AN INTRODUCTION TO TURBULENT FLOW
J. Mathieu and J. Scott, Cambridge University Press, 2000, pp: 368, ISBN 0-521-77538-8 (pbk), 57066-2 (hc); Price: $39.95 (pbk), $90.00 (hc)

Turbulent flow, its causes and development, has been a subject of serious investigation for mathematicians, physicists and engineers for over 200 years. The difficulty of the subject is shown by the fact that, in recent months a million dollar prize has been revived for a complete solution of the Navier-Stokes (N-S) equation which, in principle, should provide an accurate description of turbulence. The standard introductory text has been G.K. Batchelor's "Theory of Homogeneous Turbulence" first published in 1953 but there has been a felt need for an introductory text which discusses the progress which hes been made since this book was published. I believe that this new book will supply the want.

The first chapter provides an overview, it is interestingly written and discusses such elements as Reynolds numbers and experimental observations both historical and topical: from the hydraulic engineer to the aerodynamicist. The approach is to consider the energetics of the N-S equations and how fairly elementary physical considerations can lead to important conclusions. The only disappointing element is the minimal contribution of Chaos theory which might be assumed to have made major contributions to the understanding of turbulence.

Chapter two gives a discussion of the applications of statistical theory to turbulence. It is concise and accurate as well as being closely integrated to the energetics of N-S and is central to an understanding of the rest of the book. The third chapter discusses time scales. These are of great practical importance. For example in ocean physics the behaviour of bubble clouds generated by wave breaking is critically dependent on the scale of any turbulence which can determine whether the bubbles are returned to the atmosphere or retained in turbulent eddies until completely absorbed.

Chapter four discusses some elementary applications such as flow in ducts and leads to chapter five on jets, wakes and boundary layer flow. This is the central feature of the book, it is very well illustrated and presents methods which will be of practical utility to a variety of engineers. Chapters six and seven are more advanced and could be omitted from an introductory course, they cover spectral analysis and Kolmogorov's theories. The final chapter discusses numerical simulation. This will be invaluable to anyone involved in computer simulation and contains a number of excellent suggestions which could lead to useful research topics. Each chapter ends with a concise summary and some conclusions followed by references for further reading. There is a good index.

My own favourites were the second chapter (on statistics) and the last (on simulation) but all are uniformly good.

A.D. Booth,
Sooke, B.C.