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

小行星9625795 研究员继续研究偏微分方程的理论和应用，以解决湍流和大气/海洋科学问题。 他使用物理建模，渐近方法，随机技术，严格的数学理论和大规模计算相结合，以产生新的洞察力物理现象。 本计画研究两个领域的特定主题：1）紊流反应扩散方程式，以及2）地球物理流中快速、随机及统计波的平均。 第一部分的工作涉及发展新的随机、渐近和计算方法，用于研究湍流扩散和湍流反应扩散方程的标度行为，其中速度场具有许多时空尺度。 在大气/海洋科学的潜在应用，包括示踪剂的中尺度放大和海洋云顶边界层湍流混合在这里描述。 第二区的工作涉及四个不同的地球物理流专题：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，还没有得到很好的理解。 该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.