Turbulence in Fluids Stochastic and Numerical Modelling [Paperback]

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 Barr? 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.- 4.1.1 flow within a box:.- 4.1.2 Integral Fourier representation.- 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.- 6.8.1 The Kolmogorov-Oboukhov-Yaglom theory.- 6.8.2 The Novikov-Stewart model.- 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 resoll#[