Predictability of Lagrangian particle trajectories: Effects of smoothing of the underlying Eulerian flow

The increasing realism of ocean circulation models is leading to an increasing use of Eulerian models as a basis to compute transport properties and to predict the fate of Lagrangian quantities. There exists, however, a significant gap between the spatial scales of model resolution and that of forces acting on Lagrangian particles. These scales may contain high vorticity coherent structures that are not resolved due to computational issues and/or missing dynamics and are typically suppressed by smoothing operators. In this study, the impact of smoothing of the Eulerian fields on the predictability of Lagrangian particles is first investigated by conducting twin experiments that involve release of clusters of synthetic Lagrangian particles into true (unmodified) and model (smoothed) Eulerian fields, which are generated by a QG model with a flow field consisting of many turbulent coherent structures. The Lagrangian errors induced by Eulerian smoothing errors are quantified by using two metrics, the difference between the centers of mass (CM) of particle clusters, ρ, and the difference between scattering of particles around the center of mass, s. The results show that the smoothing has a strong effect on the CM behavior, while the scatter around it is only partially affected. The QG results are then compared to results obtained from a multi-particle Lagrangian Stochastic Model (LSM) which parameterizes turbulent flow using main flow characteristics such as mean flow, velocity variance and Lagrangian time scale. In addition to numerical results, theoretical results based on the LSM are also considered, providing asymptotics of ρ, s and predictability time. It is shown that both numerical and theoretical LSM results for the center of mass error (ρ) provide a good qualitative description, and a quantitatively satisfactory estimate of results from QG experiments. The scatter error (s) results, on the other hand, are only qualitatively reproduced by the LSM

Impact of Boundary Conditions on Entrainment and Transport in Gravity Currents

Gravity currents have been studied numerically and experimentally both in the laboratory and in the ocean. The question of appropriate boundary conditions is still challenging for most complex flows. Gravity currents make no exception - appropriate, physically and mathematically sound boundary conditions are yet to be found. This task is further complicated by the technical limitations imposed by the current oceanographic techniques. In this paper, we make a first step toward a better understanding of the impact of boundary conditions on gravity currents. Specifically, we use direct numerical simulations to investigate the effect that the popular Neumann, and less popular Dirichlet boundary conditions on the bottom continental shelf have on the entrainment and transport of gravity currents. The finding is that gravity currents under these two different boundary conditions differ most in the way they transport heat from the top towards the bottom. This major difference occurs at medium temperature ranges. Entrainment and transport at high temperatures also show significant differences

A numerical study of layer formation due to fingers in double-diffusive convection in a vertically-bounded domain

The evolution of fingers in a double-diffusive system is investigated using numerical integration of two-dimensional equations of motion for an incompressible, Boussinesq fluid. The computational domain is periodic in the horizontal direction and is closed with no-flux boundary conditions in the vertical direction. The main result of this study is the evolution of the system from initially linear profiles for both fast and slow diffusing components to a layered state characterized by a finger zone sandwiched between two mixed layers. The horizontal boundaries in this system play an important role in the development of the layered state. At the top and bottom boundaries, light and heavy finger fluxes accumulate leading to the formation of mixed layers exhibiting larger-scale eddies. In the quasi-equilibrium state, the finger zone is characterized by broken wiggly fingers which do not extend across the entire interface. The salinity flux at the mid-depth of the domain is approximately proportional to the 4/3 power of the salinity difference between the mixed layers, except for the initial phase and for the run-down phase

Diagnosing Frontal Dynamics From Observations Using a Variational Approach

Intensive hydrographic and horizontal velocity measurements collected in the Alboran Sea enabled us to diagnose the three-dimensional dynamics of a frontal system. The sampled domain was characterized by a 40 km diameter anticyclonic eddy, with an intense front on its eastern side, separating the Atlantic and Mediterranean waters. Here, we implemented a multi-variate variational analysis (VA) to reconstruct the hydrographic fields, combining the 1-km horizontal resolution of the Underway Conductivity-Temperature-Depth (CTD) system with information on the flow shape from the Acoustic Doppler Current Profiler velocities. One advantage of the VA is given by the physical constraint, which preserves fine-scale gradients better than the classical optimal interpolation (OI). A comparison between real drifter trajectories and virtual particles advected in the mapping quantified the improvements in the VA over the OI, with a 15% larger skill score. Quasi-geostrophic (QG) and semi-geostrophic (SG) omega equations enabled us to estimate the vertical velocity (w) which reached 40 m/day on the dense side of the front. How nutrients and other passive tracers leave the mixed-layer and subduct is estimated with 3D advection from the VA, which agreed with biological sampling from traditional CTD casts at two eddy locations. Downwelling warm filaments are further evidence of subduction, in line with the w from SG, but not with QG. SG better accounted for the along-isopycnal component of w in agreement with another analysis made on isopycnal coordinates. The multi-platform approach of this work and the use of variational methods improved the characterization and understanding of (sub)-mesoscale frontal dynamics.This research was supported by the Office of Naval Research Departmental Research Initiative CALYPSO under program officers Terri Paluszkiewicz and Scott Harper. The authors' ONR Grant are as follows: N000141613130 (AP, SR and AM), N000141812418 (PMP), S. Johnston N000141812416 (TMSJ), N000141812138 (TO), N000141712517 and N00014191269 (LRC), N000141812139 and N000141812420 (AS) and N000141812139and (EDA). This article is also a contribution to the PRE-SWOT project funded by the Spanish Research Agency and the European Regional Development Fund (AEI/FEDER, UE) under grant agreement (CTM2016-78607-P)

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 meters to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. \textcolor{black} {Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200m$-$50km scales and clearly indicate that dispersion at the submesoscales is \textit{local}, driven predominantly by energetic submesoscale fluctuations.} The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.Comment: 9 pages, 6 figure

Ocean convergence and the dispersion of flotsam

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change. Although this paradigm is likely valid at mesoscales, larger than 100 km in horizontal scale, recent theoretical studies of submesoscales (less than ∼10 km) predict strong surface convergences and downwelling associated with horizontal density fronts and cyclonic vortices. Here we show that such structures can dramatically concentrate floating material. More than half of an array of ∼200 surface drifters covering ∼20 × 20 km2 converged into a 60 × 60 m region within a week, a factor of more than 105 decrease in area, before slowly dispersing. As predicted, the convergence occurred at density fronts and with cyclonic vorticity. A zipperlike structure may play an important role. Cyclonic vorticity and vertical velocity reached 0.001 s−1 and 0.01 ms−1, respectively, which is much larger than usually inferred. This suggests a paradigm in which nearby objects form submesoscale clusters, and these clusters then spread apart. Together, these effects set both the overall extent and the finescale texture of a patch of floating material. Material concentrated at submesoscale convergences can create unique communities of organisms, amplify impacts of toxic material, and create opportunities to more efficiently recover such material

Ocean convergence and the dispersion of flotsam

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change. Although this paradigm is likely valid at mesoscales, larger than 100 km in horizontal scale, recent theoretical studies of submesoscales (less than ∼10 km) predict strong surface convergences and downwelling associated with horizontal density fronts and cyclonic vortices. Here we show that such structures can dramatically concentrate floating material. More than half of an array of ∼200 surface drifters covering ∼20 × 20 km2 converged into a 60 × 60 m region within a week, a factor of more than 105 decrease in area, before slowly dispersing. As predicted, the convergence occurred at density fronts and with cyclonic vorticity. A zipperlike structure may play an important role. Cyclonic vorticity and vertical velocity reached 0.001 s−1 and 0.01 ms−1, respectively, which is much larger than usually inferred. This suggests a paradigm in which nearby objects form submesoscale clusters, and these clusters then spread apart. Together, these effects set both the overall extent and the finescale texture of a patch of floating material. Material concentrated at submesoscale convergences can create unique communities of organisms, amplify impacts of toxic material, and create opportunities to more efficiently recover such material

Inertial Oscillations and Frontal Processes in an Alboran Sea Jet: Effects on Divergence and Vertical Transport

Vertical transport pathways in the ocean are still only partially understood despite their importance for biogeochemical, pollutant, and climate applications. Detailed measurements of a submesoscale frontal jet in the Alboran Sea (Mediterranean Sea) during a period of highly variable winds were made using cross-frontal velocity, density sections and dense arrays of surface drifters deployed across the front. The measurements show divergences as large as ±f implying vertical velocities of order 100 m/day for a ≈ 20 m thick surface layer. Over the 20 hr of measurement, the divergences made nearly one complete oscillation, suggesting an important role for near-inertial oscillations. A wind-forced slab model modified by the observed background frontal structure and with initial conditions matched to the data produces divergence oscillations and pattern compatible with that observed. Significant differences, though, are found in terms of mean divergence, with the data showing a prevalence of negative, convergent values. Despite the limitations in data sampling and model uncertainties, this suggests the contribution of other dynamical processes. Turbulent boundary layer processes are discussed, as a contributor to enhance the observed convergent phase. Water mass properties suggest that symmetric instabilities might also be present but do not play a crucial role, while downward stirring along displaced isopycnals is observed.This work has been supported and co-financed by the CALYPSO project, within the Office of Naval Research Departmental Research Initiative, under the following grants: N00014-18-1-2782 and N00014-22-1-2039 (GE,SD,MB,AG), N00014-18-1-2139 (AYS,EAD), N00014-18-1-2138 (TO), N00014-18-1-2418 and N00014-20-1-2754 (PMP), N00014-19-1-2692 and N00014-19-1-2380 (LC and part of the drifter data collection/analysis), N00014-18-1-2431 (JTF), N00014-18-1-2416 (TMSJ), N00014-16-1-3130 (AP,DRT,SR), N00014-21-1-2702 (AM). MF was supported by the Scripps Institutional Postdoctoral Fellowship (MAF). Investigation of front dynamics in the Mediterranean Sea from multiplatform observations is supported as well by the European Union's JERICO-S3 project through Grant 871153. Open Access Funding provided by Consiglio Nazionale delle Ricerche within the CRUI-CARE Agreement.Peer reviewe

Surface Ocean Dispersion Observations From the Ship-Tethered Aerostat Remote Sensing System

Oil slicks and sheens reside at the air-sea interface, a region of the ocean that is notoriously difficult to measure. Little is known about the velocity field at the sea surface in general, making predictions of oil dispersal difficult. The Ship-Tethered Aerostat Remote Sensing System (STARSS) was developed to measure Lagrangian velocities at the air-sea interface by tracking the transport and dispersion of bamboo dinner plates in the field of view of a high-resolution aerial imaging system. The camera had a field of view of approximately 300 × 200 m and images were obtained every 15 s over periods of up to 3 h. A series of experiments were conducted in the northern Gulf of Mexico in January-February 2016. STARSS was equipped with a GPS and inertial navigation system (INS) that was used to directly georectify the aerial images. A relative rectification technique was developed that translates and rotates the plates to minimize their total movement from one frame to the next. Rectified plate positions were used to quantify scale-dependent dispersion by computing relative dispersion, relative diffusivity, and velocity structure functions. STARSS was part of a nested observational framework, which included deployments of large numbers of GPS-tracked surface drifters from two ships, in situ ocean measurements, X-band radar observations of surface currents, and synoptic maps of sea surface temperature from a manned aircraft. Here we describe the STARSS system and image analysis techniques, and present results from an experiment that was conducted on a density front that was approximately 130 km offshore. These observations are the first of their kind and the methodology presented here can be adopted into existing and planned oceanographic campaigns to improve our understanding of small-scale and high-frequency variability at the air-sea interface and to provide much-needed benchmarks for numerical simulations

The LatMix Summer Campaign: Submesoscale Stirring in the Upper Ocean

Lateral stirring is a basic oceanographic phenomenon affecting the distribution of physical, chemical, and biological fields. Eddy stirring at scales on the order of 100 km (the mesoscale) is fairly well understood and explicitly represented in modern eddy-resolving numerical models of global ocean circulation. The same cannot be said for smaller-scale stirring processes. Here, the authors describe a major oceanographic field experiment aimed at observing and understanding the processes responsible for stirring at scales of 0.1–10 km. Stirring processes of varying intensity were studied in the Sargasso Sea eddy field approximately 250 km southeast of Cape Hatteras. Lateral variability of water-mass properties, the distribution of microscale turbulence, and the evolution of several patches of inert dye were studied with an array of shipboard, autonomous, and airborne instruments. Observations were made at two sites, characterized by weak and moderate background mesoscale straining, to contrast different regimes of lateral stirring. Analyses to date suggest that, in both cases, the lateral dispersion of natural and deliberately released tracers was O(1) m² s⁻¹ as found elsewhere, which is faster than might be expected from traditional shear dispersion by persistent mesoscale flow and linear internal waves. These findings point to the possible importance of kilometer-scale stirring by submesoscale eddies and nonlinear internal-wave processes or the need to modify the traditional shear-dispersion paradigm to include higher-order effects. A unique aspect of the Scalable Lateral Mixing and Coherent Turbulence (LatMix) field experiment is the combination of direct measurements of dye dispersion with the concurrent multiscale hydrographic and turbulence observations, enabling evaluation of the underlying mechanisms responsible for the observed dispersion at a new level.A Google Earth interactive map of shipboard, autonomous, and airborne surveys during the summer 2011 LatMix experiment is available online as supplemental material ( http://dx.doi.org/10.1175/BAMS-D-14-00015.2). To explore these maps, you need Google Earth viewer installed on your computer. The software is free and could be downloaded online (from https://www.google.com /earth/). A user guide is available online as well (at http:// earth.google.com/userguide/).This is the publisher’s final pdf. The published article is copyrighted by the American Meteorological Society and can be found at: https://www2.ametsoc.org/ams/index.cfm/publications/bulletin-of-the-american-meteorological-society-bams