Lagrangian Transport in Geophysical Jets and Waves (eBook)

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.

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The purpose of this book is to provide an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical ?ows. These methods were originally developed in the abstract mathem- ical setting of dynamical systems theory, through a geometric approach to di?erential equations that ultimately owes much to the insights of Poincar' e (1892). In the 1980s and 1990s, researchers in applied mathematics and ?uid dynamics recognized the potential of this approach for the analysis of ?uid motion. Despite these developments and the existence of a substantial body of work on geophysical ?uid problems in the dynamical systems and geophysicalliterature,nointroductorytexthasbeenavailablethatpresents these methods in the context of geophysical ?uid ?ow. The text is meant to be accessible to geophysical ?uid scientists and students familiar with the mathematics of ordinary (mostly) and partial (sometimes) di?erential equations. It assumes little or no prior knowledge of dynamical systems theory. An e?ort is made to explain concepts from a physical point of view, and to avoid the theorem and proof constructions that appear in dynamical systems texts. We hope that this book will prove usefultograduatestudents,researchscientists,andeducatorsinanybranch of geophysical ?uid science in which the motion and transport of ?uid, and ofmaterialscarriedbythe?uid,isofinterest.Wehopethatitwillalsoprove interesting and useful to applied mathematicians who seek an introduction to an intriguing and rapidly developing area of geophysical ?uid dynamics.