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Table of contents
Contents
1 Introduction
1.1 Theory of collisionless plasmas
1.1.1 What is a plasma ?
1.1.2 Kinetic and uid description of a plasma
1.1.3 The equations of MHD
1.2 From space to astrophysical plasmas
1.2.1 The Solar Wind: a turbulence laboratory
1.2.2 The Interstellar Medium and star-forming regions
1.3 Theory of turbulence
1.3.1 Basics of turbulence
1.3.2 The zeroth law of turbulence
1.3.3 Spectral approach of turbulence
1.4 Overview of the thesis
2 Exact laws in Hall MHD turbulence
2.1 Introduction
2.2 Exact law in the incompressible Hall MHD model
2.2.1 Description of the model
2.2.2 Calculation of the dynamical equation
2.2.3 From the dynamical equation to the exact law
2.2.4 Equivalence of IHMHD exact laws
2.3 Exact law in compressible models
2.3.1 Description of the compressible Hall MHD model
2.3.2 Calculation of a compressible dynamical equation
2.3.3 From the dynamical equation to the exact law
2.3.4 Limit cases and alternative compressible laws
2.4 Conclusion
3 Methodology: laws computation and numerical implementation
3.1 Introduction
3.2 Numerical calculation of exact laws
3.2.1 Generic framework
3.2.2 Isotropy hypothesis: 3D increments
3.2.3 Axisymmetry hypothesis: 3D increments
3.2.4 Axisymmetry hypothesis: 2D increments
3.3 Implementation of the numerical methods
3.3.1 Main steps of the calculation
3.3.2 Parallelization paradigm
3.3.3 Memory constraints
3.4 Conclusion
4 Understanding plasma turbulence through DNS data analysis
4.1 Introduction
4.2 Numerical test of IHMHD exact laws
4.2.1 Convergence of exact laws and model choice
4.2.2 Inuence of the mean magnetic eld
4.2.3 Summary of the study on the IHMHD laws
4.3 In-depth study with generalized CHMHD exact laws
4.3.1 Context of the study
4.3.2 Presentation of the data
4.3.3 Calculation of law F21
4.3.4 Non-stationary CHMHD laws
4.3.5 Summary of the GHOST study
4.4 Application to Landau-uid simulations
4.4.1 Context of the study
4.4.2 Theory of CGL and LF models
4.4.3 Description of the numerical code
4.4.4 Evaluation of the exact law and dissipations
4.4.5 Methods of calculation of the hyperdissipation
4.4.6 Energy cascade in presence of Landau damping
4.4.7 Calculation of the heating due to Landau damping
4.4.8 Summary: relations between uid and kinetic models
4.5 Supersonic CHD turbulence
4.5.1 Context of the study
4.5.2 Framework and presentation of the data
4.5.3 Calculation of the energy cascade rate
4.5.4 Filamentary structures and locality of turbulence
4.5.5 Insights into a two-regimes turbulence
4.5.6 Summary and link to the ISM
4.6 Conclusion
5 Application to Virtual spacecraft and MMS data in Earth’s magnetosheath
5.1 Introduction
5.2 Working with in situ data
5.2.1 Space-time ambiguity and Taylor hypothesis
5.2.2 Calculation of 3D divergences: the curlometer / gradiometer
5.3 MMS data analysis
5.3.1 Context and presentation of the data
5.3.2 Selection of the time intervals
5.3.3 Results
5.4 Gradiometer: evaluation and limitations of the method
5.4.1 Quality factor of the gradiometer
5.4.2 Causes of error of the gradiometer
5.5 Simulated MMS y-by
5.5.1 Description of the method
5.5.2 General precision of the gradiometer
5.5.3 Reaction of the gradiometer to non-linearity
5.6 Conclusion
6 Conclusions and perspectives
6.1 Summary of the thesis
6.2 Tools for turbulence analysis
6.2.1 Derivation of exact laws
6.2.2 Numerical implementation of the exact laws
6.3 Studying turbulent ows through DNSs
6.3.1 In-depth analysis of exact laws
6.3.2 Relation between the uid cascade and kinetic dissipation
6.3.3 Supersonic CHD turbulence in the ISM
6.4 MMS in situ data analysis
6.4.1 Selection and exploitation of the data
6.4.2 Investigation of the gradiometer
6.5 Final words and perspectives
A List of Acronyms
B Papers published and in preparation
