Mathematical Sciences: Nonlinear Phenomena in Fluid Dynamics and Related P.D.E.'s with Applications to Atmosphere/Ocean Science

9625795 Majda研究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。他将物理建模、渐近方法、随机技术、严格的数学理论和大规模计算相结合，对物理现象产生了新的见解。本项目研究两个领域的特定主题：1)湍流反应扩散方程，2)地球物理流中快速、随机和统计波的平均。领域1的工作涉及发展新的随机、渐近和计算方法，用于研究速度场具有许多时空尺度的湍流扩散和湍流反应扩散方程的标度行为。这里描述了在大气/海洋科学中的潜在应用，包括中尺度示踪剂的放大和海洋云顶边界层中的湍流混合。区域2的工作涉及关于地球物理流的四个不同主题：A)快速重力波的平均和平衡动力学的障碍；B)大尺度相干结构和南极绕极流的统计理论；C)斜压不稳定和地转湍流；D)热带强中尺度对流事件的参数化。主题C)和D)的研究涉及与普林斯顿GFDL和博尔德NCAR的大气/海洋科学家的具体合作。大气和海洋的行为是复杂的，还没有被很好地理解。这个项目旨在更好地了解大气和海洋流动。这样的理解可以改善天气、气候和环境现象的预测。

9625795 Majda The investigator continues research on the theory and applications of partial differential equations to problems in turbulence and atmosphere/ocean science. He uses a combination of physical modelling, asymptotic methods, stochastic techniques, rigorous mathematical theory, and large scale computing to yield new insight into physical phenomena. This project studies specific topics in two areas: 1) turbulent reaction diffusion equations, and 2) averaging over fast, random, and statistical waves in geophysical flows. The work in area 1 involves the development of new stochastic, asymptotic, and computational methods for studying scaling behavior in turbulent diffision and turbulent reaction diffusion equations where the velocity fields have many spatio-temporal scales. Potential applications to atmosphere/ocean science are described here, including tracer scale up in the mesoscale and turbulent mixing in marine cloud topped boundary layers. The work in area 2 involves four distinct topics regarding geophysical flows: A) averaging over fast gravity waves and the obstructions to balanced dynamics; B) statistical theories for large scale coherent structure and the Antarctic circumpolar current; C) baroclinic instability and geostrophic turbulence; D) parameterization of strong mesoscale convection events in the tropics. The research in topics C) and D) involves specific collaborations with atmosphere/ocean scientists at GFDL in Princeton and at NCAR in Boulder. Behaviors of the atmosphere and ocean are complex and not well understood. This project aims at a better understanding of atmosphere and ocean flows. Such an understanding could lead to improved predictions of weather, climate, and environmental phenomena.