Nonlinear Phenomena in Fluid Dynamics and Related PDE's with Applications to Atmosphere/Ocean Science

研究者继续研究偏微分方程在湍流和大气/海洋科学问题中的理论和应用。该项目重点关注大气/海洋科学中的问题，涉及四个研究领域：1)分层混合、不稳定和湍流；2)开放海洋对流统计新理论；3)热带气象中的非线性波；地球物理流动的非线性随机模拟。解决所有这些问题的方法涉及到渐进分析、数值计算和理论数学分析的复杂结合，以深入了解这些复杂而重要的现象。固有的非线性或统计方法强调贯穿始终。该项目，特别是后三个主题，强调应用数学家、大气科学家和气象学家之间的多学科合作和思想交流。大气和海洋的行为是复杂的，而且还没有得到很好的理解。该项目涉及使用新颖而复杂的数学理论和技术来提高我们对气候重要特征的理解，如厄尔尼诺现象和北大西洋的热量向极地输送。这样的理解可以提高对天气、气候和环境现象的预测。该方法涉及应用数学家、大气科学家和海洋学家之间的多学科合作和思想交流。该项目由数学科学部应用数学和计算数学研究方向、海洋科学部物理海洋学研究方向和大气科学部大尺度动力气象学研究方向资助。

Majda9972865 The investigator continues studies of the theory andapplications of partial differential equations to problems inturbulence and atmosphere/ocean science. The project emphasizesproblems in atmosphere/ocean science involving four researchareas:1) Stratified Mixing, Instability and Turbulence;2) Novel Statistical Theories for Open Ocean Convection;3) Nonlinear Waves in Tropical Meteorology;4) Nonlinear Stochastic Modelling for Geophysical Flows.The approach to all of these issues involves a sophisticatedcombination of asymptotic analysis, numerical computation, andtheoretical mathematical analysis to gain insight into thesecomplex and important phenomena. Inherently nonlinear orstatistical methods are emphasized throughout. The project,especially in the latter three topics, stressesmulti-disciplinary collaboration and exchange of ideas betweenapplied mathematicians, atmospheric scientists, andoceanographers. Behaviors of the atmosphere and ocean are complex and notwell understood. The project involves using novel andsophisticated mathematical theories and techniques to improveour understanding of important features of the climate, suchas El Nino, and the poleward transport of heat in the NorthAtlantic. Such an understanding could lead to improvedpredictions of weather, climate, and environmental phenomena.The approach involves multi-disciplinary collaboration andexchange of ideas between applied mathematicians, atmosphericscientists, and oceanographers. The project is supported by theApplied Mathematics and Computational Mathematics programs in theDivision of Mathematical Sciences, by the Physical Oceanographyprogram in the Division of Ocean Sciences, and by the Large-ScaleDynamic Meteorology program in the Division of AtmosphericSciences.