Fast and slow winds

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Table of contents

I Introduction 
1 Solar Wind
1.1 Sources of the wind and solar cycle
1.1.1 Fast and slow winds
1.2 From corona to Earth
2 Plasma description
2.1 The MHD equations
2.2 MHD equations with large scale radial flow (EBM)
3 Turbulence
3.1 Homogeneous turbulence
3.1.1 Shock formation as a simplified model of turbulence
3.1.2 3D hydrodynamic turbulence
Fourier space description: K41 phenomenology
3.1.3 3D MHD turbulence
Incompressible MHD using Elsasser variables, cross-helicity
Anisotropy of the cascade with mean magnetic field B0
Local and nonlocal interactions
3.1.4 Spectra, autocorrelations and structure functions
3.2 Turbulence with large scale radial flow
3.2.1 Inhibition of the turbulent cascade by expansion
3.2.2 Fluctuations decay: strong versus weak expansion
3.2.3 Cascade rate and turbulent heating
4 Solar Wind turbulence
4.1 In situ observations
4.2 MHD inertial range
4.3 Spectral anisotropy
4.3.1 The Maltese Cross
4.4 Proton temperature gradient and turbulent heating
4.4.1 Turbulent amplitude and proton temperature variations in the inner heliosphere Temperature gradient: a long series of studies
Possible explanations of the slow proton cooling in the inner heliosphere
4.4.2 Measuring turbulent heating via second order moments
4.4.3 Measuring turbulent heating via third order moments
5 Plan of this thesis
5.1 Spectral anisotropy: understanding the Maltese Cross
5.2 Turbulent heating in slow and fast winds
II The Maltese Cross revisited 
6 Parameters and initial conditions
6.1 Physical parameters and initial spectra
6.1.1 Expansion parameter, cross helicity, Mach number
6.1.2 Initial spectra
6.1.3 Domain aspect ratio
7 Defining spectral properties in EBM simulations
7.1 Anisotropy of 3D spectra
7.2 1D spectral slopes
8 Results
8.1 Initially ISO spectrum: expansion and cross helicity effects
8.1.1 Varying expansion at zero cross-helicity
8.1.2 Varying expansion at large cross-helicity
8.2 Systematic comparison of zero vs large cross helicity
8.2.1 ISO
8.2.2 GYRO
8.2.3 Gyro-Alfvén model
9 Discussion
9.1 Summary
9.2 Explaining the discrepancy with VG16
III Can the Maltese Cross heat? 
10 1D turbulent heating
10.1 1D HD equations with expansion
10.1.1 Modified Burgers equation and semi-analytical solutions
10.2 Simulations of shock turbulence with transverse waves
10.2.1 Initial conditions
10.2.2 Results
10.3 Discussion
11 Paper ApJ 2018: « Turbulent Heating between 0.2 and 1 au: A Numerical Study »
12 Heating fast winds
12.1 Initial conditions
12.2 Results
12.2.1 Spectral anisotropy with Mach=1
12.2.2 Turbulent heating
13 Discussion
Numerical parameters vs Helios data
IV Conclusions and future work 
14 Conclusions
14.1 Obtention of Maltese Cross components at 1AU
14.2 Can the Maltese Cross heat the solar wind?
14.3 Expectations from Solar Orbiter and Parker Solar Probe
14.4 Open questions and (partial) answers
15 Future work: Anisotropy temperature description
A Liste of symbols
B Numerical method
B.1 Computation of spatial gradients
B.2 Time integration method