Computational and Theoretical Problems in Fluid Mechanics, Meteorology and Oceanography

将讨论气象学、海洋学和流体力学的一些基本问题。将要涵盖的领域包括a)有限域模拟的开放边界条件，b)大气科学中平衡和不平衡模式的研究，c) Navier-Stokes方程和湍流的统计解。这些问题将通过先进的数学工具和高性能计算工具的强大组合来解决。从长远来看，本研究旨在改进这些现象在计算机上的数值模拟，对这些现象的理解对许多环境和能源问题至关重要。例如，问题a)对于提高当地天气预报的应用很重要，包括农业和航空。问题b)对理解大气的大尺度运动很重要；然而，所使用的技术（振荡平均）也需要在许多其他领域，特别是生物数学。问题c)本质上是更重要的，它们涉及到对湍流的理解，这是许多能源（和环境）研究中的一个严重障碍。就其性质而言，该提案具有很强的跨学科成分，高级地球物理学家直接参与主题a)和b)。该提案还具有很强的教育成分（研究生和博士后的跨学科培训）。

Some fundamental problems of meteorology, oceanography, and fluidmechanics will be addressed. The areas to be covered include a) The openboundary conditions for limited domains simulations, b) The study ofbalanced and unbalanced models in atmosphere sciences, c) Statisticalsolutions of Navier-Stokes equations and turbulence. These problems willbe addressed by a robust combination of advanced mathematical tools, andperformant computational tools. This study is aimed at improving, in the long range, the numericalsimulations on computer of these phenomena whose understanding isessential for many problems in environment and energy. For instanceproblem a) is important for improving local weather predictions withapplications including e.g. agriculture and aviation. Problems b) isimportant for understanding the large scale motion of the atmosphere;however the techniques used (averaging of oscillations) are also needed inmany other fields, in particular biomathematics. Problems c) are morefundamental in nature, they pertain to the understanding of turbulence,that is a serious impediment in many studies on energy (and environment).By its nature the proposal has a strong interdisciplinary component, withsenior geophysicists directly involved in topics a) and b). The proposalhas also a strong educational component (interdisciplinary training ofgraduate students and post docs).