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Table of contents
A Preamble
0 Présentation
0.1 Cadre d’étude
0.2 Résultats sur les instabilités grande échelle
0.3 Résultats sur les temps de corrélation
1 Introduction
2 Elements of context: Hydrodynamics
2.1 Ideal fluids (review)
2.2 Magnetic equivalences (review)
2.3 Conserved quantities (review)
B Large scale instabilities
3 Elements of context: Large scale effects
3.1 Alpha-effect (review)
3.2 AKA-effect (review)
3.3 Distribution of energy (description of a new model)
4 Elements of context: Floquet analysis (review)
4.1 Floquet theory (review)
4.2 Bloch theory (review)
4.3 Floquet Linear Analysis of Spectral MHD (review)
5 Large scale instabilities of helical flows (published in PRF)
5.1 Introduction
5.2 Methods (description of new procedures)
5.3 Results (new results)
5.4 Conclusion
5.5 Appendix: FLASHy (description of a new procedure)
6 Fate of alpha-dynamos at large Rm (published in PRL)
6.1 Introduction
6.2 Results (new results)
6.3 Discussion
C Thermalized state
7 Elements of context: Thermodynamics (review)
7.1 Ideal gas distribution (review)
7.2 The Liouville theorem (review)
7.3 Absolute equilibrium theory (review)
8 Elements of context: Time correlation
8.1 Definition and examples (review)
8.2 Hydrodynamic application (description of a new model)
8.3 Spatio-temporal measurements (description of a new procedure)
9 Large scale correlation time
9.1 Introduction
9.2 Results (new results)
9.3 Conclusion
9.4 Appendix (description of new procedures)
D Conclusion
E Numerical methods
10 Elements of context: Numeric methods
10.1 Pseudo-spectral methods (review)
10.2 Semi-Lagrangian methods (review)
11 High-order semi-Lagrangian schemes (published in IJNMF)
11.1 Introduction
11.2 Method (description of new procedures)
11.3 Conclusion
11.4 Appendix (description of new procedures)
12 Conservative semi-Lagrangian schemes
12.1 Introduction
12.2 Method (description of new procedure)
12.3 Perspectives
12.4 Appendix (convergence study)
F References
Acknowledgments
List of Figures
Bibliography
