11R6. Waves and Compressible Flow - Hilary Ockendon and John R Ockendon. Springer-Verlag, New York. 2004. 188 pp. ISBN 0-387-40399-X. $59.95.

Reviewed by Narayanan M Komerath (Sch of Aerosp Eng, Georgia Inst of Tech, Atlanta, GA 30332-0150).

This is a textbook on applied mathematics. It describes wave phenomena from the perspective of phenomena in compressible flow—following the authors’ stated belief that “fluid mechanics provides the best possible vehicle for anyone wishing to learn applied mathematics methodology.” As such it provides a familiar interface for aerospace engineers interested in going deeper into wave problems. The emphasis on compressible flow may or may not appeal to other students—this emphasis is certainly quite striking, in the detail and even in the wealth of illustrations in those chapters. One suggestion is to provide more illustrations in the other chapters, to convey a similar wealth of physical insight to the student. For example, the problem of wave propagation in rotating flows could use some illustrations.

Chapter 2 starts in an unsurprising manner for the engineering student, giving conservation equations. It is good to see a mathematical derivation of what is known in aerodynamics texts as the “Helmholtz theorems.” The exercises at the end of this chapter, as with all chapters, are very useful and well thought out.

Chapter 3 introduces acoustics from the small perturbation, linearized form of the equations of gas dynamics. It then goes on to inertial waves, waves in rotating media, and onto electromagnetic and elastic waves. This is an excellent format, but it would benefit from greater attention to the electromagnetic waves section. The treatment of the physics of electromagnetic waves is too sparse, considering that it is the only form of wave propagation across free space, devoid of a medium.

This chapter is really the most important one in this book—it integrates wave phenomena from many disciplines. As such, in any revised edition, I hope the authors will expand this to convey as much of the physics and implications as possible.

Chapter 4 describes theories for linear waves. Again, here, the treatment of two-dimensional compressible flow takes up considerable space. The illustration of a “nephroid caustic on a cup of coffee” is sure to cause some reflection (no pun intended) on the part of students. It is an example of the power of a well-done illustration.

Other illustrations in the chapter, however, are the typical mathematician’s “domain/set” type blob-sketches. The exercises at the end of Chapter 4 are extensive, as appropriate.

Chapter 5 deals with nonlinear waves. The use of compressible flow here is useful, but more attention to the Schrodinger equation would also be useful to the student. The Hodograph transformation is of historical importance, but otherwise I wonder if is useful any more.

Chapter 6 presents shocks. The presentation of the shock interaction cases, showing Mach reflection is useful. The discussion of chemically reacting flows with shocks is rather skimpy—missing so many interesting aspects of detonation theory, where applied mathematics has been used to great effect in the former Soviet/Russian literature. The section on hypersonic flow is compact and very useful.