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Abstract Because of their buoyancy, rigidity, and finite size, inertial particles do not obey the same dynamics as fluid parcels. The motion of small spherical particles in a fluid flow is described by the Maxey–Riley equations and depends nonlinearly on the velocity of the fluid in which the particles are immersed. Fluid velocities in the ocean often have a strong small-scale turbulent component which is difficult to observe or model, presenting a challenge to predicting the evolution of distributions of inertial particles in the ocean. To overcome this challenge, we assume that the turbulent velocity imposes a random force on particles and consider a stochastic analog of the Maxey–Riley equations. By performing a perturbation analysis of the stochastic Maxey–Riley equations, we obtain a simple and accurate partial differential equation for the spatial distribution of particles. The equation is of the advection–diffusion type and handles the uncertainty introduced by unresolved turbulent flow features. In several numerical test cases, distributions of particles obtained by solving the newly derived equation compare favorably with distributions obtained from Monte Carlo simulations of individual particle trajectories and with theoretical predictions. The advection–diffusion form of our newly derived equation is amenable to inclusion within many existing ocean circulation models. Significance StatementWe introduce a new model for describing spatial distributions of small rigid objects, such as plastic debris, in the ocean. The model takes into account the effects of finite particle size and particle buoyancy, which cause particle trajectories to differ from fluid parcel trajectories. Our model also represents small-scale turbulence stochastically. 

Abstract Output from a high-resolution numerical model is used to study near-surface transport in and around Cape Cod Bay using a Lagrangian approach. Key questions include the following: What are the dominant transport pathways? How do they vary in time on seasonal-to-interannual scales? What is the role of wind in driving this variability? Application to a possible release of wastewater into Cape Cod Bay from the recently closed Pilgrim Nuclear Power Station is discussed. Analysis reveals a seasonality in Cape Cod Bay transport patterns, with shorter residence times throughout the bay and an increased probability of outflow waters exiting the bay during spring and summer. Wind-induced Ekman currents are identified as a dominant driver of this variability. Significance StatementThis study is motivated by a possible release of radioisotope-contaminated wastewater into Cape Cod Bay, a region important to fishing, aquaculture, and tourist industries. The specific aim is to better understand near-surface transport patterns and mechanisms in Cape Cod Bay both in general and within the context of a wastewater release from Pilgrim Nuclear Power Station. 

Abstract During the 2019/2020 Australian bushfire season, intense wildfires generated a rising plume with a record concentration of smoke in the lower stratosphere. Motivated by this event, we use the atmospheric wind reanalysis model ERA5 to characterize the three dimensional atmospheric transport in the general region of the plume following a dynamical system approach in the Lagrangian framework. Aided by the Finite Time Lyapunov Exponent tool (FTLE), we identify Lagrangian Coherent Structures (LCS) which simplify the three‐dimensional transport description. Different reduced FTLE formulations are compared to study the impact of the vertical velocity and the vertical shear on the movement of the plume. We then consider in detail some of the uncovered LCS that are directly relevant for the evolution of the plume, as well as other LCS that are less relevant for the plume but have interesting geometries, and we show the presence of 3D lobe dynamics at play. Also, we unveil the qualitatively different dynamical fates of the smoke parcels trajectories depending on the region in which they originated. One feature that had a pronounced influence on the evolution of the smoke plume is a synoptic‐scale anticyclone that was formed near the same time as, and close to the region of, intense wildfires. We analyze this anticyclone in detail, including its formation, the entrainment of the smoke plume, and how it maintained coherence for a long time. Transport paths obtained with the inclusion of the buoyancy effects are compared with those obtained considering only the reanalysis velocity. 

Abstract The distribution of oceanic biogeochemical tracers is fundamentally tied to physical dynamics at and below the mesoscale. Since global climate models rarely resolve those scales, turbulent transport is parameterized in terms of the large‐scale gradients in the mean tracer distribution and the physical fields. Here, we demonstrate that this form of the eddy flux is not necessarily appropriate for reactive tracers, such as nutrients and phytoplankton. In an idealized nutrient‐phytoplankton system, we show that the eddy flux of one tracer should depend on the gradients of itself and the other. For certain parameter regimes, incorporating cross‐diffusion can significantly improve the representation of both phytoplankton and nutrient eddy fluxes. We also show that the efficacy of eddy diffusion parameterizations requires timescale separation between the flow and reactions. This result has ramifications for parameterizing subgrid scale biogeochemistry in more complex ocean models since many biological processes have comparable timescales to submesoscale motions. 

The parameterization of fluxes associated with representing unresolved dynamics in turbulent flows, especially in the atmosphere and ocean (which have a vast range of scales), remains a challenging task. This is especially true for Earth system models including complex biogeochemistry and requiring very long simulations. The problem of representing the dependence of the mean flux of a passive tracer in terms of the mean has a very long history; in this study, we take a somewhat different approach. We use a formalism showing that the mean flux will be a functional of the mean gradients, a formalism that can be used to calculate the structure of the functional which is non-local in both space and time. Two-dimensional turbulent simulations are used to explore the weight of nearby (in space or time) gradients. We also use stochastic velocities and iterated maps to show that the results are similar. The functional formalism provides an understanding of when non-locality needs to be considered and when a local eddy diffusivity can be a reasonably good approximation. Furthermore, the formalism provides guidance for the development of data-driven parameterizations. 

Abstract. Although the movement and aggregation of microplastics at the ocean surface have been well studied, less is known about the subsurface. Within the Maxey–Riley framework governing the movement of small, rigid spheres with high drag in fluid, the aggregation of buoyant particles is encouraged in vorticity-dominated regions. We explore this process in an idealized model that is qualitatively reminiscent of a 3D eddy with an azimuthal and overturning circulation. In the axially symmetric state, buoyant spherical particles that do not accumulate at the top boundary are attracted to a loop consisting of periodic orbits. Such a loop exists when drag on the particle is sufficiently strong. For small, slightly buoyant particles, this loop is located close to the periodic fluid parcel trajectory. If the symmetric flow is perturbed by a symmetry-breaking disturbance, additional attractors for small, rigid, slightly buoyant particles may arise near periodic orbits of fluid parcels within the resonance zones created by the disturbance. Disturbances with periodic or quasiperiodic time dependence may produce even more attractors, with a shape and location that recurs periodically. However, not all such loops attract, and rigid particles released in the vicinity of one loop may instead be attracted to a nearby attractor. Examples are presented along with mappings of the respective basins of attraction. 

We analyse a class of stochastic advection problems by conditionally averaging the passive tracer equation with respect to a given flow state. In doing so, we obtain expressions for the turbulent diffusivity as a function of the flow statistics spectrum. When flow statistics are given by a continuous-time Markov process with a finite state space, calculations are amenable to analytic treatment. When the flow statistics are more complex, we show how to approximate turbulent fluxes as hierarchies of finite state space continuous-time Markov processes. The ensemble average turbulent flux is expressed as a linear operator that acts on the ensemble average of the tracer. We recover the classical estimate of turbulent flux as a diffusivity tensor, the components of which are the integrated autocorrelation of the velocity field in the limit that the operator becomes local in space and time.