Ebook: An Introduction to the Geometry and Topology of Fluid Flows

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.

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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.

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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.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Some Remarks on Topological Fluid Mechanics....Pages 3-10
Front Matter....Pages 11-11
Differential Geometry of Curves and Surfaces....Pages 13-33
Topology in Four Days....Pages 35-55
Elements of Classical Knot Theory....Pages 57-75
An Introduction to Knot Theory....Pages 77-104
Fluid Mechanics and Mathematical Structures....Pages 105-134
Front Matter....Pages 135-135
Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems....Pages 137-165
Streamline Patterns and Their Bifurcations Using Methods from Dynamical Systems....Pages 167-182
Topological Features Of Inviscid Flows....Pages 183-201
Geometric and Topological Aspects of Vortex Motion....Pages 203-228
Topology Bounds the Energy....Pages 229-238
Measures of Topological Structure in Magnetic Fields....Pages 239-252
Diffeomorphisms, Braids and Flows....Pages 253-270
Variational Principles, Geometry and Topology of Lagrangian-Averaged Fluid Dynamics....Pages 271-291
Front Matter....Pages 293-293
The Geometry of Reconnection....Pages 295-312
Euler Singularities from the Lagrangian Viewpoint....Pages 313-328
Analysis of a Candidate Flow For Hydrodynamic Blowup....Pages 329-341
Back Matter....Pages 343-347

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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.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Some Remarks on Topological Fluid Mechanics....Pages 3-10
Front Matter....Pages 11-11
Differential Geometry of Curves and Surfaces....Pages 13-33
Topology in Four Days....Pages 35-55
Elements of Classical Knot Theory....Pages 57-75
An Introduction to Knot Theory....Pages 77-104
Fluid Mechanics and Mathematical Structures....Pages 105-134
Front Matter....Pages 135-135
Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems....Pages 137-165
Streamline Patterns and Their Bifurcations Using Methods from Dynamical Systems....Pages 167-182
Topological Features Of Inviscid Flows....Pages 183-201
Geometric and Topological Aspects of Vortex Motion....Pages 203-228
Topology Bounds the Energy....Pages 229-238
Measures of Topological Structure in Magnetic Fields....Pages 239-252
Diffeomorphisms, Braids and Flows....Pages 253-270
Variational Principles, Geometry and Topology of Lagrangian-Averaged Fluid Dynamics....Pages 271-291
Front Matter....Pages 293-293
The Geometry of Reconnection....Pages 295-312
Euler Singularities from the Lagrangian Viewpoint....Pages 313-328
Analysis of a Candidate Flow For Hydrodynamic Blowup....Pages 329-341
Back Matter....Pages 343-347
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