Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial to know the details of these laws, so that mathematical models can be properly formulated and analysed, and the phenomena in question can be more deeply understood. In this 2003 book, the author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural attributes of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.
G. I. Barenblatt is Emeritus G. I. Taylor Professor of Fluid Mechanics at the University of Cambridge, Emeritus Professor at the University of California, Berkeley, and Principal Scientist in the Institute of Oceanology of the Russian Academy of Sciences, Moscow.
Foreword; Introduction; 1. Dimensional analysis and physical similarity; 2. Self-similarity and intermediate asymptotics; 3. Scaling laws and self-similar solutions which cannot be obtained by dimensional analysis; 4. Complete and incomplete similarity; 5. Scaling and transformation groups and the renormalisation group; 6. Self-similar solutions and traveling waves; 7. Scaling laws and fractals; 8. Scaling laws for turbulent wall-bounded shear flows at very large Reynolds numbers; References; Index.