An Introduction to Turbulent Flow

Some 20 years ago, an instructor of a turbulence course had a limited choice of textbooks. Even the selection of monographs that could be used to supplement one's notes was not very large. Now a number of books are available. I count that number to be between 20 and 40, depending on how generously I include some special-purpose books. One explanation is clearly that this vast subject is getting further attention because of the strengthening of its ties to mainstream physics and modern mathematics.

Turbulence has excited--though sometimes only fleetingly--the interest of diverse groups of people, ranging from field theorists to practicing engineers, and it is no longer possible to include in a single book all the major developments that have resulted from this interest. Another intrinsic reason for the multiplicity of books is that consensus regarding the significant and essential topics does not exist among those familiar with the field. Different books, emphasizing different aspects of the subject that are at different levels of maturity, are therefore an inevitable consequence.

The authors of An Introduction to Turbulent Flow, Jean Mathieu and Julian Scott, have had extensive research and teaching experience in turbulence at their home institution (L' Ecole Centrale de Lyon) and elsewhere. They have drawn on that experience to produce a textbook meant primarily for graduate students in engineering, applied science, and applied mathematics. Their aim is to provide the students with solid grounding in physical ideas, orders of magnitude estimates, and a mathematical framework.

A brief summary might alert the reader to the book's contents: The first three, introductory, chapters are followed by the basic theory of single-point statistics arising from the equations of motion (chapter 4) and examples of classical engineering flows (chapter 5). Chapter 6 is a description of spectral (and multipoint) analysis, and chapter 7 deals with Andrei Nikolaevich Kolmogorov's ideas (in both 1941 and 1962). The book ends with a description in chapter 8 of numerical simulation of turbulent flows; direct numerical simulations, large eddy simulations, and engineering closure schemes are described briefly. The material is more or less standard for a course taught in a US engineering science department to students with a moderate background in fluid dynamics.

The character of a book is determined at least partly by the care with which the material is presented, and this one amply demonstrates the care that the authors have invested. For instance, their treatment, in chapter 3, of length and time scales is lively and refreshing, and their description of the physics of shear flows, without much use of mathematical equations, though somewhat longish, makes rewarding reading. The authors have succeeded in the task they set out to do, and I recommend the book to all students of turbulence, no matter what their persuasion. Patient students who work their way through the authors' arguments will be rewarded by an improved intuition for the subject.

What, then, are its shortcomings? One could say that some details of the analysis of the turbulent boundary layers are slightly unconventional (and the appendix A to chapter 5 is hard to penetrate); the references are sometimes idiosyncratic and incomplete; the book avoids mention of such controversies as logarithmic versus power laws in the intermediate layer of the boundary layer and the existence or otherwise of power laws in the inertial range; and so forth. These issues and more modern developments will perhaps receive their due share of attention in the second volume the authors have promised. And, for a book aimed essentially at students, it would have been better had it included some exercises on which students could test their understanding and mastery.