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Topological Fluid Dynamics (IUTAM Symposium)


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23rd July 2012 to 27th July 2012

International Scientific Committee: Yoshifumi Kimura (Nagoya)(Chair), Konrad Bajer (Warsaw)(Co-Chair), Mark Stremler (Virginia Tech.), Peter Constantin (Univ.of Chicago), David Dritschel (St Andrews), Keith Moffatt (Cambridge)(Co-Chair), Timothy Pedley (IUTAM Bureau Representative).

Workshop Theme

In an ideal fluid, vortex lines are transported with the fluid and their topology is conserved for so long as the field remains smooth; in particular, the helicity of the flow, providing a measure of the degree of linkage of vortex lines, is conserved. A central unsolved problem concerns the question of whether the vorticity field does remain smooth for all time under Euler evolution, or whether (alternatively) singularities at finite time may develop. Three-dimensional vortex interactions lie at the heart of this problem. Weak (viscous) diffusion modifies the evolution, but does not necessarily suppress singularity formation. Viscosity allows vortex reconnexion and therefore change of topology; this process provides for the finite rate of dissipation of energy in turbulence even in the limit of vanishing viscosity.

An IUTAM Symposium (Topological Fluid Dynamics I) was held in Cambridge UK in 1989, when the subject was in its infancy.[Topological Fluid Dynamics, Ed. H.K.Moffatt & A.Tsinober, CUP, 1990].

The main topics covered then were:

  • Flow kinematics and Lagrangian chaos;
  • Dynamo theory;
  • Relaxation and formation of discontinuities;
  • Two-dimensional and quasi-two-dimensional flows;
  • Topology of three-dimensional flows;
  • Vortex interaction and reconnexion;
  • Homogeneous turbulence;
  • Inhomogeneous turbulence and convective flows.

These topics remain as relevant today as they were in 1989; we propose however to focus primarily on the following topics, which are of particular current interest:

  • Steady vortical solutions of the Euler equations and their stability;
  • Interaction of vortex pairs, vortex rings, etc
  • Vortex reconnection by viscosity;
  • The finite-time singularity problem for Euler and Navier-Stokes;
  • Application to the structure of turbulence and the process of turbulent dissipation.

It is with great sadness that the International Scientific Committee of the forthcoming workshop announces the death of fellow committee member and Reynolds Metals Professor in the Department of Engineering Science and Mechanics at Virginia Tech, Hassan Aref, who died unexpectedly on 10 September 2011 aged 60.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons