Mathematics Colloquia and Seminars

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I will give an overview of some of the non-linear wave phenomena that occur on the largest length scales in the tropical troposphere - i.e. the weather layer of the atmosphere near the equator which is strongly forced by water condensation. There are two important asymptotic regimes. In the first, we have discovered a new, multi-scale, nonlinear models for an organized weather phenomenon called the Madden-Julian oscillation. In the second, we have derived a new set of non-linearly coupled, dispersive PDEs which describe the exchange of energy between the tropics and middle-latitudes. This theory elucidates an crucial phenomenon necessary for improving 2 week weather forecasting in the mid-latitudes (i.e. over the continental U.S.). I will also discuss interesting, open questions which have been spawned by this research.