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From the back cover: "Many phenomena in nature, engineering or society when seen at an appropriate—intermediate—distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as the scale changes. This property leads to great simplification of the relations that govern a phenomenon, revealed through so-called scaling laws. It is crucial to know the nature of these laws, so that mathematical models can be properly formulated and analyzed and the phenomenon in question can be more deeply understood.
"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 concept of intermediate asymptotics and the renormalization 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. By considering examples of various degrees of complexity, the development spirals to a conclusion. General ideas are illustrated in a final chapter that describes in detail the structure of an important class of turbulent flows and explains why controversies surrounding them can be attributed to an inadequate understanding of the use of scaling. This book aims to rectify such inadequacies; it is based on courses taught to undergraduate and graduate students but can also be used for self-study by biologists, chemists, physicists, astronomers, engineers and geoscientists."
BRIEF CONTENTS
Foreword by A. J. Chorin
Preface
Introduction
Chapter 1. Dimensional analysis and physical similarity
Chapter 2. Self-similarity and intermediate asymptotics
Chapter 3. Scaling laws and self-similar solutions that cannot be obtained by dimensional analysis
Chapter 4. Complete and incomplete similarity. Self-similar solutions of the first and second kind
Chapter 5. Scaling and transformation groups. Renormalization group
Chapter 6. Self-similar phenomena and travelling waves
Chapter 7. Scaling laws and fractals
Chapter 8. Scaling laws for turbulent wall-bounded shear flows at very large Reynolds numbers
