This comprehensive textbook, based on the author's course taught at Cambridge University, combines maximum physical insight with an explanation of all necessary mathematical techniques. In spite of the intensive effort of mathematicians, physicists and other scientists, there are still profound difficulties in our attempt to understand these chaotic three (or two) dimensional processes. On the other hand, impressive progress has been made over the decades while some of the best minds of the last centuries from Taylor (and arguably even Leonardo da Vinci) to Landau, Kolmogoroff and others were devoted to the subject. The book mirrors all these achievements, and gives a lucid explanation of many aspects of the phenomenon in a carefully written text, full of instructive examples, interesting comments and excellent illustrations.
In Part I, the reader can find the classical picture of turbulence (together with historical remarks and a general overview of the ubiquitous nature of turbulence), equations of fluid mechanics, origins of turbulence, turbulent shear flows, simple closure models and the phenomenology of Taylor, Richardson and Kolmogoroff. Part II includes facts on homogeneous turbulence, numerical simulations, isotropic turbulence and the Fourier transform. Part III contains special topics, such as the influence of rotation, stratification, magnetic fields and two-dimensional turbulence. The book ends with appendices (Vector identities, isolated vortices, long range pressure forces in isotropic turbulence, Hankel transforms, etc.). To summarize, this is a very useful book addressed to a wide audience, a book on “one of the greatest unsolved problems of classical physics”, a phenomenon which is all around us.

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