Linear instabilities of a two-layer geostrophic surface front near a wall

The development of linear instabilities on a geostrophic surface front in a two-layer primitive equation model on an ƒ-plane is studied analytically and numerically using a highly accurate differential shooting method. The basic state is composed of an upper layer in which the mean flow has a constant potential vorticity, and a quiescent lower layer that outcrops between a vertical wall and the surface front (defined as the line of intersection between the interface that separates the two layers and the ocean\u27s surface). The characteristics of the linear instabilities found in the present work confirm earlier results regarding the strong dependence of the growth rate (σi) on the depth ratio r (defined as the ratio between the total ocean depth and the upper layer\u27s depth at infinity) for r ≥ 2 and their weak dependence on the distance L between the surface front and the wall. These earlier results of the large r limit were obtained using a much coarser, algebraic, method and had a single maximum of the growth rate curve at some large wavenumber k. Our new results, in the narrow range of 1.005 ≤ r ≤ 1.05, demonstrate that the growth rate curve displays a second lobe with a local (secondary) maximum at a nondimensional wavenumber (with the length scale given by the internal radius of deformation) of 1.05. A new fitting function 0.183 r-0.87is found for the growth rate of the most unstable wave (σimax ) for r ranging between 1.001 and 20, and for L \u3e 2 Rd (i.e.where the effect of the wall becomes negligible). Therefore, σimax converges to a finite value for |r — 1 | \u3c\u3c 1 (infinitely thin lower layer). This result differs from quasi-geostrophic, analytic solutions that obtain for the no wall case since the QG approximation is not valid for very thin layers. In addition, an analytical solution is derived for the lower-layer solutions in the region between the wall and the surface front where the upper layer is not present. The weak dependence of the growth rate on L that emerges from the numerical solution of the eigenvalue problem is substantiated analytically by the way L appears in the boundary conditions at the surface front. Applications of these results for internal radii of deformation of 35– 45 km show reasonable agreement with observed meander characteristics of the Gulf Stream downstream of Cape Hatteras. Wavelengths and phase speeds of (180 –212 km, 39 –51 km/day) in the vicinity of Cape Hatteras were also found to match with the predicted dispersion relationships for the depth-ratio range of 1+ \u3c r \u3c 2

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

Study of the Gulf Stream-Slopewater system

A study of the Gulf Stream-Slopewater system from 4-year outputs of a high resolution numerical simulation of the North Atlantic is presented, with particular emphasis on the Slopewater Jet (SJ). The SJ is partly fed by a Gulf Stream bifurcation in the vicinity of the New England Seamount Chain (NESC). A stability analysis reveals that the NESC has a potential destabilizing effect on the Gulf Stream. However, the Taylor constraint of the NESC\u27s spatial distribution explains most of the lower-layer mean flow, and deflection of the northern portion of the Stream into the Slopewater region shortly downstream of the seamount chain. The transport of the Slope Jet indeed doubles between the NESC and the Grand Banks (and is consistent with observations), from 7--9 Sv to 19 Sv, in agreement with the transport estimations of McLellan (1957). The increase in transport is due partly to Gulf Stream water rejections, and partly to the entrainment and mixing of waters from the shelf and from the Labrador Current (LC). A statistical analysis of the pycnocline depth above the NESC shows that the chain enhances the 9 month-1 meandering variability frequency of the Gulf Stream, which affects the shape of the upper layer streamline divergence. The Gulf Stream\u27s meandering variability is the main source of SJ variability shortly downstream of the NESC, in terms of lateral oscillation of the Jet, while the main transport variability is related to the invasion of GS waters merging with the SJ on an annual basis. The seasonality of the Slopewater column manifests as an annual variation in the transports of both the SJ and the DWBC, reaching a maximum in the fall and a minimum in the spring. This apparent coupling seems to result however from independent factors, namely the proximity of the Gulf Stream\u27s mean path and anticyclonic eddies in the slopewater in the fall, versus the seasonal deep water mass formation, also leading in this numerical simulation to a maximum transport in the Mid Atlantic Bight in the fall. South of the Grand Banks, the variability of the upper slopewater is related to an annual transport of the Labrador Current and SJ in phase, with a dominant annual time scale, although the upstream SJ variability is also present and may induce direct changes in the LC transport. There is also a seasonal signal in the water mass characteristics of the eastward flow.The analysis of the numerical model has shown remarkably similar results to the most recent observations on the Slopewater system. However, the statistical study revealed sub-annual to biannual variability timescales, rather than interannual time-scales

Relative dispersion from a high-resolution coastal model of the Adriatic Sea

Synthetic drifter trajectories computed from velocity data produced by a high-resolution NCOM model are used to investigate the scaling of relative dispersion and the distribution of finite-scale Lyapunov exponent (FSLE) fields in the Adriatic Sea. The effects of varying degrees of spatial and temporal filtering of the input Eulerian velocity fields on the Lagrangian statistics are investigated in order to assess the sensitivity of such statistics to model error. It is shown that the relative dispersion in the model Adriatic circulation is generally super-diffusive, scaling nearly ballistically in close agreement with Lagrangian observations from a limited set of drifters. The large-scale dispersion is dominated by persistent separation regions and the controlling influence of the Western Adriatic Current (WAC). Temporal filtering with averaging windows up to monthly time scales only affects the relative dispersion at scales smaller than 20 km without altering the overall scaling regime. In contrast, spatial smoothing at scales as small as 5 km significantly reduces relative dispersion at all scales up to 100 km. While basin-scale dispersion statistics are strongly dependent on spatial resolution of the model WAC, maps of FSLE fields over initial conditions indicate that the detailed geometry of the dispersion is determined to a large extent by the temporal resolution of the model. In addition, the degree of spatial heterogeneity in the flow field implies that the existence, or non-existence, of a distinct exponential regime in the FSLE at small scales is extremely sensitive to the details of particle pair sampling strategies

Large eddy simulations of mixed layer instabilities and sampling strategies

► Large eddy simulations of mixed layer instabilities are conducted. ► Flow fields are sampled using Lagrangian particles and passive tracers. ► Lagrangian platforms are found to be effective in sampling submesoscale flows. Recognizing the potential role played by submesoscale processes in both the energy cascade in the ocean and biogeochemical transport, we conduct a series of large eddy simulations of isolated mixed layer instabilities. The primary objective is to generate freely evolving velocity and density fields representative of submesoscale flows and then use these to examine potential observational sampling strategies. Mixed layer instabilities are explored in two parameter regimes: a strongly-stratified regime which results in a system with surface-intensified eddies and high vertical shear, and a weakly-stratified regime exhibiting weaker, smaller scale eddies that penetrate across the entire domain depth as Taylor columns. Analysis of a variety of mixing measures derived from both particle and tracer based sampling strategies indicates the differing importance of vertical processes in the two flow regimes

The mean flow and variability of the Gulf stream-slopewater system from MICOM

The slopewater region is influenced by surface wind-driven, deep buoyancy-driven and shelf currents, whose complex interactions can affect both the northward heat transport and southward return flows. The mean flow and variability of the Gulf Stream-slopewater system are studied using four year outputs of Miami Isopycnic Coordinate Ocean Model (MICOM) realistic high-resolution simulation of the North Atlantic circulation. Special attention is focused on the eastward Slopewater Jet (SJ), a surface current characterized by a mean path coinciding with the strong outcropping temperature front in the slopewater. The water mass, path and transport of the SJ in MICOM are found to be in reasonable agreement with the existing observations. The modeled SJ is associated in part with a GS’ secondary branch, induced by a Taylor column effect of the New England Seamount Chain (NESC) on the upper GS. This upper-ocean-topographic coupling results in a spatial GS bifurcation, and advection of GS waters into the slopewater region shortly downstream of the NESC. An EOF analysis of the pycnocline depth confirms this tendency, as the first mode displays a qualitative dependence of the GS fan-shape streamline dispersion on the strength and intersecting latitude of the incident GS. Additionally, the model displays a strong influence of the Deep Western Boundary Current (DWBC) on the path of the SJ, by acting as a potential vorticity barrier. Important interactions between the two currents are suggested by the statistical EOF of the slopewater column, as in observations. Downstream of the NESC, the SJ transport variability is seasonal in MICOM, due to the north-south annual oscillation of the GS path and mergings with anticyclonic eddies. However, the variability of the SJ velocity profile is dominated (49% eigenvalue) by lateral translations of the current, at a 9-month timescale characteristic of GS meander-intensity variability. South of the Grand Banks, the transport variations of both the SJ and Labrador Current (LC) are captured by the first mode of the upper-slope water (37% of the variability), with predominant timescales corresponding to the upstream variability of the GS, and seasonality of the LC. Both modes are also in reasonable agreement with observations

How Does Drifter Position Uncertainty Affect Ocean Dispersion Estimates?

Abstract To develop methodologies to maximize the information content of Lagrangian data subject to position errors, synthetic trajectories produced by both a large-eddy simulation (LES) of an idealized submesoscale flow field and a high-resolution Hybrid Coordinate Ocean Model simulation of the North Atlantic circulation are analyzed. Scale-dependent Lagrangian measures of two-particle dispersion, mainly the finite-scale Lyapunov exponent [FSLE; λ(δ)], are used as metrics to determine the effects of position uncertainty on the observed dispersion regimes. It is found that the cumulative effect of position uncertainty on λ(δ) may extend to scales 20–60 times larger than the position uncertainty. The range of separation scales affected by a given level of position uncertainty depends upon the slope of the true FSLE distribution at the scale of the uncertainty. Low-pass filtering or temporal subsampling of the trajectories reduces the effective noise amplitudes at the smallest spatial scales at the expense of limiting the maximum computable value of λ. An adaptive time-filtering approach is proposed as a means of extracting the true FSLE signal from data with uncertain position measurements. Application of this filtering process to the drifters with the Argos positioning system released during the LatMix: Studies of Submesoscale Stirring and Mixing (2011) indicates that the measurement noise dominates the dispersion regime in λ for separation scales δ < 3 km. An expression is provided to estimate position errors that can be afforded depending on the expected maximum λ in the submesoscale regime