Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach / Edition 1

by Roger M. Samelson, Stephen Wiggins

Overview

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 flows. These methods were originally developed in the abstract mathem- ical setting of dynamical systems theory, through a geometric approach to differential equations that ultimately owes much to the insights of Poincar´ e (1892). In the 1980s and 1990s, researchers in applied mathematics and—fluid dynamics recognized the potential of this approach for the analysis of fluid motion. Despite these developments and the existence of a substantial body of work on geophysical fluid problems in the dynamical systems and geophysicalliterature,nointroductorytexthasbeenavailablethatpresents these methods in the context of geophysical fluid flow. The text is meant to be accessible to geophysical fluid scientists and students familiar with the mathematics of ordinary (mostly) and partial (sometimes) differential equations. It assumes little or no prior knowledge of dynamical systems theory. An effort 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 fluid science in which the motion and transport of fluid, and ofmaterialscarriedbythefluid,isofinterest.Wehopethatitwillalsoprove interesting and useful to applied mathematicians who seek an introduction to an intriguing and rapidly developing area of geophysical fluid dynamics.

Product Details

ISBN-13:	9781441922045
Publisher:	Springer New York
Publication date:	11/19/2010
Series:	Interdisciplinary Applied Mathematics , #31
Edition description:	Softcover reprint of hardcover 1st ed. 2006
Pages:	150
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

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.

Editorial Reviews

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)

From the Publisher