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Table of contents
1 Introduction
1.1 General interest
1.2 Turbulence in space and astrophysical plasmas
1.3 An outline of my thesis
2 Compressibilityinfluids
2.1 What is compressibility ?
2.2 Measure of compressibility for a fluid in motion
2.3 Closure for compressible fluids
2.4 Invariants in compressible barotropic fluid
2.4.1 Total energy
2.4.2 Kinetic helicity
2.4.3 Mass and linear momentum
2.5 Potential flow
2.6 Two dimensional compressible flow
2.7 One dimensional model for discontinuous compressible flow: Burgers’ equation
2.8 Compressibility ratio for a polytropic gas across a normal shock
2.9 Baroclinic vector
3 Plasmaphysics andmagnetohydrodynamics
3.1 What is a plasma ?
3.2 Two approaches to plasma
3.2.1 Kinetic approach
3.2.2 Fluid approach
3.3 Magnetohydrodynamics (MHD)
3.3.1 Mono-fluid model: Basic equations of MHD
3.3.2 Ideal MHD approximation from generalized Ohm’s law
3.3.3 Linear waves in ideal MHD
3.3.4 Invariants of ideal MHD
3.3.5 Elsässer variables in magnetohydrodynamics
4 Turbulentflow: importantnotions
4.1 Turbulence – A phenomenon or a theory ?
4.2 Turbulent regime from Navier-Stokes : Reynolds number
4.3 Chaos and/or turbulence ?
4.4 Basic assumptions
4.4.1 Statistical homogeneity
4.4.2 Statistical isotropy
4.4.3 Stationary state
4.5 Two approaches to turbulence
4.5.1 Statistical approach
4.5.2 Spectral approach
4.6 Phenomenology
4.6.1 K41 phenomenology
4.6.2 IK phenomenology
4.6.3 Utilities of phenomenology
4.7 Dynamics and energetics of turbulence
4.7.1 Turbulent forcing
4.7.2 Turbulent cascade
4.7.3 Turbulent dissipation
4.8 Intermittency
4.8.1 ! fractal model
4.8.2 Refined similarity hypothesis : Log-Normal model
4.8.3 Log-Poisson model
4.8.4 Extended self-similarity
5 Turbulence incompressiblefluids
5.1 Why is it important ?
5.2 Primitive theoretical approaches
5.3 Numerical approaches using one dimensional model
5.4 Numerical Simulations in higher dimensions
5.4.1 Numerical methods for compressible turbulence
5.4.2 Piecewise Parabolic Method (PPM)
5.4.3 Compressible intermittency
5.4.4 Compressible and solenoidal forcing
5.4.5 Choice of inertial zone and sonic scale
5.4.6 Two-point closure in EDQNM model for compressible turbulence
5.5 Observational studies
6 Exact relations inturbulence
6.1 Exact relations in incompressible turbulence
6.1.1 Incompressible hydrodynamic turbulence
6.1.2 Incompressible MHD turbulence
6.2 Previous attempts for exact relations in compressible turbulence
6.2.1 Heuristic approach by Carbone et al. (2009)
6.2.2 FFO approach for a generalized exact equation
6.3 New exact relations and phenomenologies in compressible turbulence : My research work
6.3.1 Isothermal hydrodynamic turbulence
6.3.2 A new phenomenology for compressible turbulence
6.3.3 Isothermal MHD turbulence
6.3.4 Polytropic hydrodynamic turbulence
7 Solarwinddata analysis
7.1 Introduction
7.2 The solar wind
7.2.1 The heliosphere
7.2.2 Prediction for the solar wind
7.2.3 The fast and the slow solar wind
7.2.4 Exploration of the solar wind
7.2.5 MHD fluctuations in the solar wind
7.2.6 Nature of the solar wind turbulence
7.3 Data source
7.3.1 The THEMIS mission
7.3.2 A brief description of instruments
7.4 Judicial selection of data
7.4.1 Selection of intervals
7.4.2 Relevant spatial and temporal scales
7.5 Analysis of the selected data
8 Resuming andlooking ahead.
8.1 Answered and unanswered issues of compressible turbulence
8.2 Some future projects
References
