7 August to 25 August 2000

**Organisers**: CF Barenghi (*Newcastle*), RJ Donnelly (*Oregon*), WF Vinen (*Birmingham*)

Quantum effects dominate the behaviour of liquid helium and other Bose-Einstein condensed fluids. These effects, which include the existence of discrete quantized vortices and the quantization of hydrodynamic circulation, place severe restrictions on the types of flow that can take place in the superfluid phase. Important aspects of the behaviour of the quantum vortices are still not understood. Turbulent flows in such systems are also of great interest, not only in their own right, but also because, surprisingly, they often appear to share important characteristics with those found in classical fluids. The recent discovery of Bose-Einstein condensation in alkali metal vapours at extremely low temperatures adds to the interest in these types of problem.

The aim of this Short Programme is to encourage cross-fertilization by bringing together for intensive cross-disciplinary discussions physicists and mathematicians with backgrounds ranging from quantum fluids to classical fluid mechanics and magnetohydrodynamics, and from applied mathematics to condensed matter and atomic physics.

Isaac Newton Institute for Mathematical Sciences Quantized Vortex Dynamics and Superfluid Turbulence 7 August to 25 August 2000 Organisers: CF Barenghi (Newcastle), RJ Donnelly (Oregon), WF Vinen (Birmingham) Quantum effects dominate the behaviour of liquid helium and other Bose-Einstein condensed fluids. These effects, which include the existence of discrete quantized vortices and the quantization of hydrodynamic circulation, place severe restrictions on the types of flow that can take place in the superfluid phase. Important aspects of the behaviour of the quantum vortices are still not understood. Turbulent flows in such systems are also of great interest, not only in their own right, but also because, surprisingly, they often appear to share important characteristics with those found in classical fluids. The recent discovery of Bose-Einstein condensation in alkali metal vapours at extremely low temperatures adds to the interest in these types of problem. The aim of this Short Programme is to encourage cross-fertilization by bringing together for intensive cross-disciplinary discussions physicists and mathematicians with backgrounds ranging from quantum fluids to classical fluid mechanics and magnetohydrodynamics, and from applied mathematics to condensed matter and atomic physics. Issues that will be surveyed and discussed include the dynamical behaviour of individual quantum vortices, including boundary conditions, frictional forces and reconnections; the use of the non-linear Schrödinger equation to describe the flow of helium, including turbulence, at very low temperatures; the effect of a (possibly turbulent) normal fluid; the observed similarity between classical and quantum turbulence; and the possibility that the study of quantum turbulence may be applied to the understanding of conventional flow at very high Reynolds numbers. The emphasis will be on theory and computation, but in close contact with experiment.