Collaborative Research: Towards a More Comprehensive Understanding of Eulerian and Lagrangian Transport of Active and Passive Tracers in the Ocean

生物地球化学示踪剂在海洋中的运输是一个复杂和多方面的问题，涉及许多学科，从物理海洋学到海洋生态学、渔业管理、搜索和救援行动、减轻自然和人为危害和风险评估。这项工作的广泛动机是海洋微塑料污染问题，但其他相关的海洋示踪剂可以包括营养物质、浮游生物、放射性和化学示踪剂、鱼类幼虫、马尾藻、石油等。该项目将促进理论和实践方面的理解和预测示踪剂在现实海洋流动中的演变。将开发用于预测示踪剂到达目标的概率及其状态PDF的理论处理和数值程序，弥合问题的拉格朗日，欧拉和随机描述之间的差距。当应用于海洋微塑料污染时，理论框架将包括浮力、刚体特性、粒子惯性和粒子参数不确定性影响的适当表示。然后，开发的方法将在一个简单的涡流分析模型中使用理想的示踪剂，以及在一个高分辨率的海洋环流模型中使用现实的微塑料样示踪剂进行测试。该项目将建立概率欧拉和拉格朗日示踪剂演化描述之间的联系，调和它们之间的差异，并研究每种方法的优缺点。拉格朗日方法和广义拉格朗日相干结构（LCS）技术将与示踪剂分布的概率密度函数（PDF）的福克-普朗克方程联系起来，弥合了拉格朗日、欧拉和随机描述问题之间的差距。本项目将探索拉格朗日相干结构（LCS）和广义LCS之间的联系，以及概率密度函数的输运障碍。要考虑的因素包括状态的变化、可压缩性、马克西-莱利动力学以及由球速度、扩散和斯托克漂移引起的涡流通量。目标是开发一种双拉格朗日-概率-欧拉理论方法，用于小固体颗粒（如海洋微塑料）在流体中的输运。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Transport of biogeochemical tracers in the ocean is a complex and multifaceted problem that reaches across many disciplines, from physical oceanography, to marine ecology, fishery management, search and rescue operations, natural and anthropogenic hazard mitigation and risk assessment. This work is broadly motivated by the problem of marine microplastic pollution, but other relevant oceanic tracers can include nutrients, plankton, radioactive and chemical tracers, fish larvae, Sargassum, oil, etc. This project will advance both theoretical and practical aspects of understanding and predicting the evolution of tracers in realistic oceanic flows. Theoretical treatments and numerical procedures for predicting the probability of a tracer reaching a target and the PDF of its state will be developed, bridging the gap between the Lagrangian, Eulerian, and stochastic descriptions of the problem. When applied to marine microplastics pollution, the theoretical framework will include proper representations of the effects of buoyancy, rigid-body properties, inertia of particles, and uncertainties in particle parameters. The developed methodology will then be tested using idealized tracers in a simple analytical model of an eddy, as well as realistic microplastic-like tracers in a high-resolution ocean circulation model.This project will establish links between the probabilistic Eulerian and Lagrangian descriptions of tracer evolution, reconcile differences between them, and investigate the advantages and disadvantages of each approach. Lagrangian methods and Generalized Lagrangian Coherent Structures (LCS) techniques will be linked to the Fokker-Planck equation for the probability density function (PDF) of the tracer distribution, bridging the gap between the Lagrangian, Eulerian, and stochastic descriptions of the problem. The project will explore the connections between Lagrangian Coherent Structures (LCS) and Generalized LCS, and the transport barriers for the probability density functions. Factors to be accounted for include changes in state, compressibility, Maxey-Riley dynamics, and eddy fluxes resulting from bolus velocities, diffusion, and Stoke’s drift. The goal is to develop a dual Lagrangian – probabilistic-Eulerian theoretical methodology for transport of small solid-body particles, such as marine microplastics, in fluids.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.