Scaling Up: Molecular to Meteorological via Symmetry Breaking and Statistical Multifractality
Abstract
:1. Introduction
2. Microscopic and Macroscopic Processes
2.1. Persistence of Molecular Velocity after Collision
2.2. Emergence of Fluid Flow from a Molecular Population
3. Statistical Multifractality
3.1. Vertical Scaling: Horizontal Wind, Temperature and Humidity
3.2. Scaling in Jet Streams
3.3. Molecular and Photochemical Effects
4. The Intermittency of Temperature and Its Correlation with Ozone Photodissociation Rate
5. Scaling Based Entropy and Gibbs Free Energy
6. Aerosols and Scaling
7. Models and Scaling
7.1. Scaling Issues and Tests for Models
7.2. Scaling and the Cold Bias in Models
7.3. Scaling, Molecules and Maximum Observed Wind Speeds
8. Some Examples
9. Why Turbulence?
10. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Variable | Statistical Thermodynamics | Scaling Equivalent |
---|---|---|
Temperature | T | 1/qkBoltzmann |
Partition function | f | e−K(q) |
Energy | E | γ |
Entropy | −S(E) | c(γ) |
Gibbs free energy | −G | K(q)/q |
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Tuck, A.F. Scaling Up: Molecular to Meteorological via Symmetry Breaking and Statistical Multifractality. Meteorology 2022, 1, 4-28. https://doi.org/10.3390/meteorology1010003
Tuck AF. Scaling Up: Molecular to Meteorological via Symmetry Breaking and Statistical Multifractality. Meteorology. 2022; 1(1):4-28. https://doi.org/10.3390/meteorology1010003
Chicago/Turabian StyleTuck, Adrian F. 2022. "Scaling Up: Molecular to Meteorological via Symmetry Breaking and Statistical Multifractality" Meteorology 1, no. 1: 4-28. https://doi.org/10.3390/meteorology1010003