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The emergence of large-scale coherent structure under small-scale random bombardments. (English) Zbl 1099.86001
Mathematical justification of the emergence of large-scale coherent structure is provided in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. The analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large-scale structure based on equilibrium statistical mechanics.

MSC:
86A10 Meteorology and atmospheric physics
86A05 Hydrology, hydrography, oceanography
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
76F02 Fundamentals of turbulence
76M35 Stochastic analysis applied to problems in fluid mechanics
82B99 Equilibrium statistical mechanics
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