The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unresolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressiblity, inhomogeneity, and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary. This book will be of interest to students of fluid mechanics, turbulence, and vortex methods as well as to applied mathematicians and engineers.

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.