Deterministic and Stochastic Dynamics of Some Geophysical Systems

调查人员研究由有限或无限维确定性或随机微分方程组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和混合、非局部输运的地球物理流、地球物理模型的变分方法和随机地球物理流模型。在输送和混合方面，研究人员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送和混合。非局部输运研究--当涡流扩散系数依赖于时间和空间时，被动示踪剂或污染物在地球物理飞行中的平均倡导和涡流输运。在地球物理模型的变分方法研究方面，研究者利用变分技术研究了旋转浅水动力的定常模式、时空周期模式和同宿运动，从而获得了较好的结果。最后，通过对随机风强迫和本征快波的平均，得到了一个简化的海气耦合模式，量化了平均动力学的近似误差，并利用该平均模式1研究了海洋-海洋耦合系统的某些方面。海洋和大气中的地球物理流动对我们的环境和我们的社会产生了深刻的影响。该项目的动机是需要更好地科学地了解环境和全球变化。研究人员考虑随机或不确定的影响来描述地球物理流动。他开发了日期、随机、数值和分析技术，以了解复杂的地球物理流动现象。这项研究提高了我们对污染物在环境中的扩散、传输和混合，以及地球物理流动的演化和模式形成的认识。该研究方法对研究工程中出现的其他问题也有一定的参考价值。

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