H.K. Moffatt – författare

The intimate relationship between three-dimensional vortex dynamics and topology was recognized as early as 1869 by Lord Kelvin, whose discoveries in fluid dynamics led to the development of knot theory as a well-defined branch of topology. It is only in the last 25 years, however, with the parallel stimulus of the development of magnetohydrodynamics in astrophysical and geophysical contexts, that the great potential of topological techniques in fluid and plasma dynamics has been fully recognized. This volume provides a comprehensive survey of this interdisciplinary field. The relevant background in knot theory, flow kinematics, dynamo theory, and relaxation under topological constraints, is provided by the introductory section. These themes are developed in the subsequent papers.

Modern experiments and numerical simulations show that the long-known coherent structures in turbulence take the form of elongated vortex tubes and vortex sheets. The evolution of vortex tubes may result in spiral structures which can be associated with the spectral power laws of turbulence. The mutual stretching of skewed vortex tubes, when they are close to each other, causes rapid growth of vorticity. Whether this process may or may not lead to a finite-time singularity is one of the famous open problems of fluid dynamics. This book contains the proceedings of the NATO ARW and IUTAM Symposium held in Zakopane, Poland, 2-7 September 2001. The papers presented, carefully reviewed by the International Scientific Committee, cover various aspects of the dynamics of vortex tubes and sheets and of their analogues in magnetohydrodynamics and in quantum turbulence. The book should be a useful reference for all researchers and students of modern fluid dynamics.

The intimate relationship between three-dimensional vortex dynamics and topology was recognized as early as 1869 by Lord Kelvin, whose discoveries in fluid dynamics led to the development of knot theory as a well-defined branch of topology. It is only in the last 25 years, however, with the parallel stimulus of the development of magnetohydrodynamics in astrophysical and geophysical contexts, that the great potential of topological techniques in fluid and plasma has been fully recognized. This volume provides a comprehensive survey of this interdisciplinary field. The relevant background in knot theory, flow kinematics, dynamo theory, and relaxation under topological constraints, is provided by the introductory chapters of Part I. These themes are developed in the subsequent papers which are grouped under the following headings: Part II: Relaxation and Minimum Energy States; Part III: Helicity, Linkage, and Flow Topology; Part IV: The Euler Equations: Extremal Properties and Finite-Time Singularities; Part V: Vortex Interactions and the Structure of Turbulence; Part VI: Chaos, Instability, and Dynamo Theory.