Lectures on Topological Fluid Mechanics

• Main Authors: Berger, Mitchell A. (Author), Kauffman, Louis H. (Author), Khesin, Boris (Author), Moffatt, H. Keith (Author), Ricca, Renzo L. (Editor), Sumners, De Witt (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009.
• Series: Lecture Notes in Mathematics, 1973
• Subjects: Physics.; Dynamics.; Ergodic theory.; Functions of complex variables.; Topology.; Continuum physics.; Classical Continuum Physics.; Dynamical Systems and Ergodic Theory.; Several Complex Variables and Analytic Spaces.

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting f...

Table of Contents:

• Braids and Knots
• Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants
• Tangles, Rational Knots and DNA
• The Group and Hamiltonian Descriptions of Hydrodynamical Systems
• Singularities in Fluid Dynamics and their Resolution
• Structural Complexity and Dynamical Systems
• Random Knotting: Theorems, Simulations and Applications.