Homogeneous Turbulence Dynamics

• Main Authors: Sagaut, Pierre (Author, http://id.loc.gov/vocabulary/relators/aut), Cambon, Claude (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Subjects: Fluids.; Mathematical physics.; Fluid mechanics.; Applied mathematics.; Engineering mathematics.; Fluid- and Aerodynamics.; Mathematical Applications in the Physical Sciences.; Engineering Fluid Dynamics.; Theoretical, Mathematical and Computational Physics.; Mathematical Physics.; Mathematical and Computational Engineering.

This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence  and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (s...

Table of Contents:

• 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.