Deterministic and Stochastic Dynamics of Some Geophysical Systems

段9973204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。研究重点是随机地球物理流的运输和混合，地球物理流的非局部运输，地球物理模型的变分方法和随机地球物理流建模。在输运和混合方面，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运和混合。非定域输运的研究工作-被动示踪剂或污染物在地球物理流中的平均对流和涡旋输运，其中涡旋扩散系数依赖于时间和空间。在地球物理模型的变分方法研究中，利用变分法中的插值技术，研究了浅水旋转运动的稳定模式、时空周期模式和同宿运动，较好地揭示了浅水旋转运动的动力学特征。最后，他通过对随机风强迫和内禀快波进行平均，导出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，并利用这个平均模1研究了海气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社会产生了深刻的影响。该项目的动机是需要更好地科学了解环境和全球变化。研究者考虑随机或不确定的影响来描述地球物理流。他开发了datemistle和随机，数值和分析技术，以了解复杂的地球物理流动phonanuma。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的演变和模式形成的认识。从这项研究中得到的技术也有助于研究工程中的其他新兴问题，

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