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.
Preface. Part I: Vortex Structure, Stability and Evolution. Simulation of vortex sheet roll-up: chaos, azimuthal waves, ring merger; R. Krasny, et al. Merging of non-symmetric Burgers vortices; K. Higgins, et al. Effect of stretching on vortices with an axial flow; M. Rossi, et al. Optimal two-dimensional perturbations in a stretched shear layer; S. le Dizès. Mixing and diffusion in planar vortices; K. Bajer, et al. Linear stability of a vortex ring revisited; Y. Fukumoto, Y. Hattori. Part II: Singular Vortex Filaments. Complexity measures of tangled vortex filaments; C.F. Barenghi, et al. Corotating five point vortices in a plane; T. Nakaki. On motion of a double helical vortex in a cylindrical tube; P.A. Kuibin. Intensive and weak mixing in the chaotic region of a velocity field; A. Gourjii. Evolution of the anisotropy of the quantum vortex tangle; T. Lipniacki. Motion of vortex lines in quantum mechanics; C. Sliwa, et al. Part III: Magnetic Structure, Topology and Reconnection. Magnetic dissipation: spatial and temporal structure; .Å. Nordlund. Current sheets in the sun's corona; E. Priest. A model for magnetic reconnection; H.K. Moffatt, R.E. Hunt. Reconnection in magnetic and vorticity fields; G. Hornig. Energy, helicity and crossing number relations for complex flows; R.L. Ricca helicity conservation laws; Z. Peradzynski. Part IV: Vortex Structure in Turbulent Flow. Vortex tubes, spirals, and large-eddy simulation of turbulence; D.I. Pullin. Low-pressure vortex; S. Kida, et al. Vortex bi-layers and the emergence of vortex projectiles in compressible accelerated inhomogeneous flows; N.J.Zabusky, S. Zhang. Interaction of localised packets of vorticity with turbulence; A. Leonard. Extraction of coherent vortex tubes in a 3-D mixing layer; K. Schneider, M. Farge. Vortex tubes in shear-stratified turbulent flows; M. Farge, et al. Coherent dynamics in wall turbulence; J. Jiménez. Some characteristics of the coherent structures in turbulent boundary layers; D. Poggi. Part IV: Finite-Time Singularity Problems. Discrete groups, symmetric flows and hydrodynamic blowup; R.B. Pelz Diffusion of Lagrangian invariants in the Navier-Stokes equations; P. Constantin. Evidence for singularity formation in a class of stretched solutions of the equations for ideal MHD; J.D. Gibbon, K. Ohkitani. Numerical evidence of breaking of vortex lines in an ideal fluid; E.A. Kuznetsov, et al. Sufficient condition for finite-time singularity and tendency towards self-similarity in a high-symmetry flow; C.S. Ng, A. Bhattacharjee. Finite time singularities in a class of hydrodynamic models; V.P. Ruban, et al. Part VI: Stokes Flow and Singular Behaviour Near Boundaries. Interactions between two close spheres in Stokes flow; M.L. Ekiel-Jeżewska, et al. Effective boundary conditions for creeping flow along a periodic rough surface; B. Cichocki, et al. Steady Stokes flow in a trihedral corner; V.S. Malyuga, A.M. Gomilko. 10 additional articles. After dinner speeches. List of Participants. Author Index. Topic Index.