Quantifying tracer dynamics in moving fluids: a combined Eulerian-Lagrangian approach

Abstract

Eulerian models coupling physics and biology provide a powerful tool for the study of marine systems, complementing and synthesizing in situ observations and in vitro experiments. With the monotonic improvements in computing resources, models can now resolve increasingly complex biophysical interactions. Quantifying complex mechanisms of interaction produces massive amounts of numerical data that often require specialized tools for analysis. Here we present an Eulerian-Lagrangian approach to analyzing tracer dynamics in moving fluids. As an example of its utility, we apply this tool to quantifying plankton dynamics in oceanic mesoscale coherent structures. In contrast to Eulerian frameworks, Lagrangian approaches are particularly useful for revealing physical pathways, and the dynamics and distributions of tracers along these trajectories. Using a well-referenced Lagrangian tool, we develop a method to assess the variability of biogeochemical properties (computed using an Eulerian model) along particle trajectories. We discuss the limitations of this new method, given the different biogeochemical and physical timescales at work in the Eulerian framework. We also use Lagrangian trajectories to track coherent structures such as eddies, and we analyze the dynamics of the local ecosystem using two techniques: (i) estimating biogeochemical properties along trajectories, and (ii) averaging biogeochemical properties over dynamic regions (e.g., the eddy core) defined by ensembles of similar trajectories. This hybrid approach, combining Eulerian and Lagrangian model analyses, enhances the quantification and understanding of the complex planktonic ecosystem responses to environmental forcings; it can be easily applied to the dynamics of any tracer in a moving fluid.

Lagrangian Views of the Pathways of the Atlantic Meridional Overturning Circulation

“…There is also the ability to track fluid particles back in time, which is particularly useful for determining the origin of waters passing through a specific region. Furthermore, Lagrangian model output can be used to examine water mass transformations over long distances and investigate the structure of heat and fresh water fluxes along the AMOC pathways (e.g., Berglund et al, ; Chenillat et al, ; Durgadoo et al, ; Lique et al, ; Rimaud et al, ; Rühs et al, ; Speich et al, ). Of note is that simulated trajectories are perhaps least reliable in the deep ocean, where observations (Eulerian or Lagrangian) are too sparse to provide adequate model verification.…”

Plankton dynamics in a cyclonic eddy in the Southern California Current System

“…The horizontal extent of the eddy core was defined using the results of the Lagrangian experiments (Figure a). These experiments consisted of seeding the coastline (from 29.2°N to 33.1°N, and from the surface to a maximum of 200 m depth) each month with 210 particles, from September Y1 to February Y2 [ Chenillat et al ., ]. These particles were tracked forward in time until 30 March Y2, when the coastal eddy had moved offshore.…”

“…To assess the influences of eddies on ecosystem dynamics, we focus on one particular eddy in the Southern CCS from a numerical experiment (detailed in section 2.1). The formation and kinematic evolution of a cyclonic eddy were quantified using Lagrangian particle‐tracking analyses [ Blanke and Raynaud , ; Blanke et al ., ; Chenillat et al ., ] (see Figure and section 2.2). This eddy formed at the end of the summer from a coastal meander, through instabilities of the alongshore current.…”

Environmental versus operational drivers of drifting FAD beaching in the Western and Central Pacific Ocean

“…Using time-evolving velocity fields from a high resolution ocean circulation model, large numbers of virtual particles with float characteristics that mimic dFADs can be seeded into the simulated ocean to quantify the possible pathways of these floating objects. Such simulations have been used to understand many aspects of ocean circulation and to investigate the connectivity of passively drifting larvae 20 , nutrient flow 21 , marine plastics 22 , non-passive agents such as tuna themselves 23 , as well as dFADs 24 . In the context of dFAD beaching, Lagrangian particle simulation experiments can provide an independent estimate of the broad-scale probability distribution of connectivity between the ocean and beaching events.…”