Deterministic and Stochastic Dynamics of Some Geophysical Systems

端9973204研究了由有限或无限维确定性或随机微分方程组现象模拟的复杂地球物理流动。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部输运、地球物理模型的变分方法和随机地球物理流模型。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流动中的流体输运和混合。非局地输运方面的工作研究了被动示踪剂或污染物在地球物理流动中的平均平流和涡动输送，其中涡动扩散系数依赖于时间和空间。对于地球物理模型的变分方法的研究，研究人员通过运用变分的新兴技术研究定常模式、空间和时间周期模式以及同宿运动，从而更好地了解旋转浅水动力学。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，量化了平均动力的近似误差，并用这个平均模式研究了海-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对环境和全球变化进行科学理解。调查者考虑随机或不确定的影响来描述地球物理流。他开发了确定性和随机性、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。这项研究产生的技术对研究工程和应用科学中其他新出现的问题也很有用。

Duan9973204 The investigator studies complex geophysical flow phenomenamodeled by finite or infinite-dimensional deterministic orstochastic differential equations. The research focuses ontransport and mixing in random geophysical flows, nonlocaltransport in geophysical flows, variational methods forgeophysical models, and stochastic geophysical flow modeling. Inthe area of transport and mixing, the investigator quantifiesfluid transport and mixing in geophysical flows by computingescape probability and mean resident time. The work on nonlocaltransport studies the mean advective and eddy transport ofpassive tracers or pollutants in geophysical flows, when the eddydiffusivity depends on time and space. For the research onvariational methods for geophysical models, the investigatorgains better understanding of the rotating shallow waterdynamics, by studying steady patterns, spatial and temporalperiodic patterns and homoclinic motions via emerging techniquesin calculus of variations. Finally, he derives a simplifiedcoupled atmosphere-ocean model by averaging over random windforcing and over intrinsic fast waves, quantifies theapproximation error of the averaged dynamics, and studies someaspects of the coupled atmosphere-ocean system using thisaveraged model. The geophysical flows in the oceans and the atmosphereaffect our environment and our society in profound ways. Thisproject is motivated by the need of better scientificunderstanding of the environment and global change. Theinvestigator takes random or uncertain effects into account todescribe geophysical flows. He develops both deterministic andstochastic, numerical and analytical techniques to understandcomplex geophysical flow phenomena. This research improves ourknowledge about dispersion, transport and mixing of pollutants inour environment, and about evolution and pattern formation ofgeophysical flows. The techniques resulting from this researchare also useful in studying other emerging problems inengineering and applied sciences.