9R24. Variable Density Fluid Turbulence. Fluid Mechanics and its Applications, Vol 69. - P Chassaing (Inst de Mecanique des Fluides de Toulouse, Toulouse, France), RA Antonia (Univ of Newcastle, Newcastle, NSW, Australia), F Anselmet (Inst de Recherche sur les Phenomenes hors Equilibre, Marseille, France), L Joly (Ecole Natl Superieure d’Ingenieurs de Constructions Aeronautiques, Toulouse, France), and S Sarkar (Dept of Mech and Aerospace Eng, UCSD). Kluwer Acad Publ, Dordrecht, Netherlands. 2002. 380 pp. ISBN 1-4020-0671-3. $110.00.

Reviewed by R Verzicco (Dept di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Via Re David 200, Bari, 70125, Italy).

This book attempts to address the topic of variable density fluid turbulence by reviewing several approximations for compressible flow equations, various density induced flow effects, some model homogeneous and free-shear flows, and in the last part, first- and second-order compressible turbulence modeling. The adequate statistical tools are also provided in order to better analyze the variable density turbulent motion.

This monograph is a very valuable addition to the existing literature since, although variable-density turbulence is extremely common in industrial and geophysical applications, its systematic study is very scarce.

The book consists of 11 chapters, a very large list of references, and a subject index. The chapters are gathered into three main parts—theoretical elements, physical analysis, and modeling for industrial applications.

Chapter 1 introduces the topic by a preamble with a motivation for studying compressible turbulence. Some expected density variation effects are then listed and explained. At the end, a summary of each chapter’s content, the contributions given by the individual authors, and acknowledgments are given. Chapter 2 gives an overview of variable density effects in turbulent flows. These include stability and transition of mixing layers and jets, buoyancy driven and compressed turbulence, compressible shear flows, shock turbulence interactions, and compressible turbulent boundary layers.

Chapter 3 reviews different approximations of the variable density Navier-Stokes equations including Lighthill’s acoustic analogy, Boussinesq approximation, and low-Mach number formulation. The incompressible equations are then derived as the limit of the general equations. In Chapter 4, the equations governing fluid mixtures (with particular emphasis to binary mixtures) are introduced together with the non-dimensional parameters. The dynamics of density fluctuations is then discussed for several kinds of approximations.

Chapter 5 provides the essential tools for variable density flows and derives the transport equations governing averaged and single point properties of the flow field. A detailed comparison of the terms coming from binary and ternary regrouping is performed, and the physical meaning of the arising terms is given.

In Chapter 6, some basic variable density mechanisms of turbulent flows are highlighted. This is achieved by deriving the vorticity equation for a general flow and by evidencing the terms that are absent in incompressible flows. The role of density fluctuations and their diffusive effect are analyzed in low-speed flows. The last part of the chapter is devoted to mechanisms associated with dilatation fluctuations and dissipation terms in relation with their contributions to energy balance equations.

Chapter 7 is very specific, dealing with the behavior of velocity and scalar structure functions in turbulent flows. In particular, the classical Kolmogorov and Obhukov hypotheses and results are critically considered in view of the only moderately high Reynolds number attained in laboratory conditions. This chapter should be regarded as a pedagogical background, since it is only concerned with incompressible flows.

The analysis of the structure of variable density low-speed shear flows is performed in Chapter 8. In particular, mixing layers and jets are considered, and many topics presented in previous chapters are re-introduced from a different perspective.

Chapter 9 presents those free shear flows whose density changes are induced by high velocity values. Once again, mathematical preliminaries are given and the equations are commented. The dynamics of high- speed shear layers with the stabilizing effect of the Mach number, the growth rate of the various thicknesses, and thermodynamic fluctuations are presented.

The last two Chapters, 10 and 11, are devoted to compressible turbulence modeling. Both chapters review the existing models (with zero-, one-, two-equations and for the full Reynolds Stress Tensor) with a particular look at the modifications and additional terms needed to account for density variations.

This monograph has the ambitious goal to describe in a single text all the complex dynamics of variable density turbulence. In some respects, the book is successful since many complex and poorly understood phenomena are illustrated with physical examples and the analysis of the single terms of the equations. What this reviewer has found less successful is the amalgamation of the different chapters, since many topics are discussed more than once using different notations for the equations and terminology.

This reviewer has found several misprints in the text and formulas and, even though the quality of the figures is generally good, reproducing color plots using gray levels yields misleading figures. The last two points, however, cannot be ascribed to the authors but rather to the editorial office. In conclusion, this reviewer enjoyed reading Variable Density Fluid Turbulence and advises the purchase of the text to graduate students, researchers, and engineers, as well as libraries.