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Geometry and Topology of Fluid Flows

4th September 2000 to 22nd December 2000

Organisers: H Aref (Urbana-Champaign), T Kambe (Tokyo), RB Pelz (Rutgers), RL Ricca (UCL)

Programme Theme

The goal of this programme is to bring the disciplines of fluid mechanics and magneto-hydrodynamics (MHD) together with powerful mathematical techniques in geometry and topology.

Topics will include:

  • Integrals of motion and conservation laws and their relation to the geometrical and topological structure of space;

  • Finite-time singularities in hydrodynamics and MHD;

  • Geometric and group-theoretic approaches to hydrodynamics with applications to stability, mixing and the global structure of complex flows;

  • Topological description of 3D velocity and vorticity fields;

  • Fluid kinematics and chaotic advection.

  • The geometrical and topological view of fluid mechanics and MHD tends to be more global and based on a Lagrangian representation of the flow, in contrast to the local, coordinate-based, Eulerian representation currently used in most analytical and numerical treatments of fluid mechanical problems.

    Because of the potential mutual benefits of connecting the field of fluid dynamics more closely to geometry, topology, dynamical systems, analysis and PDEs, pedagogical workshops and working groups are planned as well as advanced conferences.

    Historically, fluid mechanics has both utilized and inspired progress in mathematics. The programme will continue this tradition.

Final Scientific Report: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons