This textbook presents a modern account of turbulence, which is ubiquitous in both cosmical and natural environments.
Elementary presentations of dynamical systems ideas, of probabilistic methods including the theory of large deviations, and of fractal geometry make this a self-contained textbook. The readership is first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering.
Preface; 1. Introduction; 2. Symmetries and conservation laws; 3. Why a probabilistic description of turbulence?; 4. Probabilistic tools: a survey; 5. Two experimental laws of fully developed turbulence; 6. The Kolmogorov 1941 theory; 7. Kolmogorov and Landau: the lack of universality; 8. Phenomenology of turbulence in the sense of Kolmogorov 1941; 9. Intermittency; 10. Further reading: a guided tour; References; Author index; Subject index.