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Navier-Stokes Turbulence

Theory and Analysis

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  • Outlines fundamental difficulties and presents several approaches for their analysis and solution

  • Emphasizes mathematical treatment of turbulent flows and methods for their computation

  • Reinforces concepts presented with problems to illustrate the theory and to introduce particular examples of turbulent flows such as periodic pipe flow

  • Includes several versions of the Hopf equation derived in spatial/Eulerian and material/Lagrangean description

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  • ISBN: 978-3-030-31869-7
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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xl
  2. Introduction

    • Wolfgang Kollmann
    Pages 1-16
  3. Navier–Stokes Equations

    • Wolfgang Kollmann
    Pages 17-53
  4. Basic Properties of Turbulent Flows

    • Wolfgang Kollmann
    Pages 55-72
  5. Flow Domains and Bases

    • Wolfgang Kollmann
    Pages 73-91
  6. Phase and Test Function Spaces

    • Wolfgang Kollmann
    Pages 93-99
  7. Probability Measure and Characteristic Functional

    • Wolfgang Kollmann
    Pages 101-113
  8. Functional Differential Equations

    • Wolfgang Kollmann
    Pages 115-117
  9. Fdes for the Characteristic Functionals

    • Wolfgang Kollmann
    Pages 123-162
  10. Properties and Construction of Mappings

    • Wolfgang Kollmann
    Pages 203-216
  11. Integral Transforms and Spectra

    • Wolfgang Kollmann
    Pages 269-275
  12. Intermittency

    • Wolfgang Kollmann
    Pages 277-283
  13. Equilibrium Theory of Kolmogorov and Onsager

    • Wolfgang Kollmann
    Pages 285-293
  14. Homogeneous Turbulence

    • Wolfgang Kollmann
    Pages 295-297
  15. Length and Time Scales

    • Wolfgang Kollmann
    Pages 299-306

About this book

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.
  • Outlines fundamental difficulties and presents several approaches for their analysis and solution;
  • Emphasizes mathematical treatment of turbulent flows and methods for their computation;
  • Reinforces concepts presented with problems to illustrate the theory and to introduce particular examples of turbulent flows such as periodic pipe flow;
  • Includes several versions of the Hopf equation derived in spatial/Eulerian and material/Lagrangean description.

Keywords

  • Navier Stokes
  • Fluid dynamics
  • Characteristic functionals and the Hopf equations
  • Structure of turbulent shear flows
  • eddy
  • scales
  • intermittency
  • Wall bounded turbulent flows
  • turbulence
  • fluid- and aerodynamics

Authors and Affiliations

  • Department of Mechanical Engineering, University of California Davis, Davis, USA

    Wolfgang Kollmann

About the author

Dr. Wolfgang Kollmann is Professor, Emeritus in the Mechanical and Aerospace Engineering Department, University of California, Davis.

Bibliographic Information

Buying options

eBook
USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-31869-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 79.99
Price excludes VAT (USA)
Hardcover Book
USD 109.99
Price excludes VAT (USA)