"The Solar Wind as a Turbulence Laboratory"
Roberto Bruno and Vincenzo Carbone 
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
2.11 Yaglom’s law for MHD turbulence
2.12 Density-mediated Elsässer variables and Yaglom’s law
2.13 Yaglom’s law in the shell model for MHD turbulence
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 distribution 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 Observations of Yaglom’s Law in Solar Wind Turbulence
9 Intermittency Properties in the 3D Heliosphere: Taking a Look at the Data
9.1 Structure functions
9.2 Probability distribution functions
10 Turbulent Structures
10.1 On the statistics of magnetic field directional fluctuations
10.2 Radial evolution of intermittency in the ecliptic
10.3 Radial evolution of intermittency at high latitude
11 Solar Wind Heating by the Turbulent Energy Cascade
11.1 Dissipative/dispersive range in the solar wind turbulence
12 The Origin of the High-Frequency Region
12.1 A dissipation range
12.2 A dispersive range
13 Two Further Questions About Small-Scale Turbulence
13.1 Whistler modes scenario
13.2 Kinetic Alfvén waves scenario
13.3 Where does the fluid-like behavior break down in solar wind turbulence?
13.4 What physical processes replace “dissipation” in a collisionless plasma?
14 Conclusions and Remarks
A Some Characteristic Solar Wind Parameters
B Tools to Analyze MHD Turbulence in Space Plasmas
B.1 Statistical description of MHD turbulence
B.2 Spectra of the invariants in homogeneous turbulence
B.3 Introducing the Elsässer variables
C Wavelets as a Tool to Study Intermittency
D Reference Systems
D.1 Minimum variance reference system
D.2 The mean field reference system
E On-board Plasma and Magnetic Field Instrumentation
E.1 Plasma instrument: The top-hat
E.2 Measuring the velocity distribution function
E.3 Computing the moments of the velocity distribution function
E.4 Field instrument: The flux-gate magnetometer
F Spacecraft and Datasets

The Solar Wind as a Turbulence Laboratory

Roberto Bruno 
Istituto di Astrofisica e Planetologia Spaziali - INAF,
Via Fosso del Cavaliere 100, 00133 Rome, Italy

'External link'
Vincenzo Carbone 
Dipartimento di Fisica, Universitàdella Calabria
Ponte P. Bucci, Cubo 31C 87036 Rende (CS), Italy

'External link'
Major update of lrsp-2005-4 (see article history and change log for details).


In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Helios inner heliosphere and Ulysses’ high latitude observations, recent multi-spacecrafts measurements in the solar wind (Cluster four satellites) and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

Keywords: Solar wind, Turbulence, Interplanetary space, Dynamical systems, Magnetohydrodynamics (MHD), Nonlinear phenomena

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