Inertia-induced accumulation of flotsam in the subtropical gyres

Recent surveys of marine plastic debris density have revealed high levels in the center of the subtropical gyres. Earlier studies have argued that the formation of great garbage patches is due to Ekman convergence in such regions. In this work we report a tendency so far overlooked of drogued and undrogued drifters to accumulate distinctly over the subtropical gyres, with undrogued drifters accumulating in the same areas where plastic debris accumulate. We show that the observed accumulation is too fast for Ekman convergence to explain it. We demonstrate that the accumulation is controlled by finite-size and buoyancy (i.e., inertial) effects on undrogued drifter motion subjected to ocean current and wind drags. We infer that the motion of flotsam in general is constrained by similar effects. This is done by using a newly proposed Maxey--Riley equation which models the submerged (surfaced) drifter portion as a sphere of the fractional volume that is submerged (surfaced).Comment: Submitted to Geophys. Res. Letter

Extracting quasi-steady Lagrangian transport patterns from the ocean circulation: An application to the Gulf of Mexico

We construct a climatology of Lagrangian coherent structures (LCSs), the concealed skeleton that shapes transport, with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy-Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, thus we show that a climatological velocity may preserve meaningful transport information. Also, the climatological transport patterns we report agree well with GoM kinematics and dynamics, as described in several previous observational and numerical studies. For example, cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact, are regions of maximal attraction. Also, we show examples where cLCSs are remarkably similar to transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand LAgrangian Deployment (GLAD) experiment. Thus, it is shown that cLCSs are an efficient way of synthesizing vast amounts of Lagrangian information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.Comment: To be submitte

Travel time stability in weakly range-dependent sound channels

Travel time stability is investigated in environments consisting of a range-independent background sound-speed profile on which a highly structured range-dependent perturbation is superimposed. The stability of both unconstrained and constrained (eigenray) travel times are considered. Both general theoretical arguments and analytical estimates of time spreads suggest that travel time stability is largely controlled by a property $\omega ^{\prime}$ of the background sound speed profile. Here, $2\pi/\omega (I)$ is the range of a ray double loop and $I$ is the ray action variable. Numerical results for both volume scattering by internal waves in deep ocean environments and rough surface scattering in upward refracting environments are shown to confirm the expectation that travel time stability is largely controlled by $\omega ^{\prime}$.Comment: Submitted to J. Acoust. Soc. Am., 30 June 200

Coherent spore dispersion via drop-leaf interactions

Dispersion of plant pathogens, such as rust spores, is responsible for a large portion of global crop production loss every year, in addition to the threat they pose to human health. However, the release mechanism of pathogens and other allergic particles from flexible plant surfaces into canopy turbulence has not been well understood. Focusing on the phenomenon of increased air-borne aerosols after rainfall, the present study elucidates how the coupling of leaf elasticity and drop momentum directly modulates surrounding airflow and spore transport. We found that drop impacts on leaves shed asymmetric vortex dipoles (about the leaf width axis $\hat{y}$) and generate stream flows that enable pathogens to escape. To understand the mechanics, we first built and experimentally validated a joint model of impact mechanics and airfoil potentials to parametrically link drop momentum, vibration speed, and dispersion capacity. Then with Lagrangian diagnostics, we uncovered different sets of coherent structures around the leaf, providing a dynamical description for how spores escape during rainfall. The work proposes here a stand-alone, direct dispersion mechanics that incorporates the role of plant substrate elasticity and emergent flow coherence. The physical insights extracted here can help build physically informed analytics models for local crop disease management.Comment: 12 pages, 4 figure

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

Geodesic theory of transport barriers in two-dimensional flows

We introduce a new approach to locating key material transport barriers in two-dimensional, non-autonomous dynamical systems, such as unsteady planar fluid flows. Seeking transport barriers as minimally stretching material lines, we obtain that such barriers must be shadowed by minimal geodesics under the Riemannian metric induced by the Cauchy–Green strain tensor. As a result, snapshots of transport barriers can be explicitly computed as trajectories of ordinary differential equations. Using this approach, we locate hyperbolic barriers (generalized stable and unstable manifolds), elliptic barriers (generalized KAM curves) and parabolic barriers (generalized shear jets) in temporally aperiodic flows defined over a finite time interval. Our approach also yields a metric (geodesic deviation) that determines the minimal computational time scale needed for a robust numerical identification of generalized Lagrangian Coherent Structures (LCSs). As we show, an extension of our transport barrier theory to non-Euclidean flow domains, such as a sphere, follows directly. We illustrate our main results by computing key transport barriers in a chaotic advection map, and in a geophysical model flow with chaotic time dependence. ► Transport barriers are sought as least stretching material lines in 2D. ► Approach yields differential equations for barriers. ► Actual barriers are solutions closest to geodesics of the Cauchy–Green metric. ► Results are illustrated on an advection map and an unsteady meandering jet model

Statistics of Simulated and Observed Pair Separations in the Gulf of Mexico

Abstract Pair-separation statistics of in situ and synthetic surface drifters deployed near the Deepwater Horizon site in the Gulf of Mexico are investigated. The synthetic trajectories derive from a 1-km-resolution data-assimilative Navy Coastal Ocean Model (NCOM) simulation. The in situ drifters were launched in the Grand Lagrangian Deployment (GLAD). Diverse measures of the dispersion are calculated and compared to theoretical predictions. For the NCOM pairs, the measures indicate nonlocal pair dispersion (in which pair separations grow exponentially in time) at the smallest sampled scales. At separations exceeding 100 km, pair motion is uncorrelated, indicating absolute rather than relative dispersion. With the GLAD drifters, however, the statistics are ambiguous, with some indicating local dispersion (in which pair separations exhibit power-law growth) and others suggesting nonlocal dispersion. The difference between the two datasets stems in part from inertial oscillations, which affect the energy levels at small scales without greatly altering pair dispersion. These were significant in GLAD but much weaker in the NCOM simulation. In addition, the GLAD drifters were launched over a limited geographical area, producing few independent realizations and hence lower statistical significance. Restricting the NCOM set to pairs launched at the same locations yields very similar results, suggesting the model is for the most part capturing the observed dispersion

Underwater acoustic beam dynamics

Ray- and mode-based theoretical predictions of the spreads of directionally narrow beams are presented and compared to parabolic-equation-based simulations in deep-ocean environments. Both the spatial and temporal spreads of beams are considered. The environments considered consist of a range-independent deep-ocean background sound channel on which a highly structured sound-speed perturbation, associated with either internal waves or homogeneous isotropic single-scale turbulence, is superimposed. The simulation results are shown to be in good agreement with simple theoretical expressions which predict that beam spreading, in both the unperturbed and perturbed environments, is largely controlled by a property of the background sound channel-the ray-based stability parameter alpha or the asymptotically equivalent mode-based waveguide invariant beta. These results are consistent with earlier results showing that wavefield structure and stability are largely controlled by alpha (or beta)