## Turbulence in fluids : stochastic and numerical modelling

by Marcel Lesieur

[目次]

• I Introduction to turbulence in fluid mechanics.- 1 Is it possible to define turbulence?.- 2 Examples of turbulent flows.- 3 Fully developed turbulence.- 4 Fluid turbulence and "chaos".- 5 "Deterministic" and statistical approaches.- 6 Why study isotropic turbulence?.- 7 One-point closure modelling.- 8 Outline of the following chapters.- II Basic fluid dynamics.- 1 Eulerian notation and Lagrangian derivatives.- 2 The continuity equation.- 3 The conservation of momentum.- 4 The thermodynamic equation.- 5 The incompressibility assumption.- 6 The dynamics of vorticity.- 7 The generalized Kelvin theorem.- 8 The Boussinesq approximation.- 9 Internal inertial-gravity waves.- 10 Barre de Saint-Venant equations.- 2.10.1 Derivation of the equations.- 2.10.2 The potential vorticity.- 2.10.3 Inertial-gravity waves.- 2.10.3.1 Analogy with two-dimensional compressible gas.- 11 Gravity waves in a fluid of arbitrary depth.- III Transition to turbulence.- 1 The Reynolds number.- 2 Linear-instability theory.- 3.2.1 The Orr-Sommerfeld equation.- 3.2.2 The Rayleigh equation.- 3.2.2.1 Kuo equation.- 3 Transition in shear flows.- 3.3.1 Free-shear flows.- 3.3.1.1 Mixing layers.- 3.3.1.2 Mixing layer with differential rotation.- 3.3.1.3 Plane jets and wakes.- 3.3.2 Wall flows.- 3.3.2.1 The boundary layer.- 3.3.2.2 Poiseuille flow.- 3.3.3 Transition, coherent structures and Kolmogorov spectra.- 3.3.3.1 Linear stability of a vortex filament within a shear.- 3.3.4 Compressible turbulence.- 3.3.4.1 Compressible mixing layer.- 3.3.4.2 Compressible wake.- 3.3.4.3 Compressible boundary layer.- 4 The Rayleigh number.- 5 The Rossby number.- 3.5.1 Quasi-two-dimensional flow submitted to rotation.- 3.5.1.1 Linear analysis.- 3.5.1.2 The straining of absolute vorticity.- 6 The Froude Number.- 7 Turbulence, order and chaos.- IV The Fourier space.- 1 Fourier representation of a flow.- 4.1.1 Flow "within a box":.- 4.1.2 Integral Fourier representation.- 2 Navier-Stokes equations in Fourier space.- 3 Boussinesq approximation in the Fourier space.- 4 Craya decomposition.- 5 Complex helical waves decomposition.- V Kinematics of homogeneous turbulence.- 1 Utilization of random functions.- 2 Moments of the velocity field, homogeneity and stationarity.- 3 Isotropy.- 4 The spectral tensor of an isotropic turbulence.- 5 Energy, helicity, enstrophy and scalar spectra.- 6 Alternative expressions of the spectral tensor.- 7 Axisymmetric turbulence.- VI Phenomenological theories.- 1 Inhomogeneous turbulence.- 6.1.1 The mixing-length theory.- 6.1.2 Application of mixing-length to turbulent-shear flows.- 6.1.2.1 The plane jet.- 6.1.2.2 The round jet.- 6.1.2.3 The plane wake.- 6.1.2.4 The round wake.- 6.1.2.5 The plane mixing layer.- 6.1.2.6 The boundary layer.- 2 Triad interactions and detailed conservation.- 6.2.1 Quadratic invariants in physical space.- 6.2.1.1 Kinetic energy.- 6.2.1.2 Helicity.- 6.2.1.3 Passive scalar.- 3 Transfer and Flux.- 4 The Kolmogorov theory.- 6.4.1 Oboukhov's theory.- 5 The Richardson law.- 6 Characteristic scales of turbulence.- 6.6.1 The degrees of freedom of turbulence.- 6.6.1.1 The dimension of the attractor.- 6.6.2 The Taylor microscale.- 6.6.3 Self-similar decay.- 7 Skewness factor and enstrophy divergence.- 6.7.1 The skewness factor.- 6.7.2 Does enstrophy blow up at a finite time?.- 6.7.2.1 The constant skewness model.- 6.7.2.2 Positiveness of the skewness.- 6.7.2.3 Enstrophy blow up theorem.- 6.7.2.4 A self-similar model.- 6.7.2.5 Oboukhov's enstrophy blow up model.- 6.7.2.6 Discussion.- 6.7.3 The viscous case.- 8 The internal intermittency.- 6.8.1 The Kolmogorov-Oboukhov-Yaglom theory.- 6.8.2 The Novikov-Stewart (1964) model.- 6.8.3 Experimental and numerical results.- 6.8.4 Temperature and velocity intermittency.- VII Analytical theories and stochastic models.- 1 Introduction.- 2 The Quasi-Normal approximation.- 3 The Eddy-Damped Quasi-Normal type theories.- 4 The stochastic models.- 5 Phenomenology of the closures.- 6 Numerical resolution of the closure equations.- 7 The enstrophy divergence and energy catastrophe.- 8 The Burgers-M.R.C.M. model.- 9 Isotropic helical turbulence.- 10 The decay of kinetic energy.- 11 The Renormalization-Group techniques.- 7.11.1 The R.N.G. algebra.- 7.11.2 Two-point closure and R.N.G. techniques.- 7.11.2.1 The k-5/3 range.- 7.11.2.2 The infrared spectrum.- VIII Diffusion of passive scalars.- 1 Introduction.- 2 Phenomenology of the homogeneous passive scalar diffusion.- 8.2.1 The inertial-convective range.- 8.2.2 The inertial-conductive range.- 8.2.3 The viscous-convective range.- 3 The E.D.Q.N.M. isotropic passive scalar.- 8.3.1 A simplified E.D.Q.N.M. model.- 8.3.2 E.D.Q.N.M. scalar-enstrophy blow up.- 4 The decay of temperature fluctuations.- 8.4.1 Phenomenology.- 8.4.1.1 Non-local interactions theory.- 8.4.1.2 Self-similar decay.- 8.4.1.3 Anomalous temperature decay.- 8.4.2 Experimental temperature decay data.- 8.4.3 Discussion of the L.E.S. results.- 8.4.4 Diffusion in stationary turbulence.- 5 Lagrangian particle pair dispersion.- 6 Single-particle diffusion.- 8.6.1 Taylor's diffusion law.- 8.6.2 E.D.Q.N.M. approach to single-particle diffusion.- IX Two-dimensional and quasi-geostrophic turbulence.- 1 Introduction.- 2 The quasi-geostrophic theory.- 9.2.1 The geostrophic approximation.- 9.2.2 The quasi-geostrophic potential vorticity equation.- 9.2.3 The n-layer quasi-geostrophic model.- 9.2.4 Interaction with an Ekman layer.- 9.2.4.1 Geostrophic flow above an Ekman layer.- 9.2.4.2 The upper Ekman layer.- 9.2.5 Barotropic and baroclinic waves.- 3 Two-dimensional isotropic turbulence.- 9.3.1 Fjortoft's theorem.- 9.3.2 The enstrophy cascade.- 9.3.3 The inverse energy cascade.- 9.3.4 The two-dimensional E.D.Q.N.M. model.- 9.3.5 Freely-decaying turbulence.- 4 Diffusion of a passive scalar.- 5 Geostrophic turbulence.- 9.5.1 Rapidly-rotating stratified fluid of arbitrary depth.- X Absolute equilibrium ensembles.- 1 Truncated Euler Equations.- 2 Liouville's theorem in the phase space.- 3 The application to two-dimensional turbulence.- 4 Two-dimensional turbulence over topography.- XI The statistical predictability theory.- 1 Introduction.- 2 The E.D.Q.N.M. predictability equations.- 3 Predictability of three-dimensional turbulence.- 4 Predictability of two-dimensional turbulence.- XII Large-eddy simulations.- 1 The direct-numerical simulation of turbulence.- 2 The Large Eddy Simulations.- 12.2.1 Large and subgrid scales.- 12.2.2 L.E.S. and the predictability problem.- 3 The Smagorinsky model.- 4 L.E.S. of 3-D isotropic turbulence.- 12.4.1 Spectral eddy-viscosity and diffusivity.- 12.4.2 Spectral large-eddy simulations.- 12.4.3 The anomalous spectral eddy-diffusivity.- 12.4.4 Alternative approaches.- 12.4.5 A local formulation of the spectral eddy-viscosity.- 5 L.E.S. of two-dimensional turbulence.- XIII Towards real-world turbulence.- 1 Introduction.- 2 Stably-stratified turbulence.- 13.2.1 The so-called "collapse" problem.- 13.2.2 A numerical approach to the collapse.- 3 The two-dimensional mixing layer.- 13.3.1 Generalities.- 13.3.2 Two-dimensional turbidence in the mixing layer.- 13.3.3 Two-dimensional unpredictability.- 13.3.4 Two-dimensional unpredictability and 3D growth.- 4 3D numerical simulations of the mixing layer.- 13.4.1 Direct-numerical simulations.- 13.4.2 Large-eddy simulations of mixing layers.- 13.4.3 Recreation of the coherent structures.- 13.4.4 Rotating mixing layers.- 5 Conclusion.

「Nielsen BookData」より

書名 Turbulence in fluids : stochastic and numerical modelling Lesieur, Marcel Fluid mechanics and its applications Kluwer Academic Publishers c1990 2nd rev. ed xv, 412 p. 25 cm 9789401067263 BA11411485 ※クリックでCiNii Booksを表示 英語 オランダ
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