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Vortex dynamics. (English) Zbl 0777.76004
Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge: Cambridge University Press. xi, 311 p. (1992).
This monograph, written by a well-known expert in the field of fluid mechanics, has involved from lectures on vortex dynamics to graduate students given by the author during the past twenty years at Caltech. The main aim of the book is to provide a treatment of inviscid incompressible flows containing finite regions of vorticity. The discussion focuses on only those aspects of fluid motion which are primarily controlled by the vorticity and are such that the effects of other fluid properties (viscosity, compressibility, stratification etc.) are secondary. On this purpose, the author omits deliberately many related subjects such as numerical vortex methods or boundary layer interaction. However, an impressive material is covered in the book. The following list of chapters may serve as concise table of contents: 1. Fundamental properties of vorticity; 2. Singular distributions of vorticity; 3. Vortex momentum; 4. Motion with surfaces; 5. Some applications; 6. Creation of vorticity; 7. Dynamics of line vortices in two-dimensional flow; 8. Vortex sheets in two dimensions; 9. Dynamics of two-dimensional vortex patches; 10. Axisymmetric vortex rings; 11. Dynamics of vortex filaments; 12. Three-dimensional vortex instability; 13. Effects of viscosity; 14. Miscellaneous topics.
All topics are presented in clear, mathematically attractive manner that will certainly be appreciated by the reader. The book is also supported by many expressive figures and an excellent list of references starting from the original pioneer works of Helmholtz and Lord Kelvin. Very useful subject index completes this well-organized book, which, in the reviewer’s opinion, is a wellcome addition to the existing literature on classical hydromechanics.
Reviewer: O.Titow (Berlin)

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76B47 Vortex flows for incompressible inviscid fluids
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