## Topological Fluid Mechanics: Proceedings of the IUTAM Symposium, Cambridge, UK, 13-18 August, 1989There 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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Astrophys axial axisymmetric Batchelor boundary conditions chaotic advection component computations constant contour coordinates curl current sheet curves diffusion dimensional discontinuity displacement dissipation Dritschel dynamical systems eddies electric field energy enstrophy equation equilibrium Euler flows evolution field lines Figure finite fixed points flow field fluctuations Fluid Mech fluid particle flux surfaces force-free function Geophys gradient Hamiltonian initial instability integral invariant islands Kida Lagrangian Lagrangian turbulence layer linear magnetic diffusivity magnetic field magnetic flux magnetic reconnection magnetostatic mechanism mixing modes Moffatt motion Navier-Stokes equations nonlinear orbits Ottino parameters Parker perturbation Phys plane plasma Poincaré section potential vorticity problem quantities rational surface region resonance result Reynolds number rotation scalar scalar fields scale separatrix shown simulations solution spatial stable steady stochastic strain stream stream function streamlines structure symmetry tangent tensor theory three-dimensional topology tubes two-dimensional values vector velocity field vortex vorticity ZASLAVSKY zero