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

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.