The Physics of Fluid Turbulence

Since 1960 the study of turbulence has been enhanced by developments in areas such as laser anemometry, powerful computers, digital data processing and theoretical methods from quantum physics. Turbulence is the archetypal non-linear, non-equilibrium problem of statistical physics; the fundamental problems of turbulence are still unsolved, but there is a growing interest in their solution. This book aims to look at fluid turbulence from the point of view of engineering science and physics to produce an integrated treatise on the nature of the physics of fluid turbulence as a universal phenomenon with a universal behaviour. It is designed for those who are new to the subject and also for those familiar with the more traditional branches of the study of turbulence but not with the usages of quantum physics. For the first group of readers, a concise summary of the theory and practice of turbulence up to about 1960 is given as an introduction. This is followed by a detailed analysis of modern (post 1960) turbulence theory, including rigorous formulation of the turbulence problem as an example of a non-equilibrium statistical system with strong coupling and the application of renormalized perturbation theory to turbulence.

1. The semi-empirical picture of turbulent shear flow; 2. The fundamental approach; 3. Some recent developments in the study of turbulence; 4. Statistical formulation of the general problem; 5. Renormalized perturbation theory and the turbulence closure problem; 6. Renormalized perturbation theories of the first kind; 7. Renormalized perturbation theories of the second kind; 8. An assessment of renormalized perturbation theories; 9. Renormalization group theories; 10. Numerical simulation of turbulence; 11. Coherent structures; 12. Turbulent diffusion: the Lagrangian picture; 13. Turbulent diffusion: the Eulerian picture; 14. Non-Newtonian fluid turbulence; 15. Appendices