The N-Vortex Problem

- N-Vortices in the Plane
- Domains with Boundaries
- Vortex Motion on a Sphere
- Geometric Phases
- Statistical Point Vortex Theories
- Vortex Patch Models
- Vortex Filament Models
- References.

From the reviews:ZENTRALBLATT MATH"Exercises given at the end of each chapter could be very useful to the readers to enhance their knowledge...the first three chapters deal with the basic classical two-dimensional point vortex theory, and the rest of the book takes care of the recent applications and extensions of the basic theory. The references are adequate for further study. Many open problems associated with N-vortex motion are also listed. The book is a welcome addition to the book shelves of researchers pursuing the N-vortex problem."MATHEMATICAL REVIEWS"Although several other books on vortex dynamics have appeared in recent years, none have the level of detail on these discrete vortex models that Newton achieves. The book is sure to be a key reference work on this area for many years to come. Students of fluid mechanics will find much valuable material here on modern dynamics applied to problems of interest to them. Applied mathematicians will find an entree to frontline problems of fluid mechanics using tools with which they are eminently familiar.""This is a very timely addition to the literature. ... Exercises are scattered throughout the book, many of them quite substantial. ... A massive bibliography - a treasure in itself - concludes the text. Although several other books on vortex dynamics have appeared in recent years, none have the level of detail on these discrete vortex models that Newton achieves. The book is sure to be a key reference work on this area for many years to come." (Hassan Aref, Mathematical Reviews, Issue 2002 f)"The goal of this book is to describe the Hamilton aspects of vortex dynamics in such a way that graduate students and researchers can use this book as an entry level text to the rather large literature on integrable and non-integrable vortex problems ... . The book is well written with each chapter containing useful biographical notes and exercises. Of particular note is the extensive list of seven hundred and seventy four