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

研究人员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。该项目强调大气/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)新的公海对流统计理论；3)热带气象中的非线性波；4)地球物理流动的非线性随机模拟。所有这些问题的方法都涉及到渐近分析、数值计算和理论数学分析的复杂组合，以深入了解这些复杂而重要的现象。自始至终都强调固有的非线性或统计学方法。该项目，特别是在后三个主题中，强调应用数学家、大气科学家和海洋学家之间的多学科合作和思想交流。大气和海洋的行为是复杂的，人们对此知之甚少。该项目涉及使用新颖和复杂的数学理论和技术来提高我们对气候的重要特征的理解，例如厄尔尼诺现象和北大西洋向极地输送的热量。这样的理解可以改善对天气、气候和环境现象的预测。这种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。该项目得到了数学科学部的应用数学和计算数学计划、海洋科学部的物理海洋学计划和大气科学部的大尺度动力气象计划的支持。

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.