The Solar Wind as a Turbulence Laboratory

"The Solar Wind as a Turbulence Laboratory"

Roberto Bruno and Vincenzo Carbone

	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
	References
	Footnotes
	Figures