Turbulence in Fluids

• 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?.- 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 equations.- 9 Internal inertial-gravity waves.- 10 Barré de Saint-Venant equations.- III Transition to turbulence.- 1 The Reynolds number.- 2 The Rayleigh number.- 3 The Rossby number.- 4 The Froude Number.- 5 Turbulence, order and chaos.- IV The Fourier space.- 1 Fourier representation of a flow.- 2 Navier-Stokes equations in Fourier space.- 3 Boussinesq equations 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 The closure problem of turbulence.- 2 Karman-Howarth equations in Fourier space.- 3 Transfer and Flux.- 4 The Kolmogorov theory.- 5 The Richardson law.- 6 Characteristic scales of turbulence.- 7 The skewness factor.- 8 The internal intermittency.- VII Analytical theories and stochastic models.- 1 Introduction.- 2 The Quasi-Normal approximation.- 3 The Eddy-Damped Quasi-Normal type theories.- 4 The stochasticmodels.- 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 E.D.Q.N.M. and R.N.G. techniques.- VIII Diffusion of passive scalars.- 1 Introduction.- 2 Phenomenology of the homogeneous passive scalar diffusion.- 3 The E.D.Q.N.M. isotropic passive scalar.- 4 The decay of temperature fluctuations.- 5 Lagrangian particle pair dispersion.- IX Two-dimensional and quasi-geostrophic turbulence.- 1 Introduction.- 2 The quasi-geostrophic theory.- 3 Two-dimensional isotropic turbulence.- 4 Diffusion of a passive scalar.- 5 Geostrophic turbulence.- 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.- 3 L.E.S. of 3-D isotropic turbulence.- 4 L.E.S. of two-dimensional turbulence.- XIII Towards “real world turbulence”.- 1 Introduction.- 2 Stably Stratified Turbulence.- 3 The Mixing Layer.- 4 Conclusion.- References.

'Turbulence in Fluids will serve as a graduate-text to follow up... ' Pageoph 'The book that Professor Lesieur has written on turbulence is an irreplaceable subject. Lesieur's work mixes rigor and intuition. ... it is the spirit in which it is written that is striking. Moreover the book is attractively presented. At the present time is seems difficult to ignore this book which fits very well into the collection of classical works on the subject.' Prof. J. Mathieu, Laboratoire de Mecanique des Fluides et d'Acoustique 'The book is attractively produced ... some beautiful photographs ... this is an interesting and attractive book. Everyone interested in the more theoretical aspects of turbulence will want to read it. ' D.C. Leslie in Journal of Fluid Mechanics, 194 ' .. a useful text for a first course in turbulence for physicists, or as a second course for engineering students who have already had a more phenomenological introduction to the subject. It is a useful reference for the specialist who may not keep at his fingertips some of the details of the analytical theories and stochastic models. ' AIAA Journal, 26:10