Inviscid Incompressible Flow , Jeffrey S.Marshall Wiley, New York, 2001. $90.00 (378 pp.). ISBN 0-471-37566-7

Jeffrey S. Marshall’s Inviscid Incompressible Flow is a refreshing compendium of classical topics in the repertoire of fluid dynamists, physicists, and mathematicians. It also contains some computational tools that a current student and practitioner of inviscid fluid dynamics must have. The author, who works in continuum mechanics, has been active in both theoretical and computational mechanics—hence a book with a viewpoint, and perhaps some coloration, which reflects his personal experience. The motivation for the book is the success of the inviscid flow formulation in describing the behavior of fluids as we ordinarily encounter them—in breathing, or flying, or experiencing the interplay of oceanic and atmospheric currents.

In Marshall’s book, the fluid flow problem is formulated first in integral and then in differential form, after the reader is carefully guided through a series of mathematical and kinematical preliminaries needed for rigorous deductions from the conservation laws of mechanics. The formulation is completed with a chapter-long discussion of interfaces. Marshall next discusses the general conclusions regarding the global features of flows in terms of velocity, vorticity, and pressure theorems. The bulk of the discussions of flows is nearly equally divided between potential flows and vortical flows in chapters dispersed throughout the text. The book’s final two chapters are on interfacial waves and flow instabilities.

Given that ample computing capacity has now become the norm, the book provides some computational tools needed to break free of classical analytical techniques and employ instead numerical calculations for the study of flows. This computational aspect is particularly suitable for instruction at universities where computational proficiency is expected of both undergraduate and graduate students.

Marshall’s presentation of mathematical preliminaries prior to the formulation of problems is rigorous, which reflects his training in continuum mechanics; a novice might find his approach somewhat overpowering.

Although Marshall’s discussion of the requirements for incompressibility is meticulous, a parallel presentation of the inviscid flow assumption, which would have made the discussion more thorough, is missing. Further, the last two chapters, on waves and instability, seem not to cover their material at the level comparable to, say, the coverage of vortex dynamics in earlier chapters. And some inclusion of observations and experiments would have been valuable to experimentalists like me; after all, it is the experiments that guide us.

Nonetheless, Marshall’s book fills an important gap. It provides a rigorous formulation of the fluid flow problem and presents a compendium of fundamentally and technically important problems in inviscid incompressible flow. Additionally, it poses problems at the end of each chapter that can be used to further explore the preceding topics. An important achievement of the book from my point of view is that so much is done in a volume of reasonable size. Not a trivial task!

Even though the author sees Inviscid Incompressible Flows as a textbook for graduate-level teaching, I also envision it as a textbook for advanced undergraduate teaching in physics, mathematics, and engineering, as well as a complementary reference book for graduate courses in fluid mechanics. I certainly welcome the book as a nice addition to my own collection. In particular, I find the treatment of vortex filaments and vortex panel methods very useful, since I discuss those topics in the senior and first-year graduate courses I teach at Berkeley.