Tubes, Sheets and Singularities in Fluid Dynamics

1. Front Matter

   Pages i-xvi

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2. Vortex Structure, Stability and Evolution

   1. Simulation of vortex sheet roll-up: chaos, azimuthal waves, ring merger

      • Robert Krasny, Keith Lindsay, Monika Nitsche

      Pages 3-12

   2. Merging of non-symmetric Burgers vortices

      • Keith Higgins, M. S. Chong, Andrew Ooi

      Pages 13-18

   3. Effect of stretching on vortices with axial flow

      • Maurice Rossi, Ivan Delbende, Stéphane Le Dizès

      Pages 19-24

   4. Optimal two-dimensional perturbations in a stretched shear layer

      • Stéphane Le Dizès

      Pages 25-30

   5. Advection-diffusion of a passive scalar in the flow of a decaying vortex

      • Konrad Bajer, Andrew P. Bassom, Andrew D. Gilbert

      Pages 31-36

   6. Linear stability of a vortex ring revisited

      • Yasuhide Fukumoto, Yuji Hattori

      Pages 37-48

   7. The vortex-in-cell method for the study of three-dimensional vortex structures

      • Henryk Kudela, Pawel Regucki

      Pages 49-54

   8. L-transition from right- to left-handed helical vortices

      • Valery Okulov, Jens N. SØrensen, Lars K. Voigt

      Pages 55-60

   9. Dynamical behaviour of counter-curren axisymmetric shear flows

      • Xilin Xie, Weiwei Ma, Huiliang Zhou

      Pages 61-66

3. Singular Vortex Filaments

   1. Complexity measures of tangled vortex filaments

      • Carlo F. Barenghi, David C. Samuels, Renzo L. Ricca

      Pages 69-74

   2. Corotating five point vortices in a plane

      • Tatsuyuki Nakaki

      Pages 75-80

   3. On motion of a double helical vortex in a cylindrical tube

      • Pavel A. Kuibin

      Pages 81-86

   4. Intensive and weak mixing in the chaotic region of a velocity field

      • Alexandre Gourjii

      Pages 87-92

   5. Evolution of the anisotropy of the quantum vortex tangle

      • Tomasz Lipniacki

      Pages 93-98

   6. Motion of vortex lines in quantum mechanics

      • Cezary Sliwa, Iwo Bialynicki-Birula, Zofia Bialynicka-Birula, Tomasz Mloduchowski

      Pages 99-104

4. Magnetic Structure, Topology and Reconnection

   1. Magnetic dissipation: spatial and temporal structure

      • Åke Nordlund

      Pages 107-114

   2. Current sheets in the Sun’s corona

      • Eric Priest

      Pages 115-124

   3. A model for magnetic reconnection

      • H. K. Moffatt, R.E. Hunt

      Pages 125-132

   4. Reconnection in magnetic and vorticity fields

      • Gunnar Hornig

      Pages 133-138

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.

• Dissipation
• Navier-Stokes equation
• dynamics
• fluid dynamics
• magnetohydrodynamics
• mechanics
• mixing
• simulation
• stability
• turbulence
• turbulent flow
• vortices
• waves
• fluid- and aerodynamics

"...the authors merit considerable credit for so succinctly and effectively presenting and summarizing their contributions. [...] Finally, the editors, K. Bajer and H.K. Moffatt, and the publisher deserve praise for the typography of the papers, their uniformity of style and being easy on the eyes, and the brief time that was allowed to elapse between the oral presentations at the meeting and their appearance in print. This volume is an invaluable guide to the state of research in some of the most important areas of vortex dynamics at the commencement of this decade."
(Stanley A. Berger, University of California, Berkeley in AIAA Journal, 41:10 (2003)

• Institute of Geophysics, Warsaw University, Warsaw, Poland

  K. Bajer

• Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

  H. K. Moffatt

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