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An Introduction to the Geometry and Topology of Fluid Flows : NATO Science Series II - Renzo L. Ricca

An Introduction to the Geometry and Topology of Fluid Flows

NATO Science Series II

By: Renzo L. Ricca (Editor)

Hardcover Published: 30th November 2001
ISBN: 9781402002069
Number Of Pages: 347

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Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics.
Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples.
In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.

Preface
Photograph of H. K. Moffatt
Eight Problems for the XXI Centuryp. 1
Some Remarks on Topological Fluid Mechanicsp. 3
Mathematics Backgroundp. 11
Differential Geometry of Curves and Surfacesp. 13
Topology in Four Daysp. 35
Elements of Classical Knot Theoryp. 57
An Introduction to Knot Theoryp. 77
Fluid Mechanics and Mathematical Structuresp. 105
Geometry and Topology of Fluid Flowsp. 135
Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systemsp. 137
Streamline Patterns and their Bifurcations Using Methods from Dynamical Systemsp. 167
Topological Features of Inviscid Flowsp. 183
Geometric and Topological Aspects of Vortex Motionp. 203
Topology Bounds the Energyp. 229
Measures of Topological Structure in Magnetic Fieldsp. 239
Diffeomorphisms, Braids and Flowsp. 253
Variational Principles, Geometry and Topology of Lagrangian-Averaged Fluid Dynamicsp. 271
Reconnections and Singularitiesp. 293
The Geometry of Reconnectionp. 295
Euler Singularities from the Lagrangian Viewpointp. 313
Analysis of the Candidate Flow for Hydrodynamic Blowupp. 329
Subject Indexp. 343
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781402002069
ISBN-10: 1402002068
Series: NATO Science Series II
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 347
Published: 30th November 2001
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 1.51