Introduction to the Geometry and Topology of Fluid Flows

An introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the world of geometric and topological fluid mechanics. This volume examines geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities. It contains more than 160 figures and examples. In the opening article, H.K. Moffatt proposes eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other open problems.