Weather and Climate Without Fluid Mechanics
Abstract
Even if it were possible, attempting to model the motion of a fluid in a pipe by tracking each individual molecule would be an extraordinary waste of computation. The emergent laws of fluid mechanics accomplish the same goal on a laptop instead of a datacenter. But a sufficiently complex fluid such as in Earth's atmosphere again requires a datacenter, this time to resolve the many contortions in the fields making up our weather. Might there be some analogous set of emergent laws that would represent the effect of these perturbations without needing their explicit representation on a numerical grid? We argue that the existence of a symmetry principle implies such laws are likely to exist. The atmosphere is scale invariant, implying that the observed structure at one scale is nothing but a stretched version of that at any other scale, at least within the invariant regime. Though some emergent laws built on scale invariance exist, they are built on a challenging ontological foundation, making them hard to develop further. We propose a path forward, first by introducing a new fundamental building block of the atmosphere that we term a ``turbulon'', inspired by a lesser-known generalization of turbulence theory that accounts for buoyancy. We then construct the Superposition of Turbulons and Eddies Atmospheric Model (STEAM), and show that simulated atmospheric volumes are broadly plausible when compared to state-of-the-art hydrodynamic simulation output. Some aspects of STEAM clearly need improvement, though other statistics reproduce observations better than hydrodynamic models, and visualizations of simulated clouds are strikingly realistic. We estimate STEAM's computational cost to be up to a million times less than hydrodynamic models, suggesting that the Navier-Stokes equations may not, in fact, be required for simulation and prediction of Earth's weather and climate.
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BibTeX
@misc{dewitt2026weather,
title = {{Weather and Climate Without Fluid Mechanics}},
author = {Thomas D. DeWitt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30589},
eprint = {2609.30589},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30589},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weather and Climate Without Fluid Mechanics
AU - Thomas D. DeWitt
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30589
UR - https://arxiv.org/abs/2609.30589
AB - Even if it were possible, attempting to model the motion of a fluid in a pipe by tracking each individual molecule would be an extraordinary waste of computation. The emergent laws of fluid mechanics accomplish the same goal on a laptop instead of a datacenter. But a sufficiently complex fluid such as in Earth's atmosphere again requires a datacenter, this time to resolve the many contortions in the fields making up our weather. Might there be some analogous set of emergent laws that would represent the effect of these perturbations without needing their explicit representation on a numerical grid? We argue that the existence of a symmetry principle implies such laws are likely to exist. The atmosphere is scale invariant, implying that the observed structure at one scale is nothing but a stretched version of that at any other scale, at least within the invariant regime. Though some emergent laws built on scale invariance exist, they are built on a challenging ontological foundation, making them hard to develop further. We propose a path forward, first by introducing a new fundamental building block of the atmosphere that we term a ``turbulon'', inspired by a lesser-known generalization of turbulence theory that accounts for buoyancy. We then construct the Superposition of Turbulons and Eddies Atmospheric Model (STEAM), and show that simulated atmospheric volumes are broadly plausible when compared to state-of-the-art hydrodynamic simulation output. Some aspects of STEAM clearly need improvement, though other statistics reproduce observations better than hydrodynamic models, and visualizations of simulated clouds are strikingly realistic. We estimate STEAM's computational cost to be up to a million times less than hydrodynamic models, suggesting that the Navier-Stokes equations may not, in fact, be required for simulation and prediction of Earth's weather and climate.
ER -