SpringerBriefs in Mathematics

The Kolmogorov-Obukhov Theory of Turbulence

A Mathematical Theory of Turbulence

Authors: Birnir, Bjorn

  • ​​​This book presents the first mathematical theory of fully-developed turbulence
  • Shows  the stochastic Navier-Stokes Equation is the appropriate model and the statistical theory of this equation is developed
  • Proves the Kolmogorov-Obukhov statistical theory of turbulence with the correct intermittency corrections
  • Probability distribution functions of velocity differences of turbulent fluids are found and compared with simulations and experiments​
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eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-6262-0
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Softcover $49.95
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  • ISBN 978-1-4614-6261-3
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About this book

​​​​​​​Turbulence is a major problem facing modern societies. It makes airline passengers return to their seats and fasten their seatbelts but it also creates drag on the aircraft that causes it to use more fuel and create more pollution. The same applies to cars, ships and the space shuttle. The mathematical theory of turbulence has been an unsolved problems for 500 years and the development of the statistical theory of the Navier-Stokes equations describes turbulent flow has been an open problem. The Kolmogorov-Obukhov Theory of Turbulence develops a statistical theory of turbulence from the stochastic Navier-Stokes equation and the physical theory, that was proposed by Kolmogorov and Obukhov in 1941. The statistical theory of turbulence shows that the noise in developed turbulence is a general form which can be used to present a mathematical model for the stochastic Navier-Stokes equation. The statistical theory of the stochastic Navier-Stokes equation is developed in a pedagogical manner and shown to imply the Kolmogorov-Obukhov statistical theory. This book looks at a new mathematical theory in turbulence which may lead to many new developments in vorticity and Lagrangian turbulence. But even more importantly it may produce a systematic way of improving direct Navier-Stokes simulations and lead to a major jump in the technology both preventing and utilizing turbulence.

Table of contents (4 chapters)

  • The Mathematical Formulation of Fully Developed Turbulence

    Birnir, Björn

    Pages 1-34

  • Probability and the Statistical Theory of Turbulence

    Birnir, Björn

    Pages 35-54

  • The Invariant Measure and the Probability Density Function

    Birnir, Björn

    Pages 55-73

  • Existence Theory of Swirling Flow

    Birnir, Björn

    Pages 75-88

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-6262-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-6261-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Kolmogorov-Obukhov Theory of Turbulence
Book Subtitle
A Mathematical Theory of Turbulence
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Björn Birnir
eBook ISBN
978-1-4614-6262-0
DOI
10.1007/978-1-4614-6262-0
Softcover ISBN
978-1-4614-6261-3
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 108
Number of Illustrations and Tables
11 illustrations in colour
Topics