Collaborative Research: U.S.-Turkey Cooperative Research: Stochastic Modeling of Turbulent Flows for the Prediction of Lagrangian Trajectories in the Ocean

0352637 OzgokmenDescription：该项目支持佛罗里达州迈阿密米迈大学海洋与大气科学学院的Tamay Ozgokman博士、南加州大学洛杉矶分校数学系Leonid Piterbarg博士和土耳其伊斯坦布尔Koc大学数学系Mine Caglar博士之间的合作研究。该项目的目的是汇集跨学科研究人员的专业知识，开发和实施模拟海洋湍流的数学方法。这种模拟的主要目的是研究拉格朗日运动的可预测性，并将其应用于海上救援和搜索行动、污染物和鱼苗的扩散、观测系统和航道的设计。PIS将利用现有的随机流动理论、数值模拟和海洋的拉格朗日研究，以建立统一的方法。该项目旨在从时间/空间观测中贡献新的拉格朗日预测算法和模型识别程序。在佛罗里达海岸观测的高分辨率速度场资料中，亚中尺度涡旋十分明显。目前的海洋模式能够分辨海洋中的中尺度结构，但是小的涡旋不能分辨，应该被参数化。范围：该项目的潜在影响包括通过对这种涡旋结构进行随机建模来加强拉格朗日预测研究，以及在海洋模型中表示亚网格湍流的能力。所采用的方法将是根据海洋数据对随机流动模型参数进行统计估计，将随机模拟纳入中尺度海洋过程的数值模拟，以及建立在存在相干结构时表现良好的预测算法。该项目预期的科学效益包括：(1)通过物理海洋学、应用数学、概率和统计学等学科之间的合作了解湍流；(2)通过一个复杂问题对随机过程统计理论作出贡献，即研究空间和时间数据以拟合矢量场的参数；(3)为海洋学应用建立更好的拉格朗日随机模型。该项目的广泛影响是：(I)将支持两个美国学术机构之间的合作；(Ii)将通过科学出版物开发和传播预测算法；(Iii)该项目的成果将在应用数学、概率和物理海洋学的国际会议上公布；(Iv)来自美国和土耳其的科学家将发展未来在研究和教育方面的国际合作，如交换或招收研究生；(V)该项目有助于了解环境并解决一个非常实际的安全问题。

0352637 OzgokmenDescription: This project supports a cooperative research between Dr. Tamay Ozgokmen, School of Marine and Atmospheric Science, University of Mimai, Miami, Florida, Dr. Leonid Piterbarg, Department of Mathematics, University of Southern California, Los Angeles, California and Dr. Mine Caglar, Department of Mathematics, Koc University, Istanbul, Turkey. The aim of this project is to bring together the expertise of interdisciplinary researchers to develop and implement mathematical methods for modeling turbulent flows in the ocean. The main goal of such modeling is to studythe Lagrangian motion predictability with application to rescue and search operations in the sea, dispersion of pollutants and fish larvae, design of observing systems and navigation routes. The PIs will draw upon existing theory of stochastic flows, numerical modeling and Lagrangian studies of the ocean for establishing a united approach. The project aims to contribute novel Lagrangian prediction algorithms and model identification procedures from time/space observations. Submesoscale eddies are evident in the high-resolution velocity field data observed along Florida coast. Current ocean models are able to resolve meso-scale structures in the ocean, however small eddies cannot be resolved and should be parameterized. Scope: The potential impact of the project includes the enhancement of Lagrangian prediction studies by stochastic modeling of such eddy structures, and the capability to represent sub-grid turbulence in the ocean models. The methods employed will be statistical estimation of stochastic flow model parameters from ocean data, incorporation of stochastic modeling into numerical modeling of mesoscale oceanic processes, and construction of prediction algorithms that perform well in the presence of coherent structures. The expected scientific benefits of this project include: (i) understanding of turbulent flows through the collaboration of disciplines, namely physical oceanography, applied mathematics, probability and statistics; (ii) contribution to the theory of statistics of stochastic processes by a complex problem, namely the study of spatial and temporal data for fitting the parameters of a vector field; (iii) establishment of better Lagrangian stochastic models for oceanographic applications. The broader impacts of this project are: (i) collaboration among two US academic institutions will be supported; (ii) algorithms for prediction will be developed and disseminated through scientific publications; (iii) the results of the project will be publicized in international conferences of applied mathematics and probability, and physical oceanography; (iv) scientists from US and Turkey will develop future international collaborations for both research and also education such as exchange or recruitment of graduate students ; (v) the project contributes to understanding the environment and addresses a very practical safety problem.