05107nam a22005535i 4500 978-3-031-59578-3 DE-He213 20251030112058.0 cr nn 008mamaa 240525s2024 sz | s |||| 0|eng d 9783031595783 978-3-031-59578-3 10.1007/978-3-031-59578-3 doi QA808.2 PHD bicssc SCI065000 bisacsh PHD thema Kollmann, Wolfgang. author. aut http://id.loc.gov/vocabulary/relators/aut 77399 Navier-Stokes Turbulence [electronic resource] : Theory and Analysis / by Wolfgang Kollmann. 2nd ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XLV, 819 p. 163 illus., 122 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. . . Continuum mechanics. Fluid mechanics. Aerospace engineering. 66335 Astronautics. 66336 Soft condensed matter. 66723 Continuum Mechanics. Engineering Fluid Dynamics. Aerospace Technology and Astronautics. 66339 Soft and Granular Matter. 76980 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031595776 Printed edition: 9783031595790 Printed edition: 9783031595806 https://doi.org/10.1007/978-3-031-59578-3 ZDB-2-PHA ZDB-2-SXP 60110 60110