Deterministic and Stochastic Dynamics of Some Geophysical Systems

研究者研究由有限维或无限维确定性或随机微分方程模拟的复杂地球物理流动现象。重点研究了随机地球物理流中的输运与混合、地球物理流中的非局域输运、地球物理模型的变分方法和随机地球物理流模拟。在输运和混合方面，通过计算逃逸概率和平均停留时间来量化地球物理飞行中的流体输运和混合。非局域输运研究——涡旋扩散系数随时间和空间变化时被动示踪剂或污染物在地球物理飞行中的平均主动输运和涡旋输运。在地球物理模型变分方法研究方面，利用变分演算的新兴技术，研究了稳定模式、时空周期模式和同斜运动，对旋转浅水动力学有了更好的理解。最后，他通过对随机风强迫和固有快波进行平均，推导出简化的大气-海洋耦合模式，量化了平均动力学的近似误差，并利用该平均模1研究了大气-海洋耦合系统的某些方面。海洋和大气中的地球物理流动以深刻的方式影响着我们的环境和社会。这个项目的动机是需要对环境和全球变化有更好的科学理解。研究者考虑随机或不确定的影响来描述地球物理流动。他开发了这两种数据。以及随机、数值和分析技术来理解复杂的地球物理流动现象。这项研究提高了我们对环境中污染物的扩散、运输和混合，以及地球物理流动的演化和模式形成的认识。本研究所产生的技术也可用于研究其他工程和工程领域的新兴问题

Duan9973204The investigator studies complex geophysical flow phenomena modeled by finite or infinite-dimensional deterministic or stochastic differential equations. The research focuses on transport and mixing in random geophysical flows, nonlocal transport in-geophysical flows, variational methods for geophysical models, and stochastic geophysical flow modelling. In the area of transport and mixing, the investigator quantifies fluid transport and mixing in geophysical flown by computing escape probability and mean resident time. The work on nonlocal transport studies-the mean advoctive and eddy transport of passive tracers or pollutants in geophysical flown, when the eddy diffusivity depends on time and space. For the research on variational methods for geophysical models, the investigator gains better ' uncftrotanding of the rotating shallow water dynamics, by studying steady patterns, spatial and temporal periodic patterns and homoclinic motions via emrging techniques in calculus of variations. Finally, he derives a simplified coupled atmosphere-ocean model by averaging over random wind forcing and over intrinsic fast waves, quantifies the approximation error of the averaged dynamics, and studies some aspects of the coupled atmosphere-ocean system using this averaged mod 1.The geophysical flows in the oceans and the atmosphere affect our environment and our society in profound ways. This project is motivated by the need of better scientific understanding of the environment and global change. The investigator takes random or uncertain effects into account to describe geophysical flows. He develops both daterministle.and stochastic, numerical and analytical techniques to understand complex geophysical flow phonanuma. This research improves our knowledge about dispersion, transport and mixing of pollutants in our environment, and about evolution and pattern formation of geophysical flows. The techniques resulting from this research are also useful in studying other emerging problem in engineering and