Navier-Stokes Turbulence

Introduction.- Navier-Stokes equations.- Basic properties of turbulent flows.- Flow domains and bases.- Phase and test function spaces.- Probability measure and characteristic functional.- Functional differential equations.- Characteristic functionals for incompressible turbulent flows.- Fdes for the characteristic functionals.- Solution of Hopf type equations in the spatial description.- The role of the pressure .- Properties and construction of Mappings.- M(): Single scalar in homogeneous turbulence.- M(N): Mappings for velocity-scalar and position-scalar Pdfs.- Integral transforms and spectra.- Intermittency.- Equilibrium theory of Kolmogorov and Onsager.- Homogeneous turbulence.- Length and time scales.- The structure of turbulent ows.- Wall-bounded turbulent ows.- The limit of in_nite Reynolds number for incompressible uids.- Appendix A: Mathematical tools.- Appendix B: Example for a measure on a ball in Hilbert space.- Appendix C: Scalar and vector bases for periodic pipe ow.- Modi_ed Jacobi polynomials Pa;b.- n (r).- Orthonormalisation of the modi_ed polynomials Pa;b.- n (r).- Test function space Np: Scalar _elds.- (i) Bases for the test function space Np.- Function spaces: Vector _elds.- (i) Construction of a general vector basis.- (ii) Construction of a solenoidal vector basis.- Gram-Schmidt orthonormalisation.- Appendix D: Green's function for periodic pipe ow.- .- Leray version of the Navier-Stokes pdes.- Appendix E: Semi-empirical treatment of simple wall-bounded ows.- Appendix F: Solutions to problems.- Bibliography.