In many oceanic and atmospheric flows, the collection of trajectories of fluid elements - the Lagrangian motion - is of fundamental importance, determining the transport of fluid properties as well as basic characteristics of the flow itself. In the presence of large-scale, coherent structures, this motion can be analyzed using methods developed originally in the geometric theory of ordinary differential equations. The last two decades have seen the rapid development of this dynamical systems approach to Lagrangian transport for the analysis of engineering and geophysical fluid flows. Geophysical fluid problems presented a new set of mathematical and computational challenges for this approach; in turn, these methods have provided new perspectives on Lagrangian motion in geophysical flows. This is the first introductory textbook to describe this approach in the context of geophysical fluid dynamics. and in parallel, in an accessible style, and will serve both to introduce the necessary mathematical framework to geophysical fluid dynamicists, and to introduce an active area of geophysical fluid research to applied nonlinear dynamicists. The text is suitable for graduate and advanced undergraduate students, and will also serve as a useful reference for researchers and scientists in either field.

Written jointly by a specialist in geophysical fluid dynamics and an applied mathematician, this is the first accessible introduction to a new set of methods for analysing Lagrangian motion in geophysical flows. The book opens by establishing context and fundamental mathematical concepts and definitions, exploring simple cases of steady flow, and touching on important topics from the classical theory of Hamiltonian systems. Subsequent chapters examine the elements and methods of Lagrangian transport analysis in time-dependent flows. The concluding chapter offers a brief survey of rapidly evolving research in geophysical fluid dynamics that makes use of this new approach.