Turbulence. An introduction for scientists and engineers. (English) Zbl 1061.76001

Davidson, P. A.

Oxford: Oxford University Press (ISBN 0-19-852949-X/pbk). xix, 657 p. (2004).

The aim of this textbook is to bridge a gap between elementary accounts of turbulence to be found in undergraduate texts and the more rigorous accounts given in the many monographs. The author seeks to combine the maximum of physical insight with the minimum of mathematical detail.
The first part, namely “The classical picture of turbulence”, is given by chapters 1–5. Here the mathematics is kept to a minimum. The first chapter: “The ubiquitous nature of turbulence”, focuses mainly on experiments of Taylor and Bénard, the flow over a cylinder, the Reynolds experiment, on different scales in a turbulent flow and on the closure problem of turbulence. The second chapter: “The equations of fluid mechanics” covers Navier-Stokes equations, the relationship between pressure and velocity, the vorticity dynamics and the definition of turbulence.
The third chapter: “The origins and nature of turbulence”, focuses on the nature of chaos and on some elementary properties of freely evolving turbulence. The fourth chapter: “Turbulent shear flows and simple closure models” deals with the exchange of energy between the mean flow and the turbulence, with the wall-bounded shear flow and the log-law of the wall, with free shear and homogeneous shear flows, heat transfer in wall-bounded shear flows and wiith one-point closure models. The fifth chapter: “The phenomenology of Taylor, Richardson and Kolmogorov” includes the Richardson’s energy cascade, Kolmogorov’s theory of small scales, turbulent diffusion and the closure problem.
The second part “Free decaying, homogeneous turbulence” contains three chapters, from 6 to 8, and is intended to the fundamental problem of homogeneous turbulence. A distinguishing feature is that the discussion is made in real space (rather than in Fourier space). Another distinguishing feature is that equal emphasis is given to both large and small scales. Chapter six “Isotropic turbulence (in real space)” concerns the governing equations of isotropic turbulence, the dynamics of the large scales, the characteristic signature of eddies of different shapes, the intermittency in inertial-range eddies, and the distribution of energy and vorticity across different sizes. Chapter seven “The role of numerical simulations” focuses on direct numerical simulations – DNS and on large eddy simulations – LES, on the danger of periodicity and on the structure in chaos.
There are also presented a set of pictures, tables 1–16, in an excellent graphical form, representing some visualisations and numerical simulations using DNS or LES for the turbulence in some practical cases like arround the surface of delta wing of an aicraft, behind a chimmey, in the boundary layer etc. Chapter eight “Isotropic turbulence (in spectral space)” deals with kinematics in spectral space and dynamics in spectral space.
The third part entitled “Special topics” is constitued by the chapters 9–10 and covers some subjects rarely discussed in introductory texts. The ninth chapter: “The influence of rotation, stratification and magnetic fields on turbulence” is devoted to body forces in geophysics and astrophysics, to the influence of magnetic fields, and to combined effects of Coriolis and Lorentz forces.
The tenth chapter: “Two-dimensional turbulence” focuses on the classical picture of two-dimensional turbulence, on coherent vortices, the variational principles for predicting the final state in confined domains, and on the quasi-two-dimensional turbulence.
At the end, there are five appendices concerning vector identities and tensor notation, properties of isolated vortices, long-range pressure forces in isotropic turbulence, Hankel transforms and hypergeometric functions, and the kinematics of homogeneous axisymmetric turbulence.

Reviewer: R. Militaru (Craiova)

MSC:

76-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
76Fxx	Turbulence

Keywords:

Navier-Stokes equations; closure models; boundary layer; numerical simulations