1R41. N-Vortex Problem: Analytical Techniques. - PK Newton (Dept of Aerospace and Mech Eng, Dept of Math, Univ of S California, Los Angeles CA 90089-1191). Springer-Verlag, New York. 2001. 415 pp. ISBN 0-387-95226-8. $59.95.

Reviewed by MF Platzer (Dept of Aeronaut and Astronaut, Naval Postgraduate Sch, Code AA/PL, Monterey CA 93943-5000).

In this book the author presents a comprehensive treatment of the Hamiltonian aspects of incompressible vortex dynamics, complementing recent books on vortex dynamics by Saffman, Pulvirenti, Doering and Gibbon, and Majda and Bertozzi, by concentrating in depth on integrable and nonintegrable point vortex motion. In the first chapter, he presents an overview of vorticity dynamics and Hamiltonian systems, followed by chapters on the planar N-vortex problem with and without boundaries, the N-vortex problem on a spherical shell, and the problem of determining the growth rate of spiral interfaces in vortex-dominated flows. The remainder of the book is devoted to the statistical mechanics treatment of point vortex motion and to vortex patch and vortex filament models.

Newton’s goal in writing this book was to provide graduate students and researchers in the field of vortex dynamics with a thorough and rigorous introduction to current work. He deliberately limited himself to the discussion of analytical methods and omitted numerical techniques. The book, therefore, will be of greatest value to readers interested in rigorous analytical solutions. Nevertheless, atmospheric scientists, aero-, and hydrodynamicists will also find N-Vortex Problem: Analytical Techniques a useful reference book for the analysis of vortex dynamics.