........ published in NEWSLETTER # 48
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........ published in NEWSLETTER # 48
TOPOLOGICAL ASPECTS OF THE DYNAMICS OF FLUIDS AND PLASMAS
by Professor H.K. Moffatt, University of Cambridge, Cambridge (U.K.)
There is a natural affinity between the scientific discipline of fluid dynamics (which deals with the dynamics of continuous deformation) and the mathematical discipline of topology, which is concerned with properties of objects that remain invariant under continuous deformation. This affinity was perceived by Lord Kelvin, whose fluid dynamical investigations in 1968 provided the initial motivation for the development of knot theory as a recognizable branch of modern topology.
Developments in fluid dynamics and also in plasma dynamics (or magnetohydrodynamics) over the past 30 years have focussed new attention on topological aspects of the problems that arise, particularly when dissipative processes (viscosity and resistivity) are weak, so that vortex and/or magnetic structures are 'frozen in the fluid'. Such problems arise in the classical fluid mechanics of vorticity, in the modern approach to turbulence, in the magnetodynamics of thermonuclear fusion plasmas and of the solar atmosphere, and in the fundamental (dynamo) process by which magnetic fields are generated in cosmic bodies.
This volume (NATO ASI SERIES E218) treats all these topics, together with a full introduction to the results of knot theory that are applicable in these fields. The first 150 pages of the volume (Part I) contain introductory chapters by authorities in fluid and plasma dynamics and knot theory. These are followed by papers grouped under the following headings:
_Relaxation and Minimum Energy States
_Helicity, Linkage and Flow Topology
_The Euler Equations: Extremal Properties and Finite Time Singularities
_Vortex Interactions and the Structure of Turbulence
_Chaos, Instability and Dynamo Theory
The volume recalls James Clerk Maxwell's immortal words (c. 1873):
My soul's an amphicheiral knot Upon a liquid vortex wrought By Intellect, in the Unseen residing ...
The wheel has now turned full cycle, and the preoccupations of Kelvin and Maxwell with many more recent inflexions, are once again in the forefront of research in fluid and plasma dynamics. This volume is essential reading for anyone wishing to enter this exciting field of investigation.
Reference books: C337, C375, E178, E218