5R49. Inviscid Incompressible Flow. - JS Marshall (Dept of Mech Eng, Iowa Inst of Hydraul Res, Univ of Iowa, Iowa City IA). Wiley, New York. 2001. 378 pp. ISBN 0-471-37566-7. \$90.00.

Reviewed by TF Balsa (Dept of Aerospace and Mech Eng, Univ of Arizona, Tucson AZ 85721).

When the invitation came to review this book, this reviewer was very surprised by its title. Curiosity, more than anything else, drove me to review the book. Such classical subject! Since several excellent, scholarly, and comprehensive treatments already exist, both in the fluid mechanics as well as in the aerodynamics contexts, this reviewer saw little need for another book. Consider, for example, An Informal Introduction to Theoretical Fluid Mechanics by Lighthill.

The book under review is primarily a textbook, most suitable for an introductory graduate-level course in fluid mechanics. The book is attractively prepared, relatively free from obvious major errors, contains illustrative examples (more so in the first half than in the second half), provides a good set of homework problems, including some focusing on computational projects, and supplies a partial list of modern references at chapters’ end. Even the best of students will be challenged by the content. The book’s secondary focus, complementing the classical concepts and results, may be labeled as vorticity methods.

The book (378 pages long; including one short appendix on the geometry of orthogonal coordinate systems) is on theoretical fluid mechanics with some computational flavor. Many of the main results are stated in the form of theorems. Reference to experimental data or comparison with such is virtually absent. This is very unwise in the subject. For example, Figure 11.8 displays computational contours of vorticity in the roll-up process in a shear layer. This reviewer thinks experimental data and flow visualization pictures would strengthen the presentation.

The 16, well-organized and relatively brief chapters span the usual topics such as: kinematics, the equations of motion, vorticity and pressure theorems, examples of two- and three-dimensional potential flows (ie, sources, dipoles, etc) and forces on bodies in these flows. The chapters on two-dimensional flow are treated by the use of complex variables. There is more emphasis on flows with concentrated vorticity (ie, vortex tubes, sheets, etc) than in most similar textbooks. This is the secondary focus mentioned above. There is also some discussion of discontinuities, flow instability, and interfacial wave motion. The latter two, treated at the end of the book, are sketchy.

It seems to me that Chapter 6 on velocity representations (ie, velocity potential, Laplace equation, the Biot-Savart equation, and far fields) breaks up the continuity in the presentation of fluid mechanics. This reviewer thinks a better place for this material would be in an appendix; this comment should also apply to a review of vectors and tensors in Chapter 1.

The vorticity transport theorems (Ch 7) are undeniably the most important results in fluid mechanics. The formal analysis is competently done—no surprises. Yet the issue of why vorticity (other than that generated by the baroclinic effect) appears in an inviscid fluid motion started from rest is not discussed deeply. This is unfortunate. Clearly, some connection must be made to large Reynolds number flows, viscous boundary layers, and the like. Establishing a stronger link between vorticity and viscous effects, even qualitatively, is imperative (see the attempt on pages 3-4) so this connection becomes engrained in the fresh and open minds of students. Otherwise, inviscid incompressible fluid mechanics is a beautiful and sterile subject of the pre-Prandtl era. The book could be improved in this general direction. For example, the Index contains no entry under separation.

All in all, this is a good introductory book, and this reviewer would not hesitate to use chapters of it in some courses. Obviously, the sections to be covered are at the discretion of the instructor. There are some places where the presentation should be improved. Here are three examples, ranging from the trivial to the bothersome:

1) The cross product of unit vectors is defined as $ei×ej=εijkek.$ Therefore the expression written in Eq (2.3.2) for $u×v$ is inconsistent with this.

2) The derivation of the rate of change of a material volume can be done simply by the use of a sketch and a physical argument. The formal derivation (Section 3.4) is unnecessarily dry. There are other instances where more intuitive derivations should be given.

3) Finally, the relationship between the doublet and vortex sheet strengths (Eq 11.6.13) is incorrect. For one thing, $∇$ is a spatial operator, so the application of this to a quantity which is defined only on a surface is unclear.

There is also a major omission, namely, the control volume analysis of forces and moments acting on bodies that shed a trailing vortex system. This analysis would place the D’Alembert paradox in the proper perspective and would identify the concept of induced drag. This consideration would also bring some life to kinetic energy and impulse.

Again, on balance, Inviscid Incompressible Flow is a fine book on the classical material. It also contains some more recent (10-20 year old) vorticity-related results that are normally not found in textbooks at this introductory level for graduate students. Any student who has mastered this material will have an excellent understanding of inviscid incompressible fluid mechanics. The person will also gain some understanding of discrete methods to track regions of concentrated vorticity and the limitations of the methods. On the last point, even an expert may gain a quick overview of the available techniques.