1R9. Plasma and Fluid Turbulence: Theory and Modelling. Series in Plasma Physics. - A Yoshizawa (Inst of Indust Sci, Univ of Tokyo, Japan), S-I Itoh (Res Inst for Appl Mech, Kyushu Univ, Japan), K Itoh (Natl Inst for Fusion Sci, Toki, Japan). Inst Phys Publ, Bristol, UK. 2003. 459 pp. ISBN 0-7503-0871-0. $135.00.

Reviewed by Toshi Tajima (Kansai Res Est, JAERI, 8-1 Umemidai, Kizu, Kyoto, 619-0215, Japan).

This book is a good reference book for researchers on complex phenomena of turbulence that determine the major aspect of the fundamental behavior of many plasmas and fluids. The first author is an expert in fluid mechanics, while the latter two are specialist in fusion plasmas. This book takes statistical mechanical viewpoints into account to the extent reasonable to the subject of turbulence. This way the authors consciously try to broaden the field that they embarked on, which seems to be one of the book’s objectives. In particular the book details on the nonlinear behavior of plasmas and fluids that exhibit the phenomenon of hysteresis. These chapters (Chs 16, 19, 22-25) are based on the authors’ own frontier research and show their depth and connect to a broader discipline of nonlinear science (and once popular mathematical field of catastrophe theory), yielding the flavor and appeal central to this book. It would have been even more powerful, if the authors had more deeply incorporated the strong Russian school of nonlinear applied mathematics and science, such as the works of Nonlinear Oscillations (Lefschetz), Fluid Mechanics (Landau-Lifshitz), and those by Ginzburg, that lay some of the important cornerstones of nonlinear science. (Ginzburg-Landau’s nonlinear potential alone spawned out many important ideas in physics such as superconductivity theory and Higgs bosons as well as the bifurcation theory.)

In fact, broader references are desired for this book, that I suppose, tries to bury gaps among several fields, including fluid turbulence plasma turbulence, statistical mechanics, chaos theory, nonlinear science, and astrophysics, which all embrace states far from equilibrium. Some of the more important references that the reader have get benefit from, if cited, include:

  • — Parker’s reference on his first paper on dynamo and a book by Krueger on the same topic (on the mean filed theory of dynamo) (Chs 6 and 10),

  • — Transport coefficients and their symmetry by Onsager (Chs 12 and 25),

  • — Geometry influence such as the toroidicity on the stability and transport of plasmas pioneered by Chen, Kishimoto and others (Chs 17 and 18). One of the most spectacular examples of progress in recent times in plasma theory is that it has gained predictive capacity in the description of kinetic behavior. This originates from the ability to incorporate global geometrical effects such as the toroidicity even for microscopic kinetic modes.

  • — First paper on ionizational bifurcation by Drane and Sutin (1987) relevant to the later L-H transition the authors discuss (Ch 22), disk oscillations/bifurcations in astrophysical plasmas (Mineshige) (Chs 16 and 22), for example.

  • — It was a bit sobering to learn that the theory of turbulence has not progressed much since the reviewer’s student time, when theories of Heisenberg and Kolmogorov were the fundamental literature. However, some treatments of the renormalization group theoretic approach and the Pade approximation in turbulence (Chs 14 and 16) have educated this reviewer. Insights into turbulence derived from computer simulation should be among the new sections to this difficult and age-old subject. Turbulence behavior not touched by classical turbulence theory that has been recently studied includes fractal structures, intermittence, and kurtosis. The reviewer would like to see some discussion like these at the level of this book. In spite of these complaints, Plasma and Fluid Turbulence has succeeded in its difficult mission to explain themes of the authors weaving through esoteric subjects of numerous plasma instabilities.