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 from the impressive progress in knot theory and geometric
topology on the one hand, and in mathematical and computational fluid
dynamics on the other.
This volume contains a wide-ranging collection of up-to-date, valuable
research papers written by some of the most eminent experts in the
field. Topics range from fundamental aspects of mathematical fluid
mechanics, including topological vortex dynamics and
magnetohydrodynamics, integrability issues, Hamiltonian structures and
singularity formation, to DNA tangles and knotted DNAs in sedimentation.
A substantial introductory chapter on knots and links, covering elements
of modern braid theory and knot polynomials, as well as more advanced
topics in knot classification, provides an invaluable addition to this
material.