This book provides an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical flows. These methods were originally developed in the abstract mathematical setting of dynamical systems theory, through a geometric approach to differential equations. Despite the recent developments in this field and the existence of a substantial body of work on geophysical fluid problems in the dynamical systems and geophysical literature, this is the first introductory text that presents these methods in the context of geophysical fluid flow. The book is organized into seven chapters; the first introduces the geophysical context and the mathematical models of geophysical fluid flow that are explored in subsequent chapters. The second and third cover the simplest case of steady flow, develop basic mathematical concepts and definitions, and touch on some important topics from the classical theory of Hamiltonian systems. The fundamental elements and methods of Lagrangian transport analysis in time-dependent flows that are the main subject of the book are described in the fourth, fifth, and sixth chapters. The seventh chapter gives a brief survey of some of the rapidly evolving research in geophysical fluid dynamics that makes use of this new approach. Related supplementary material, including a glossary and an introduction to numerical methods, is given in the appendices.

Written 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. Early chapters establish context and fundamental mathematical concepts and definitions, explore simple cases of steady flow, and touch on important topics from the classical theory of Hamiltonian systems. The main body of the book examines elements and methods of Lagrangian transport analysis in time-dependent flows. A concluding chapter surveys research in geophysical fluid dynamics that makes use of this new approach. Supplementary material is provided in the appendices. The book will appeal to graduate students, research scientists, and educators in any branch of geophysical science in which the motion and transport of fluid, and of materials carried by the fluid, is of interest. It will also interest applied mathematicians seeking an introduction to this area of geophysical fluid dynamics.

Steadily Translating Waves and Meanders.- Integrability of Lagrangian Motion.- Fluctuating Waves and Meanders.- Material Manifolds, Flow Regimes, and Fluid Exchange.- Lobe Transport and Flux.- Transport and Dynamics.