Introduction.- Scope of the book.- Structure and contents of the second edition of the book.- Governing equations, from dynamics to statistics.- Background deterministic equations.- Briefs about statistical and probabilistic approaches.- Reynolds Stress tensor and related equations.- Anisotropy in physical space. Single-point correlations.- Spectral analysis, from random fields to two-point correlations. Local frame, helical modes.- Anisotropy for multipoint correlations.- A synthetic scheme of the closure problem: non-linearity and non-locality.- On the use of Lagrangian formalism.- Additional reminders: compressible turbulence description.- Navier-Stokes equations for compressible flows and shock jump conditions.- Introduction to modal decomposition of turbulent fluctuations.- Mean flow equations, Reynolds Stress Tensor and energy balance in compressible flows.- Incompressible homogeneous isotropic turbulence.- Observations and measures in forced and freely decaying turbulence.- Classical statistical analysis: energy cascade, local isotropy, usual characteristic scales.- Models for single-time and two-time energy spectra and velocity correlation functions.- Free decay theories: self-similarity, self-preservation, symmetries and invariants.- Recent results about decay regimes.- Reynolds Stress tensor and analysis of related equations.- Differential models for energy transfer.- Advanced analysis of energy transfers in Fourier space.- Pressure field: spectrum, scales and time evolution.- Topological analysis, coherent events and related dynamics.- Non-linear dynamics in the physical space.- What are the proper features of three-dimensional Navier-Stokes turbulence?.- Isotropic turbulence with coupled microstructures: Visco-elastic turbulence.- Introduction to turbulence in dilute polymer solutions.- Governing equations.- Description of turbulence with FENE-P model.- Turbulence régimes in dilute polymer solution.- Visco-elastic effects on flow topology.- Isotropic turbulence with coupled microstructures. Quantum Turbulence.- Introductory phenomenology to Quantum Turbulence.- The three levels of description and physical modelling.- Quantized vortices and Kelvin Waves: facts and models.- Quantum Turbulence dynamics at zero or nearly-zero temperature.- The decay of isotropic Quantum Turbulence.- Mutual friction: microscopic origin and models.- Incompressible homogeneous anisotropic turbulence: pure rotation.- Physical and numerical experiments.- Governing equation.- Advanced analysis of energy transfer via DNS.- Balance of RST equations. A case without "production". New tensorial modeling.- Inertial waves. Linear régime.- Nonlinear theory and modeling: Wave Turbulence and EDQNM.- Fundamental issues: solved and open questions.- Coherent structures, description and dynamics.- Scale-by-scale anisotropy.- Incompressible homogeneous anisotropic turbulence: With strain.- Main observations.- Experiments for turbulence in the presence of mean strain. Kinematics of the mean flow.- First approach in physical space to irrotational mean flows.- The fundamentals of homogeneous RDT.- Final RDT results for mean irrotational strain.- Towards a fully nonlinear approach.- Return to isotropy.- Nonhomogeneous flow cases. Coherent structures in strained homogeneous turbulence .- Incompressible homogeneous anisotropic turbulence: pure shear.- Physical and numerical experiments: kinetic energy, RST, lengthscales, anisotropy.- Reynolds Stress tensor and analysis of related equations.- Rapid Distortion Theory: equations, solutions, algebraic growth.- Nonlinear spectral analysis, simplified closure and selfsimilarity.- Return to isotropy in shear-released homogeneous turbulence.-Models for space- and space-time correlations.- Pressure field: theory and models.- Vortical structures dynamics in homogeneous shear turbulence.- Self-sustaining turbulent cycle in quasi-homogeneous sheared turbulence.- Self-sustaining processes in non-homogeneous sheared turbulence: exact coherent states and travelling wave solutions.- Incompressible homogeneous anisotropic turbulence: buoyancy force and mean stratification.- Observations, propagating and non-propagating motion. Collapse of vertical motion and layering.- Simplified equations, using Navier-Stokes and Boussinesq approximations, with uniform density gradient.- Eigenmode decomposition. Physical interpretation.- The toroidal cascade as a strong nonlinear mechanism explaining the layering.- The viewpoint of modelling and theory: RDT, Wave-Turbulence, EDQNM.- Coherent structures : dynamics and scaling of the layered flow, "pancake" dynamics, instabilities.- Unstable Stratified Homogeneous Turbulence.- Extension to the mixing zone resulting from Rayleigh-Taylor instability and beyond.- Coupled effects : rotation, stratification, strain and shear.- Governing equations for the dynamics of coupled effects.- Rotating stratified turbulence.- Rotation or stratification with mean shear.- Shear, rotation and stratification. Approach to baroclinic instability.- The elliptical flow instability from \homogeneous" RDT.- Axisymmetric strain with rotation.- Relevance of RDT and WKB RDT variants for analysis of transient growth and exponential instabilities.- Incompressible homogeneous anisotropic turbulence: Magnetohydrodynamic turbulence.- Generalities, analogies and differences with respect to the purely hydrodynamic case.- Governing equations.- Alfvén waves and Ohmic damping. Linear régime.- The Quasi-Static régime, from linear to nonlinear dynamics.- A first statistical approach, Kolmogorov-Monin laws, without mean magnetic field.- Refined analysis: Triadic interactions in MHD without mean magnetic field.- MHD turbulence and interactions with other body forces and mean gradients.- Homogeneous incompressible MHD turbulence and beyond.- Compressible homogeneous isotropic turbulence.- Different régimes in compressible turbulence.- Structures in the physical space.- Compressible homogeneous isotropic turbulence.- Different regimes in compressible turbulence.- Quasi-isentropic turbulent regime.- Low-Mach thermal regimes.- Nonlinear subsonic regimes.- Supersonic regime.- Structures in the physical space.- Compressible homogeneous anisotropic turbulence.- Effects of compressibility in free shear flows. Observations.- A general quasi-isentropic approach to homogeneous compressible shear flows.- Incompressible turbulence with compressible mean flow effects: compressed turbulence.- Compressible turbulence in the presence of pure plane shear.- Perspectives and open issues.- Topological analysis, coherent events and related dynamics.- Canonical isotropic turbulence/shock interaction and beyond.- Brief survey of existing interaction regimes.- Wrinkled shock régime: Linear interaction.- Wrinkled shock régime: Nonlinear interaction.- Broken shock régime.- Beyond canonical case. I: Spherical shock waves.- Beyond canonical case. II: Planar shock interacting with turbulence in a non-reacting binary mixture.- Beyond canonical case. III: Planar detonation interacting with turbulence.- Linear Interaction Approximation for shock/perturbation interaction.- Shock description and emitted fluctuating field.- Calculation of wave vectors of emitted waves.- Calculation of amplitude of emitted waves.- Distinguishing between poloidal and toroidal vorticity modes.- Reconstruction of the second order moments.- Further analytical work: exact and asymptotic LIA solutions based on Laplace transform.- A posteriori assessment of LIA in the canonical interaction case.- Extending LIA: I. Interaction with rarefaction waves.- Extending LIA: II. Case of non-reacting binary mixtures of perfect gas.- Extending LIA: III. Thin strong detonation/turbulence interaction.- The essentials of linear and nonlinear theories and models.- Rapid Distortion Theory for homogeneous turbulence.- Zonal RDT and short-wave stability analysis.- Application to statistical modeling of inhomogeneous turbulence.- Other perspectives in extended linearized approaches.- Generalities on triadic closures.- Solving the linear operator to account for strong anisotropy.- A general EDQN closure. Different levels of markovianization.- Detailed equations from EDQNM1 in the model by Mons, Cambon and Sagaut.- Application of three EDQNM(1-2-3) versions to the rotating turbulence.- Other cases of flows with and without production.- Connection with self-consistent theories: single-time or two-time?.- Applications to weak or moderate anisotropy.- Open numerical problems.- Conclusions and perspectives.- Homogenization of turbulence. Local or global homogeneity? Physical space or Fourier space?.- Linear theory, `homogeneous' RDT, WKB variants, and LIA.- Multi-point closures for weak and strong turbulence.- Structure formation, structuring effects and individual coherent structures.- Anisotropy including dimensionality, a main theme.- Deriving practical models.- Bibliography.- Index.
