Topological Fluid Mechanics: Proceedings of the IUTAM Symposium, Cambridge, UK, 13-18 August, 1989

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Cambridge University Press, Apr 12, 1990 - Mathematics - 805 pages
There has been developing interest in the aspects of fluid mechanics and of magnetohydrodynamics that can be properly described as topological, rather than exclusively analytical in character. This book contains the proceedings of the IUTAM symposium on Topological Fluid Mechanics held at Cambridge UK, 13-18 August, 1989. Topics covered include the kinematic and dynamical problems in laminar and turbulent flows, as well as the range of problems that arise from the magnetohydrodynamics of highly conducting flows. The papers presented cover all approaches; theoretical, computational and experimental, and each paper has been edited by a member of the International Scientific Committee.
 

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Contents

Vortex Interaction and Reconnection 467
4
Experimental and Computational
13
Inhomogeneous Turbulent and 647
33
On Chaotic Flow around the Kida Vortex
34
Numerical Simulation of the Lagrangian Flow Structure in a
54
Attractors in Problems of Magnetohydrodynamics 782
73
The Geometry of Lagrangian Orbits
75
Homogeneous Turbulence 547
81
Island Formation in Magnetostatics and Euler Flows
206
Vortex Filaments and Turbulence Theory 607
212
Steady Motion with Helical Symmetry at Large Reynolds Number
216
General Magnetic Reconnection in 3D Systems
225
Spontaneous Formation of Electric Current Sheets in Astrophysical
235
Current Sheets in Linetied Magnetic Fields with Pressure
244
Flux Constraints on Magnetic Energy Release in a Highly Conducting
251
Distortion of Material Surfaces in Steady and Unsteady Flows 617
253

Symmetries and Topological Transitions of the 689
85
Algorithms for Classification of Turbulent Structures
95
Knots for Threedimensional Vector Fields 787
104
Chaotic Advection by a Point Vortex in a Semidisk
105
SelfExcitation and Reconnections of Magnetic Field in Random Flow
117
Dynamo Action at Large Magnetic Reynolds Number in Spatially
127
Generation of Steady and Oscillatory Magnetic Fields Through Inverse
138
The Helical MHD Dynamo
147
Relations Between Helicities in MeanField Dynamo Models
157
Boundary Effects on the MHD Dynamo in Laboratory Plasmas
164
High Velocities in QuasiStatic Magnetic Singularities
179
Current Sheet Formation in Magnetostatic Equilibria
187
Minimum Dissipation States and Vortical Flow in MHD
196
Coherent Structures Homoclinic Cycles and Vorticity Explosions in
265
List of Participants 789
273
Isovortical Constraints on the StatisticalDynamical Behaviour of
278
The Survivability of Vortices in a TwoDimensional Fluid at
288
Isovortical Relaxation to Stable TwoDimensional Flows
294
A Simple Hydrodynamic System with Oscillating Topology
304
SmallScale Structures of TwoDimensional MHD Turbulence
315
The FiniteTime Formation of Singularities on the Boundaries of
325
Steadily Rotating Quasigeostrophic Vortices in a Stratified Fluid
335
Nonlinear Vorticity or Potential Vorticity Inversion
355
Topological Changes of Axisymmetric and Nonaxisymmetric
372
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