Turbulence: An Introduction for Scientists and Engineers , P. A. Davidson , Oxford U. Press, New York, 2004. $174.50, $74.50 paper (657 pp.). ISBN 0-19-852948-1, ISBN 0-19-852949-X paper
In Turbulence: An Introduction for Scientists and Engineers , Peter Davidson begins the first chapter by writing “The study of turbulence is not easy, requiring a firm grasp of applied mathematics, and considerable physical insight into the dynamics of fluids. Worse still, even after the various theoretical hypotheses have been absorbed, there are relatively few situations in which we can make definite predictions!”
I agree with Davidson’s assessment. Historically, there have been two main schools of thought on the theory of turbulence. One emphasizes the study of coherent vortical structures in a turbulent flow; the other emphasizes a statistical approach. Until recently, researchers who followed one of the two methods were reluctant to acknowledge the importance of the other. My own approach is definitely statistical and looks for analogies of turbulence with other problems in statistical physics. Davidson does a nice job in presenting both points of view and in explaining how those views can come together. He keeps the discussion lively with an elegant writing style, frequently quoting a range of experts from Winnie the Pooh to Richard Feynman to Keith Moffatt.
The first three chapters of Turbulence give a clear introduction to the classical picture of turbulence. Chapter 4 concerns turbulent shear flows and simple closure models. In chapters 5 through 8, the author develops the physics of homogeneous isotropic turbulence in further detail. For example, chapter 6 covers isotropic turbulence in real, physical space and gives a good description of the conflict between statistical phenomenology and deterministic cartoons. Davidson gives considerable thought to the conflict and explains the problem clearly. In chapter 7, which covers the role of numerical simulation, Davidson summarizes research that was current a few years ago; however, the field is moving very fast, so it is hard for a textbook on the topic to remain current. In chapter 8, on isotropic turbulence in spectral space, Davidson conveniently collects many of the important results.
Chapters 9 and 10 are unusual and welcome additions to a textbook on turbulence. In chapter 9, Davidson focuses on the influence of rotation, stratification, and magnetic fields on turbulence. In chapter 10, he covers two-dimensional turbulence.
I do have a fundamental disagreement with Davidson: He largely ignores the Lagrangian description of turbulence, in which one follows a fluid particle, in favor of the Eulerian description at a fixed spatial point. Considerable evidence exists that a valid statistical theory of the turbulent cascade requires a Lagrangian description. The idea that the smaller eddies are swept by the larger ones without dynamical distortion is fundamental to turbulence dynamics and can be expressed only in Lagrangian terms. A more radical position to which I subscribe is that a turbulent cascade does not exist dynamically but is instead a descriptive property of a statistical steady state.
Davidson’s book can be compared with another text on turbulence, Turbulent Flows (Cambridge U. Press, 2000) by Stephen B. Pope, a book intended primarily for graduate engineering students. The first half of Pope’s book largely overlaps with the first eight chapters of Davidson’s. The second half of Pope’s book is devoted to the engineering modeling of turbulence. As one might expect, Pope’s presentation of the fundamentals is straightforward, and he spends less time on the subtleties and basic difficulties of the subject. Another difference between the two books is in the layout: The layout of Pope’s book is easy to read, and the type size and fonts are clear. By contrast, Davidson’s book is visually unsatisfactory, and just two-thirds of the width of each page is used for text. The remaining third contains captions and occasional figures. In addition, the book’s type is unpleasantly small and the font too light for easy reading. The color plates in the middle of the book, however, are nice.
In brief, Davidson presents a thoughtful and detailed discussion of the basic physics of incompressible fluid turbulence. He is careful, if somewhat repetitive, in emphasizing the many places where our knowledge about the field is far from certain. For someone who wants to understand the fundamentals of turbulence, this book is a good start. But for those who want to learn the accepted wisdom on turbulence and then use it, Pope’s book is the better choice.
