Modal Projection for Quasi-Homogeneous Anisotropic Turbulence
Abstract
:1. Introduction
2. The Craya–Herring Frame of Reference and Beyond
2.1. Related Modal Projections, Analogies, and Differences
2.2. Including Other Coupled Fields, Buoyancy, Magnetic Field
3. Application to Two-Point Second Order Statistics for Strong Anisotropy
3.1. Decomposition in Terms of Scalar Spherical Harmonics (SSH)
3.2. Angular Harmonics for the Polarization Term
4. SSH Decomposition in Rotating Shear Turbulence
4.1. Recalling ZCG Model
4.1.1. Spectral Models for Homogeneous Anisotropic Turbulence
4.1.2. Numerical Simulations for Rotating Shear Flows
4.2. Numerical Validation of the Equivalency of SO(3) Expansion and SSH Decomposition
4.3. Analysis on High-Degree Anisotropy
5. Towards a More General Decomposition for a Vector Field
5.1. Using a General Toroidal/Poloidal Decomposition
5.2. Recent Progresses towards Stochastic Fields and Multifractal Approach
6. Conclusions, Perspectives of Turbulence from Earth to Planets, Stars, and Galaxies
6.1. Linear and Quasi-Linear Models from Geophysics to Accretion Discs in Astrophysics
6.2. Models with Explicit Nonlinearity for Cascades
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Degenerated Craya Equations Exactly at the Pole
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Zhu, Y.; Cambon, C. Modal Projection for Quasi-Homogeneous Anisotropic Turbulence. Atmosphere 2023, 14, 1215. https://doi.org/10.3390/atmos14081215
Zhu Y, Cambon C. Modal Projection for Quasi-Homogeneous Anisotropic Turbulence. Atmosphere. 2023; 14(8):1215. https://doi.org/10.3390/atmos14081215
Chicago/Turabian StyleZhu, Ying, and Claude Cambon. 2023. "Modal Projection for Quasi-Homogeneous Anisotropic Turbulence" Atmosphere 14, no. 8: 1215. https://doi.org/10.3390/atmos14081215
APA StyleZhu, Y., & Cambon, C. (2023). Modal Projection for Quasi-Homogeneous Anisotropic Turbulence. Atmosphere, 14(8), 1215. https://doi.org/10.3390/atmos14081215