Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach

ISBN-13: 9781441922045 / Angielski / Miękka / 2010 / 150 str.

Roger M. Samelson; Stephen Wiggins

Opis

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.

Recenzje

From the reviews:

"A strong understanding of Lagrangian approaches to the transport and stirring of fluid often benefits from mental visualization. One must picture diverging fluid and evolving material curves that deform and tangle about each other. A successful introduction to this subject should facilitate this description, and this fine monograph by Roger Samelson and Steve Wiggins does so effectively. The book is written primarily for students and researchers in the geosciences." (Larry Pratt, SIAM Review, Vol. 49 (4), 2007)

"Samelson and Wiggins aim to provide an accessible introduction to modern mathematical techniques to explore transport and exchange in geophysical flows. ... The book is very well structured. ... Each chapter has a good introduction and concludes with a good summary. The book undoubtedly reads well. ... The four appendices provide interesting extra information. The two page index is adequate. Over nine pages of references ensures the bibliography provides valuable pointers into recent research. ... In summary: lovely material, well written ... ." (Anthony John Roberts, Mathematical Reviews, Issue 2008 f)

"The purpose of the monograph is to explore some of the new insights into Lagrangian motion in geophysical flows followed from such approach and to present an accessible introduction to the basic elements of some of these methods. ... The monograph will be useful for applied mathematicians, especially working in geophysical fluid dynamics." (Boris V. Loginov, Zentralblatt MATH, Vol. 1132 (10), 2008)

Spis treści

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.

Blurb

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.

This book will prove useful to graduate students, research scientists, and educators in any branch of geophysical fluid science in which the motion and transport of fluid, and of materials carried by the fluid, is of interest. It will also prove interesting and useful to the applied mathematicians who seek an introduction to an intriguing and rapidly developing area of geophysical fluid dynamics. The book was jointly authored by a geophysical fluid dynamicist, Roger M. Samelson of the College of Oceanic and Atmospheric Sciences at Oregon State University, USA and an applied mathematician, Stephen Wiggins of the School of Mathematics, University of Bristol, UK.