Vorticity and Turbulence

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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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.

• applied mathematics
• mechanics
• statistical mechanics
• statistical theory
• turbulence

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

  Alexandre J. Chorin

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