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Vorticity and Turbulence

  • Textbook
  • © 1994

Overview

Authors:
  1. Alexandre J. Chorin

    1. Department of Mathematics, University of California, Berkeley, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 103)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Alexandre J. Chorin
    Pages 1-4

  3. The Equations of Motion

    • Alexandre J. Chorin
    Pages 5-24

  4. Random Flow and Its Spectra

    • Alexandre J. Chorin
    Pages 25-48

  5. The Kolmogorov Theory

    • Alexandre J. Chorin
    Pages 49-65

  6. Equilibrium Flow in Spectral Variables and in Two Space Dimensions

    • Alexandre J. Chorin
    Pages 67-89

  7. Vortex Stretching

    • Alexandre J. Chorin
    Pages 91-111

  8. Polymers, Percolation, Renormalization

    • Alexandre J. Chorin
    Pages 113-134

  9. Vortex Equilibria in Three-Dimensional Space

    • Alexandre J. Chorin
    Pages 135-155

  10. Back Matter

    Pages 157-176
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Keywords

About this book

This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro­ duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.

Authors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Alexandre J. Chorin

Bibliographic Information

  • Book Title: Vorticity and Turbulence

  • Authors: Alexandre J. Chorin

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4419-8728-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94197-4Published: 24 June 1994

  • Softcover ISBN: 978-1-4612-6459-0Published: 04 December 2013

  • eBook ISBN: 978-1-4419-8728-0Published: 01 December 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: VIII, 176

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics, Statistics, general

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