Navier-Stokes Turbulence: Theory and Analysis

Description

The book serves as a core text for graduate courses in advanced fluid mechanics and applied science. It consists 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. Subsequent chapters are devoted to mapping methods, homogeneous turbulence based upon the hypotheses of Kolmogorov and Onsager, intermittency, structural features of turbulent shear flows and their recognition. Front Matter ....Pages i-xl Introduction (Wolfgang Kollmann)....Pages 1-16 Navier–Stokes Equations (Wolfgang Kollmann)....Pages 17-53 Basic Properties of Turbulent Flows (Wolfgang Kollmann)....Pages 55-72 Flow Domains and Bases (Wolfgang Kollmann)....Pages 73-91 Phase and Test Function Spaces (Wolfgang Kollmann)....Pages 93-99 Probability Measure and Characteristic Functional (Wolfgang Kollmann)....Pages 101-113 Functional Differential Equations (Wolfgang Kollmann)....Pages 115-117 Characteristic Functionals for Incompressible Turbulent Flows (Wolfgang Kollmann)....Pages 119-121 Fdes for the Characteristic Functionals (Wolfgang Kollmann)....Pages 123-162 Solution of Hopf-Type Equations in the Spatial Description (Wolfgang Kollmann)....Pages 163-177 Finite-Dimensional Characteristic Functions, Pdfs and Cdfs Based on the Dirac Distribution (Wolfgang Kollmann)....Pages 179-201 Properties and Construction of Mappings (Wolfgang Kollmann)....Pages 203-216 \(\mathcal{M}_1(1)\): Single Scalar in Homogeneous Turbulence (Wolfgang Kollmann)....Pages 217-247 \(\mathcal{M}_1(N)\): Mappings for Velocity–Scalar and Position–Scalar Pdfs (Wolfgang Kollmann)....Pages 249-267 Integral Transforms and Spectra (Wolfgang Kollmann)....Pages 269-275 Intermittency (Wolfgang Kollmann)....Pages 277-283 Equilibrium Theory of Kolmogorov and Onsager (Wolfgang Kollmann)....Pages 285-293 Homogeneous Turbulence (Wolfgang Kollmann)....Pages 295-297 Length and Time Scales (Wolfgang Kollmann)....Pages 299-306 The Structure of Turbulent Flows (Wolfgang Kollmann)....Pages 307-332 Wall-Bounded Turbulent Flows (Wolfgang Kollmann)....Pages 333-357 The Limit of Infinite Reynolds Number for Incompressible Fluids (Wolfgang Kollmann)....Pages 359-380 Appendix A: Mathematical Tools (Wolfgang Kollmann)....Pages 381-446 Appendix B: Example for a Measure on a Ball in Hilbert Space (Wolfgang Kollmann)....Pages 447-449 Appendix C: Scalar and Vector Bases for Periodic Pipe Flow (Wolfgang Kollmann)....Pages 451-506 Appendix D: Green’s Function for Periodic Pipe Flow (Wolfgang Kollmann)....Pages 507-539 Appendix E: Semi-empirical Treatment of Simple Wall-Bounded Flows (Wolfgang Kollmann)....Pages 541-558 Appendix F: Solutions to Problems (Wolfgang Kollmann)....Pages 559-711 Back Matter ....Pages 713-725