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Introduction: Recent advances in vortex dynamics and turbulence

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  • As the subject of vortex dynamics and its applications to two-dimensional fluid flows mature, we have witnessed an explosion in the number of research works in the field. It is the aim of this special issue to collate some of this recent advance and at the same time point to several new directions. One of these new directions is the re-entry of equilibrium statistical mechanics into the field. Many years after the classical papers of Onsager, Kraichnan, Leith, Montgomery, Lundgren, Pointin and Chorin, we are at a point where the Kraichnan, Batchelor and Leith energy-enstrophy theories in two-dimensional turbulence have been studied from new analytical and numerical points of views. A second emerging direction is in the use of a particular type of large-scale scientific computing in vortex statistics, namely Monte-Carlo simulations of vortex gas in the plane and sphere which explore an extended range of parameter values such as temperature and chemical potentials.
    Mathematics Subject Classification: 82F, 76F, 60G.


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