By H. K. Moffatt (ed.), G. M. Zaslavsky (ed.), P. Comte (ed.), M. Tabor (ed.)
The intimate courting among three-d vortex dynamics and topology was once well-known as early as 1869 through Lord Kelvin, whose discoveries in fluid dynamics ended in the improvement of knot conception as a well-defined department of topology. it's only within the final 25 years, even though, with the parallel stimulus of the improvement of magnetohydrodynamics in astrophysical and geophysical contexts, that the good capability of topological suggestions in fluid and plasma has been totally well-known. This quantity presents a complete survey of this interdisciplinary box. The appropriate historical past in knot idea, stream kinematics, dynamo idea, and leisure lower than topological constraints, is equipped through the introductory chapters of half I. those topics are constructed within the next papers that are grouped below the next headings: half II: rest and minimal power States; half III: Helicity, Linkage, and circulate Topology; half IV: The Euler Equations: Extremal houses and Finite-Time Singularities; half V: Vortex Interactions and the constitution of Turbulence; half VI: Chaos, Instability, and Dynamo idea
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