9R23. Flow Control by Feedback: Stabilization and Mixing. - OM Aamo (Norwegian Univ of Sci and Tech, Trondheim, N-7491, Norway) and M Krstic (Univ of California, San Diego, La Jolla CA 92093-0411). Springer-Verlag London Ltd, Surrey, UK. 2003. 198 pp. ISBN 1-85233-669-2. $99.00.

Reviewed by W Shyy (Dept of Aerospace Eng, Mech and Eng Sci, Univ of Florida, 231 Aerospace Bldg, PO Box 116250, Gainsville FL 32611-6250).

Flow control is a multidisciplinary topic and, by definition, requires expertise in both fluid dynamics and control theory. Many papers and some books have been published on this topic. However, successful efforts, at least for those amenable to physical implementation, are essentially all based on open-loop practices with no feedback mechanisms. To date, very few concrete examples and little comprehensive framework have been developed for closed-loop control. From this viewpoint, the present book is a welcomed addition in a timely and challenging area.

The book is relatively thin, with 183 pages of text. However, its coverage is rather broad, including summaries of governing equations for fluid dynamics, preliminary concepts of the control theory, and detailed discussion of selected case studies in feedback flow control. Overall, the presentation is uneven. In particular, certain equations and theoretical derivations are given in lengthy details, but with little discussion of their physical implications. An obvious example is the governing equations for fluid dynamics. After devoting Chapter 2, totaling 24 pages, to review the subject, anyone who is not already familiar with fluid dynamics will have gained little improved understanding of the subject. A brief discussion of the meaning, implication, and significance of each term in the governing equations would help. Some of the most critical issues related to fluid dynamics: nonlinearity and associated stability issues, different mathematical characteristics of the equations governing the individual flow variables such as velocity and pressure, and the implications of boundary conditions and geometry should have been given attention, especially in the context of flow control. Furthermore, the lead paragraph in Chapter 4 (Stabilization), which motivates flow control, contains inaccurate or incorrect statements. Similar complaints can be made about Chapter 3, which reviews control theory.

In contrast, Chapters 4 and 5 contain significant and state-of-the-art information. Chapter 4 focuses on stabilization of channel flows and suppression of vortex structures, while Chapter 5 discusses mixing and dispersion. Well-established tools such as the Lyapunov stability analysis and useful models such as the Gingsburg-Landau equation have been presented and fruitfully employed. Nice fluid flow examples based on numerical simulations are offered to demonstrate the implications of the theoretical framework. Some of the detailed presentations of the fluid flow computations also suggest that the resolution of the numerical simulation presented may not be sufficient for certain problems. Computational cost and resolution requirement are main concerns in simulation-based flow control development and can be fruitfully addressed in the book. More interpretation and explanation of the fluid physics associated with the case studies would also substantially strengthen the content. Finally, several important topics are missing, including reduced order representation of the full field simulation data (which is to be differentiated from reduced order model to approximate physical laws), scalability of the control strategies with respect to flow parameters (such as the Reynolds number), and physical implementation of control strategies.

Chapter 6 presents sensors and actuators. Needless to say, it is difficult to do justice within 4.5 pages of the text for such fast developing and diverse topics.

Flow Control by Feedback: Stabilization and Mixing has recorded the experience of two active researchers pursuing theoretical flow control. It is not suitable as a textbook, but can be useful for experienced scholars in need of specialized references.