Living Reviews in Solar Physics

"The Solar Wind as a Turbulence Laboratory"
by
Roberto Bruno and Vincenzo Carbone  

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Abstract
1 Introduction
1.1 What does turbulence stand for?
1.2 Dynamics vs. statistics
2 Equations and Phenomenology
2.1 The Navier-Stokes equation and the Reynolds number
2.2 The coupling between a charged fluid and the magnetic field
2.3 Scaling features of the equations
2.4 The non-linear energy cascade
2.5 The inhomogeneous case
2.6 Dynamical system approach to turbulence
2.7 Shell models for turbulence cascade
2.8 The phenomenology of fully developed turbulence: Fluid-like case
2.9 The phenomenology of fully developed turbulence: Magnetically-dominated case
2.10 Some exact relationships
3 Early Observations of MHD Turbulence in the Ecliptic
3.1 Turbulence in the ecliptic
3.2 Turbulence studied via Elsässer variables
4 Observations of MHD Turbulence in the Polar Wind
4.1 Evolving turbulence in the polar wind
4.2 Polar turbulence studied via Elsässer variables
5 Numerical Simulations
5.1 Local production of Alfvénic turbulence in the ecliptic
5.2 Local production of Alfvénic turbulence at high latitude
6 Compressive Turbulence
6.1 On the nature of compressive Turbulence
6.2 Compressive turbulence in the polar wind
6.3 The effect of compressive phenomena on Alfvénic correlations
7 A Natural Wind Tunnel
7.1 Scaling exponents of structure functions
7.2 Probability density functions and self-similarity of fluctuations
7.3 What is intermittent in the solar wind turbulence? The multifractal approach
7.4 Fragmentation models for the energy transfer rate
7.5 A model for the departure from self-similarity
7.6 Intermittency properties recovered via a shell model
8 Intermittency Properties in the 3D Heliosphere: Taking a Look at the Data
8.1 Structure functions
8.2 Probability distribution functions
9 Turbulent Structures
9.1 Radial evolution of intermittency in the ecliptic
9.2 Radial evolution of intermittency at high latitude
10 Conclusions and Remarks
11 Acknowledgments
12 Appendix A: Some Characteristic Solar Wind Parameters
13 Appendix B: Tools to Analyze MHD Turbulence in Space Plasmas
13.1 Statistical description of MHD turbulence
13.2 Spectra of the invariants in homogeneous turbulence
13.3 Introducing the Elsässer variables
14 Appendix C: Wavelets as a Tool to Study Intermittency
15 Appendix D: Reference Systems
15.1 Minimum variance reference system
15.2 The mean field reference system
16 Appendix E: On-board Plasma and Magnetic Field Instrumentation
16.1 Plasma instrument: The top-hat
16.2 Measuring the velocity distribution function
16.3 Computing the moments of the velocity distribution function
16.4 Field instrument: The flux-gate magnetometer
17 Appendix F: Spacecraft and Datasets
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Footnotes
Figures