Homogeneous turbulence dynamics

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