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

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

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)

A Regional Modeling Study of the Entraining Mediterranean Outflow

[1] We have evaluated a regional-scale simulation of the Mediterranean outflow by comparison with field data obtained in the 1988 Gulf of Cadiz Expedition. Our ocean model is based upon the Hybrid Coordinate Ocean Model (HYCOM) and includes the Richardson number-dependent entrainment parameterization of Xu et al. (2006). Given realistic topography and sufficient resolution, the model reproduces naturally the major, observed features of the Mediterranean outflow in the Gulf of Cadiz: the downstream evolution of temperature, salinity, and velocity profiles, the mean path and the spreading of the outflow plume, and most importantly, the localized, strong entrainment that has been observed to occur just west of the Strait of Gibraltar. As in all numerical solutions, there is some sensitivity to horizontal and vertical resolution. When the resolution is made coarser, the simulated currents are less vigorous and there is consequently less entrainment. Our Richardson number-dependent entrainment parameterization is therefore not recommended for direct application in coarse-resolution climate models. We have used the high-resolution regional model to investigate the response of the Mediterranean outflow to a change in the freshwater balance over the Mediterranean basin. The results are found in close agreement with the marginal sea boundary condition (MSBC): A more saline and dense Mediterranean deep water generates a significantly greater volume transport of the Mediterranean product water having only very slightly greater salinity

Mixing and entrainment in the Red Sea outflow plume. Part I : plume structure

Author Posting. © American Meteorological Society, 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 35 (2005): 569–583, doi:10.1175/JPO2679.1.When the salty and heavy water of the Red Sea exits from the Strait of Bab el Mandeb, it continues downslope into the Gulf of Aden mainly along two channels. The 130-km-long “Northern Channel” (NC) is topographically confined and is typically only 5 km wide. In it, the Red Sea plume shows unanticipated patterns of vertical structure, turbulent mixing, and entrainment. Above the seafloor a 25–120-m-thick weakly stratified layer shows little dilution along the channel. Hence this bottom layer undergoes only weak entrainment. In contrast, a 35–285-m-thick interfacial layer shows stronger entrainment and is shown in a companion paper to undergo vigorous turbulent mixing. It is thus the interface that exhibits the bulk of entrainment of the Red Sea plume in the NC. The interfacial layer also carries most of the overall plume transport, increasingly so with downstream distance. The “Southern Channel” (SC) is wider than the NC and is accessed from the latter by a sill about 33 m above the floor of the NC. Entrainment into the bottom layer of the SC is diagnosed to be strong near the entry into the SC such that the near-bottom density and salinity are smaller in the SC than in the NC at the same distance from Bab el Mandeb. In comparison with winter conditions, the authors encountered weaker outflow with shallower equilibration depths during the summer cruise. Bulk Froude numbers computed for the whole plume varied within the range 0.2–1. Local maxima occurred in relatively steep channel sections and coincided with locations of significant entrainment.The Red Sea Outflow Experiment was funded by the National Science Foundation under Contracts OCE-9819506 and OCE-9818464. Additional support was provided to the “Climate Process Team Gravity Currents” under OCE-0336799

Horizontal Approximate Deconvolution for Stratified Flows: Analysis and Computations

In this paper we propose a new Large Eddy Simulation model derived by approximate deconvolution obtained by means of wave-number asymptotic expansions. This LES model is designed for oceanic flows and in particular to simulate mixing of fluids with different temperatures, density or salinity. The model -which exploits some ideas well diffused in the community- is based on a suitable horizontal filtering of the equations. We prove a couple of a-priori estimates, showing certain mathematical properties and we present also the results of some preliminary numerical experiments

Equilibration and circulation of Red Sea Outflow water in the western Gulf of Aden

Author Posting. © American Meteorological Society, 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 35 (2005): 1963–1985, doi:10.1175/JPO2787.1.Hydrographic, direct velocity, and subsurface float observations from the 2001 Red Sea Outflow Experiment (REDSOX) are analyzed to investigate the gravitational and dynamical adjustment of the Red Sea Outflow Water (RSOW) where it is injected into the open ocean in the western Gulf of Aden. During the winter REDSOX cruise, when outflow transport was large, several intermediate-depth salinity maxima (product waters) were formed from various bathymetrically confined branches of the outflow plume, ranging in depth from 400 to 800 m and in potential density from 27.0 to 27.5 σθ, a result of different mixing intensity along each branch. The outflow product waters were not dense enough to sink to the seafloor during either the summer or winter REDSOX cruises, but analysis of previous hydrographic and mooring data and results from a one-dimensional plume model suggest that they may be so during wintertime surges of strong outflow currents, or about 20% of the time during winter. Once vertically equilibrated in the Gulf of Aden, the shallowest RSOW was strongly influenced by mesoscale eddies that swept it farther into the gulf. The deeper RSOW was initially more confined by the walls of the Tadjura Rift, but eventually it escaped from the rift and was advected mainly southward along the continental slope. There was no evidence of a continuous boundary undercurrent of RSOW similar to the Mediterranean Undercurrent in the Gulf of Cadiz. This is explained by considering 1) the variability in outflow transport and 2) several different criteria for separation of a jet at a sharp corner, which indicate that the outflow currents should separate from the boundary where they are injected into the gulf.This work was supported by the U.S. National Science Foundation under Grants OCE-9818464 (WHOI) and OCE-9819506 (RSMAS)

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

Dynamics of the head of gravity currents

The present work experimentally investigates the dynamics of unsteady gravity currents produced by lock-release of a saline mixture into a fresh water tank. Seven different experimental runs were performed by varying the density of the saline mixture in the lock and the bed roughness. Experiments were conducted in a Perspex flume, of horizontal bed and rectangular cross section, and recorded with a CCD camera. An image analysis technique was applied to visualize and characterize the current allowing thus the understanding of its general dynamics and, more specifically, of the current head dynamics. The temporal evolution of both head length and mass shows repeated stretching and breaking cycles: during the stretching phase, the head length and mass grow until reaching a limit, then the head becomes unstable and breaks. In the instants of break, the head aspect ratio shows a limit of 0.2 and the mass of the head is of the order of the initial mass in the lock. The average period of the herein called breaking events is seen to increase with bed roughness and the spatial periodicity of these events is seen to be approximately constant between runs. The rate of growth of the mass at the head is taken as a measure to assess entrainment and it is observed to occur at all stages of the current development. Entrainment rate at the head decreases in time suggesting this as a phenomenon ruled by local buoyancy and the similarity between runs shows independence from the initial reduced gravity and bed roughness. © 2013 Springer Science+Business Media Dordrecht