Theory and Analysis Kollmann, Wolfgang. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 2nd ed. 2024. monographic eng

electronic

electronic resource

access XLV, 819 p. 163 illus., 122 illus. in color. online resource. This updated/augmented second edition retains it class-tested content and pedagogy as a core text for graduate courses in advanced fluid mechanics and applied science. The new edition adds revised sections, clarification, problems, and chapter extensions including a rewritten section on Schauder bases for turbulent pipe flow, coverage of Cantwell’s mixing length closure for turbulent pipe flow, and a section on the variational Hessian. Consisting of two parts, the first provides an introduction and general theory of fully developed turbulence, where treatment of turbulence is based on the linear functional equation derived by E. Hopf governing the characteristic functional that determines the statistical properties of a turbulent flow. In this section, Professor Kollmann explains how the theory is built on divergence free Schauder bases for the phase space of the turbulent flow and the space of argument vector fields for the characteristic functional. The second segment, presented over subsequent chapters, is devoted to mapping methods, homogeneous turbulence based upon the hypotheses of Kolmogorov and Onsager, intermittency, structural features of turbulent shear flows and their recognition. Adds section on Plancherel’s theorem and a detailed problem on analytic solution of functional differential equations; Extends chapter nine on characteristic functionals to greater explain the role of convection; Reinforces concepts with problems on the theory and particular examples of turbulent flows such as periodic pipe flow. . . 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. by Wolfgang Kollmann. Continuum mechanics Fluid mechanics Aerospace engineering Astronautics Soft condensed matter Continuum Mechanics Engineering Fluid Dynamics Aerospace Technology and Astronautics Soft and Granular Matter QA808.2 9783031595783 https://doi.org/10.1007/978-3-031-59578-3 https://doi.org/10.1007/978-3-031-59578-3 240525 20251030112058.0 978-3-031-59578-3