The physics of fluid turbulence. Paperback ed. with corrections.

*(English)*Zbl 0748.76005
Oxford Engineering Science Series. 25. Oxford: Clarendon Press,. xxiv, 572 p. (1991).

In this book our aim is to deal with certain topics which form a subset of both engineering science and physics. In doing so, we hope to assist two broad classes of reader. First there are those who are new to the subject, and secondly there are those who are already familiar with one or more of the traditional branches of the study of turbulence, but whose background and experience does not prepare them for the usages of quantum physics. The first two chapters set out to give a concise summary of the theory and practice of turbulence up to about 1960. Chapter 3 serves two purposes. First, it tries to give the reader a broad picture of what the rest of the book is about. The second purpose of this chapter is to cover topics which would not easily fit into the main part of the book, yet are important. Section 3.1 on anemometry and data processing is an example of such a topic.

Chapters 4-10 constitute the main part of the book and deal with modern (post–1960) turbulence theory. Chapter 4 begins by presenting some background material on the statistical mechanics of the classical \(N\)- body system. This introduces useful concepts and terminology, and provides a context for the subsequent rigorous formulation of the turbulence problem as an example of a non-equilibrium statistical system with strong coupling. Chapter 5 aims to ‘de-mystify’ the application of renormalized perturbation theory (RPT) to turbulence. RPT is introduced for some simpler problems by considering (a) the virial cluster expansion in dilute \(N\)-body systems and (b) the Debye-Hückel screened potential for the classical plasma as an example of long-range interaction. Then, a general treatment of the perturbation expansion of the Navier-Stokes equations (based on a modified version of Wyld’s analysis) follows, and the chapter closes with a consideration of Kraichnan’s direct interaction approximation as an example of a second-order truncation of the renormalized expansion.

Chapter 6 deals with those RPTs which do not yield the Kolmogorov spectrum as a solution and Chapter 7 deals with those that do. Chapter 8 attempts to provide a critical assessment of RPTs. The main emphasis is on the comparison of numerical solutions of the spectral and response equations with the results of laboratory and computer experiments.

In Chapter 9 we introduce the newer method of renormalizing the transport coefficients in turbulence: the renormalization group (RG). Both this and RPT method crop up again in Chapter 10, where we discuss the numerical simulation of turbulence. The final part of the book, consisting of Chapters 11-14, can be seen as offering some sort of counterpoise to the exclusive theoretical (and often esoteric) nature of most of the preceding chapters.

Chapters 4-10 constitute the main part of the book and deal with modern (post–1960) turbulence theory. Chapter 4 begins by presenting some background material on the statistical mechanics of the classical \(N\)- body system. This introduces useful concepts and terminology, and provides a context for the subsequent rigorous formulation of the turbulence problem as an example of a non-equilibrium statistical system with strong coupling. Chapter 5 aims to ‘de-mystify’ the application of renormalized perturbation theory (RPT) to turbulence. RPT is introduced for some simpler problems by considering (a) the virial cluster expansion in dilute \(N\)-body systems and (b) the Debye-Hückel screened potential for the classical plasma as an example of long-range interaction. Then, a general treatment of the perturbation expansion of the Navier-Stokes equations (based on a modified version of Wyld’s analysis) follows, and the chapter closes with a consideration of Kraichnan’s direct interaction approximation as an example of a second-order truncation of the renormalized expansion.

Chapter 6 deals with those RPTs which do not yield the Kolmogorov spectrum as a solution and Chapter 7 deals with those that do. Chapter 8 attempts to provide a critical assessment of RPTs. The main emphasis is on the comparison of numerical solutions of the spectral and response equations with the results of laboratory and computer experiments.

In Chapter 9 we introduce the newer method of renormalizing the transport coefficients in turbulence: the renormalization group (RG). Both this and RPT method crop up again in Chapter 10, where we discuss the numerical simulation of turbulence. The final part of the book, consisting of Chapters 11-14, can be seen as offering some sort of counterpoise to the exclusive theoretical (and often esoteric) nature of most of the preceding chapters.

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76Fxx | Turbulence |