non-Equilibrium Atmospheric Turbulence: Geostrophic Dual Cascades, First-Principles Subgrid Stress Closure, and Mesoscale Transition Dynamics in Rotating Planetary Atmospheres
Abstract
We construct a non-perturbative, operator-theoretic field theory of atmospheric turbulence across synoptic, mesoscale, and microphysical boundary-layer regimes within the framework of Detection Ontology (DO). Classical geophysical fluid dynamics models atmospheric motions via the Navier–Stokes equations under the Boussinesq approximation, relying on empirical eddy-viscosity parameterizations, heuristic closure schemes (such as Smagorinsky and Leith models), and phenomenological geostrophic balance. However, terrestrial observations and planetary exploration spacecraft (Juno, Cassini) reveal five persistent structural anomalies.
We resolve those anomalies by compiling atmospheric flow fields upon the discrete Tetrahedral Quantum Point (TQP) complex over the global Adèle Class Space \mathbb{X}_{\mathbb{Q}} \equiv \mathbb{A}_{\mathbb{Q}}/\mathbb{Q}^\times, bounded by the universal Information-Viscosity Floor: \nu_{\text{info}} \equiv \frac{1}{\theta^*} \approx 4.21786208\text{ bits/cell} derived as the unique positive real root of the Unitary Feedback Equation: \theta^* \exp\bigl(\theta^*(1 + \ln 2 + \theta^*)\bigr) = \frac{1}{e}.
Related
- Growth of small localized perturbations in Surface Quasi-Geostrophic turbulence
- Wave-driven geostrophic vortices in rotating turbulence
- Score-based stochastic reduced-order models of barotropic quasi-geostrophic turbulence
- Internal heating in rapidly rotating convection is not a shortcut to geostrophic turbulence
- Online learning of subgrid-scale models for quasi-geostrophic turbulence in planetary interiors
BibTeX
@misc{tudor2026nonequilibrium,
title = {{Non-Equilibrium Atmospheric Turbulence: Geostrophic Dual Cascades, First-Principles Subgrid Stress Closure, and Mesoscale Transition Dynamics in Rotating Planetary Atmospheres}},
author = {August Tudor},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23547059},
url = {https://zenodo.org/records/23547059},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Equilibrium Atmospheric Turbulence: Geostrophic Dual Cascades, First-Principles Subgrid Stress Closure, and Mesoscale Transition Dynamics in Rotating Planetary Atmospheres
AU - August Tudor
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23547059
UR - https://zenodo.org/records/23547059
AB - We construct a non-perturbative, operator-theoretic field theory of atmospheric turbulence across synoptic, mesoscale, and microphysical boundary-layer regimes within the framework of Detection Ontology (DO). Classical geophysical fluid dynamics models atmospheric motions via the Navier–Stokes equations under the Boussinesq approximation, relying on empirical eddy-viscosity parameterizations, heuristic closure schemes (such as Smagorinsky and Leith models), and phenomenological geostrophic balance. However, terrestrial observations and planetary exploration spacecraft (Juno, Cassini) reveal five persistent structural anomalies. We resolve those anomalies by compiling atmospheric flow fields upon the discrete Tetrahedral Quantum Point (TQP) complex over the global Adèle Class Space \mathbb{X}_{\mathbb{Q}} \equiv \mathbb{A}_{\mathbb{Q}}/\mathbb{Q}^\times, bounded by the universal Information-Viscosity Floor: \nu_{\text{info}} \equiv \frac{1}{\theta^*} \approx 4.21786208\text{ bits/cell} derived as the unique positive real root of the Unitary Feedback Equation: \theta^* \exp\bigl(\theta^*(1 + \ln 2 + \theta^*)\bigr) = \frac{1}{e}.
ER -