01-7 IUTAM Symposium on Tubes, Sheets and Singularities in Fluid Dynamics
Zakopane, Poland, September 2-7, 2001
a) Scientific Committee
K. Bajer (Poland, Co-Chair), M. Farge (France), J. Jimenez (Spain), S. Kida (Japan),
R. Krasny (USA), H.K. Moffatt (UK, Co-Chair, IUTAM repres.), A. Nordlund
(Denmark), A.E. Perry (Australia), D.I. Pullin (USA)
b) Short summary of scientific progress achieved
Some fifty years ago coherent structures in turbulence were discovered by statistical
analysis of the velocity measurements, but their geometrical form remained unknown for
more than three decades. Direct numerical simulations (DNS) and skilful visualisation
show them to be elongated vortices whose cross-sectional structure seems to be
controlled by viscosity, but the dynamics of their creation still remains a puzzle.
Filaments can result from instabilities of vortex sheets and various aspects of this process
in both steady and unsteady sheets, possibly stretched in either direction, are of great
interest. The new evidence (from DNS) inspired much theoretical work, both on the
steady state, and on the interaction and stability of vortices. Interaction of vortex
filaments results in spirals, which are the structures in physical space that can be
associated with the spectral power laws of turbulence. Such interactions also produce
extremely strong gradients of either velocity or its derivatives which, in the high
Reynolds number limit, control the process of viscous energy dissipation, and which may
lead to the formation of singularities. The existence of the finite-time singularities in the
solutions of the Navier-Stokes equation is one of the fundamental Millennium Prize
Problems listed by Clay Mathematics Institute (www.claymath.org).
Vortex filaments are in many ways analogous to the magnetic flux tubes, which are
coherent structures, found in magnetohydrodynamics (MHD), especially prominent in
the solar dynamo process. Interacting flux tubes create current sheets and, in the ideal
limit, tangential discontinuities - the generic MHD singularities which form in the
process of relaxation towards magnetostatic equilibrium. The conditions in the solar
photosphere are nearly ideal, so the topological constraints imposed by non-dissipative
MHD are important, as are the singularities where these constraints are most easily
Both slender vortices and flux tubes can have topologically complex form (e.g. knotted
or linked) and the mathematical apparatus necessary to describe and classify the topology
is the same. Their steady states are mathematically equivalent, but there are important
differences in their evolution. The influence of the topology on the dynamics provides an
important common ground.
All these aspects of coherent structures were covered in four days devoted to `Vortices’,
`MHD’, `Turbulence’ and `Singularities’. The last session, `Other topics’, included
papers on the new perspectives and problems hitherto regarded as separate from the main
theme yet either related by the similarity of the methods employed or making an
interesting comparison or analogy.
The details of the program can be found on www.igf.fuw.edu.pl/IUTAM
c) Countries represented and number of participants
Australia (2), France (7), Poland (15), Ukraine (2), China (1), Germany (3), Russia (9),
UK (7), Denmark (1), Japan (4), Spain (2), USA (9)
d) Publication of Proceedings of the Symposium
A volume containing approximately 40 papers will be published by Kluwer in 2002.
e) Financial support
The following institutions kindly provided the essential financial support
• International Union of Theoretical and Applied Mechanics (USD 5000 = Zl 19 926)
• NATO (BEF 1 000 000 = Zl 88 500)
• US Office of Naval Research, International Field Office (USD 10 000 = Zl 39 500)
We are grateful to Warsaw University, Department of Physics, for the use of their
facilities during the preparation of the Symposium.
f) Scientific program (All presentations were oral)
B.J. Bayly, Asymptotic structure of fast dynamo eigenfunctions.
P. Constantin, Near identity transformations for the Navier-Stokes equations.
S.C. Cowley, Singularity formation in MHD.
S.J. Cowley, An exponentially small massacre of BLT and DNS.
M. Farge, K. Schneider, Wavelet approach to study tubes, sheets and singularities in
U. Frisch, Singularities and the distribution of density in the Burgers/adhesion model.
Y. Fukumoto, Y. Hattori, Stability of vortex ring revisited.
J.D. Gibbon, A study of singularity formation in a class of solutions of the Euler & ideal
J. Jimenez, Coherent dynamics in near-wall turbulence.
S. Kida, Life, structure, and dynamical role of vortical motion in turbulence.
R. Krasny, K. Lindsay and M. Nitsche, Vortex sheet roll-up: chaos and ring merger.
A. Leonard, Interaction of localized packets of vorticity with turbulence.
H.K. Moffatt, R. Hunt, A model for magnetic reconnection.
A. Nordlund, K. Galsgaar, The structure of dissipating and quiescent magnetic fields.
R. Pelz, Point collapse in octahedral, vortical flows.
R.E. Priest, Current sheets in the Sun's corona.
D.I. Pullin, Vortex tubes, spirals and large-eddy simulation.
N. Zabusky, Vortex layers and `projectiles' in accelerated inhomogeneous (Richtmayer-
Meshkov and Rayleigh-Taylor) flows: Emerging 2D and 3D structures in
shocked/interface, curtain-&-bubble interactions.
P.M. Akhmetev, A high-order analog of the helicity number for a pair of divergent-free
K. Bajer, A. P. Bassom and A. D. Gilbert, Mixing and diffusion in planar vortices.
C.F. Barenghi, D. C. Samuels and R. L. Ricca, Complexity measures of tangled vortex
A. Bhattacharjee, C. S. Ng, Sufficient condition for finite-time singularity in a highly
symmetric Euler flow.
A. Bhattacharjee, Z. W. Ma, C. S. Ng and X. Wang, Current singularities in two and
C. Brun, J. Jiménez, Detection of vortical structures in inertial and dissipation ranges.
B. Cichocki, P. Szymczak and F. Feuillebois, Effective boundary condition for creeping
M. Ekiel-Jezewska, N. Lecoq, R. Anthore, F. Bostel and F. Feuillebois , Interactions
between two close spheres in Stokes flow.
T. Gomez, M. Larcheveque, H. Politano and A. Pouque, Spiral small-scale structures in
compressible turbulent flows.
A.A. Gourji, Intensive and weak mixing in the chaotic region of velocity field.
R. Herczynski, Historical remarks on fluid mechanics.
K. Higgins, M. S. Chong and A. Ooi, Merging of non--symmetric Burgers vortices.
G. Hornig, Reconnection in magnetic and vorticity fields.
P.A. Kuibin, On motion of a double helical vortex in a cylindrical tube.
E.A. Kuznetsov, Collapse of vortex lines in hydrodynamics and its sequences.
S. Le Dizes, Optimal two-dimensional perturbations in a stretched shear layer.
T. Lipniacki, Evolution of the anisotropy of the quantum vortex tangle.
V.S. Malyuga, A. M. Gomilko, Steady Stokes flow in a trihedral corner.
C. Mayer, G. Hornig, Higher order topological invariants.
Muravnik, A.B., On Cauchy problem for quasi-linear singular parabolic equations with
T. Nakaki, Co-rotating five point vortices in a plane.
V.L. Okulov, J. N. Sorensen and L. K. Voigt, L-transition from right- to left-handed
V. Pankrashkin, S. Yu. Dobrokhotov and E. S. Semenov, On Maslov conjecture about
the structure of weak point vortical singularities of the shallow water equations.
Z. Peradzynski, On helicity conservation laws.
R.L. Ricca, Energy, helicity and crossing number relations for complex flows.
M. Rossi, I. Delbende and S. Le Dizes, Effect of stretching on vortices with axial flow: a
three-dimensional stability study.
V.P. Ruban, D. I. Podolsky and J. J. Rasmusen, Finite time singularities in a class of
K. Schneider, M. Farge, Extraction and analysis of coherent vortex tubes in turbulent
C. Sliwa, Motion of vortex lines in the hydrodynamic formulation of quantum mechanics.
A.D. Verga, M. Abid, Stability of vortex sheet roll-up.
X. Xie, W. W. Mar and H. L. Zhou, Helical structure in axisymmetric shear layer flows.
V. Zheligovsky, O. Podvigina, An example of development of singularity in a solution to
the force-free Euler equation.
Report composed by Konrad Bajer & Keith Moffat