Journal articles on the topic 'Western boundary current instability'
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Hristova, Hristina G., Joseph Pedlosky, and Michael A. Spall. "Radiating Instability of a Meridional Boundary Current." Journal of Physical Oceanography 38, no. 10 (October 1, 2008): 2294–307. http://dx.doi.org/10.1175/2008jpo3853.1.
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Abstract A linear stability analysis of a meridional boundary current on the beta plane is presented. The boundary current is idealized as a constant-speed meridional jet adjacent to a semi-infinite motionless far field. The far-field region can be situated either on the eastern or the western side of the jet, representing a western or an eastern boundary current, respectively. It is found that when unstable, the meridional boundary current generates temporally growing propagating waves that transport energy away from the locally unstable region toward the neutral far field. This is the so-called radiating instability and is found in both barotropic and two-layer baroclinic configurations. A second but important conclusion concerns the differences in the stability properties of eastern and western boundary currents. An eastern boundary current supports a greater number of radiating modes over a wider range of meridional wavenumbers. It generates waves with amplitude envelopes that decay slowly with distance from the current. The radiating waves tend to have an asymmetrical horizontal structure—they are much longer in the zonal direction than in the meridional, a consequence of which is that unstable eastern boundary currents, unlike western boundary currents, have the potential to act as a source of zonal jets for the interior of the ocean.
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Goldsworth, Fraser W., David P. Marshall, and Helen L. Johnson. "Symmetric Instability in Cross-Equatorial Western Boundary Currents." Journal of Physical Oceanography 51, no. 6 (June 2021): 2049–67. http://dx.doi.org/10.1175/jpo-d-20-0273.1.
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AbstractThe upper limb of the Atlantic meridional overturning circulation draws waters with negative potential vorticity from the Southern Hemisphere into the Northern Hemisphere. The North Brazil Current is one of the cross-equatorial pathways in which this occurs: upon crossing the equator, fluid parcels must modify their potential vorticity to render them stable to symmetric instability and to merge smoothly with the ocean interior. In this work a linear stability analysis is performed on an idealized western boundary current, dynamically similar to the North Brazil Current, to identify features that are indicative of symmetric instability. Simple two-dimensional numerical models are used to verify the results of the stability analysis. The two-dimensional models and linear stability theory show that symmetric instability in meridional flows does not change when the nontraditional component of the Coriolis force is included, unlike in zonal flows. Idealized three-dimensional numerical models show anticyclonic barotropic eddies being spun off as the western boundary current crosses the equator. These eddies become symmetrically unstable a few degrees north of the equator, and their PV is set to zero through the action of the instability. The instability is found to have a clear fingerprint in the spatial Fourier transform of the vertical kinetic energy. An analysis of the water mass formation rates suggest that symmetric instability has a minimal effect on water mass transformation in the model calculations; however, this may be the result of unresolved dynamics, such as secondary Kelvin–Helmholtz instabilities, which are important in diabatic transformation.
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Qiu, Bo, Shuiming Chen, Daniel L. Rudnick, and Yuji Kashino. "A New Paradigm for the North Pacific Subthermocline Low-Latitude Western Boundary Current System." Journal of Physical Oceanography 45, no. 9 (September 2015): 2407–23. http://dx.doi.org/10.1175/jpo-d-15-0035.1.
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AbstractSubthermocline western boundary circulation along the low-latitude North Pacific Ocean (2°–25°N) is investigated by using profiling float and historical CTD/expendable CTD (XCTD) data and by analyzing an eddy-resolving global OGCM output. In contrast to the existing paradigm depicting it as a reversed pattern of the wind-driven circulation above the ventilated thermocline (i.e., depth < 26.8 σθ), the subthermocline western boundary circulation is found to comprise two components governed by distinct dynamical processes. For meridional scales shorter than 400 km, the boundary flows along the Philippine coast exhibit convergent patterns near 7°, 10°, 13°, and 18°N, respectively. These short-scale boundary flows are driven by the subthermocline eastward zonal jets that exist coherently across the interior North Pacific basin and are generated by the triad instability of wind-forced annual baroclinic Rossby waves. For meridional scales longer than 400 km, a time-mean Mindanao Undercurrent (MUC) is observed from 6° to 13°N together with another northward-flowing boundary flow beneath the Kuroshio from 16° to 24°N. Rather than remote eddy forcing from the interior Pacific Ocean, both of these broad-scale subthermocline boundary flows are induced by baroclinic instability of the overlying wind-driven western boundary currents, the Mindanao Current, and Kuroshio.
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Fantini, Maurizio, and Ka-Kit Tung. "On Radiating Waves Generated from Barotropic Shear Instability of a Western Boundary Current." Journal of Physical Oceanography 17, no. 8 (August 1987): 1304–8. http://dx.doi.org/10.1175/1520-0485(1987)017<1304:orwgfb>2.0.co;2.
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Waterman, Stephanie, and Brian J. Hoskins. "Eddy Shape, Orientation, Propagation, and Mean Flow Feedback in Western Boundary Current Jets." Journal of Physical Oceanography 43, no. 8 (August 1, 2013): 1666–90. http://dx.doi.org/10.1175/jpo-d-12-0152.1.
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Abstract This manuscript revisits a study of eddy–mean flow interactions in an idealized model of a western boundary current extension jet using properties of the horizontal velocity correlation tensor to diagnose characteristics of average eddy shape, orientation, propagation, and mean flow feedback. These eddy characteristics are then used to provide a new description of the eddy–mean flow interactions observed in terms of different ingredients of the eddy motion. The diagnostics show patterns in average eddy shape, orientation, and propagation that are consistent with the signatures of jet instability in the upstream region and wave radiation in the downstream region. Together they give a feedback onto the mean flow that gives the downstream character of the jet and drives the jet's recirculation gyres. A breakdown of the eddy forcing into contributions from individual terms confirms the expected role of cross-jet gradients in meridional eddy tilt in stabilizing the jet to its barotropic instability; however, it also reveals important roles played by the along-jet evolution of eddy zonal–meridional elongation. It is the mean flow forcing derived from these patterns that acts to strengthen and extend the jet downstream and forces the time-mean recirculation gyres. This understanding of the dependence of mean flow forcing on eddy structural properties suggests that failure to adequately resolve eddy elongation could underlie the weakened jet strength, extent, and changed recirculation structure seen in this idealized model for reduced spatial resolutions. Further, it may suggest new ideas for the parameterization of this forcing.
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Nishigaki, Hajime, and Humio Mitsudera. "Subtropical Western Boundary Currents over Slopes Detaching from Coasts with Inshore Pool Regions: An Indication to the Kuroshio Nearshore Path." Journal of Physical Oceanography 42, no. 2 (February 1, 2012): 306–20. http://dx.doi.org/10.1175/jpo-d-11-076.1.
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Abstract The dynamics of subtropical western boundary currents over slopes detaching from coasts with inshore pool regions, where the water of the subtropical gyre does not enter and the velocity is small, are investigated. This study is intended to understand the dynamics of the nearshore path of the Kuroshio, which has a distinct boundary between the boundary current and the coastal water. Numerical experiments under idealized conditions are made. The results show flow patterns with pool regions similar to the Kuroshio under simple conditions. A deep countercurrent is present on the lower bottom slope, which represents observed deep currents. This is part of a deep cyclonic recirculation north of the jet, which extends to the lower bottom slope despite steep topography. This extension can be explained by the geostrophic contours. In this region, the upper boundary current feels the bottom slope and the westward intensification is blocked. In the other region, where the bottom-layer velocity is very small, the upper boundary current is free from the bottom slope and westward intensification occurs at the coast. The sensitivity to the volume transport of the boundary current is investigated by case studies. The pool regions are broken in cases with large volume transports. It is indicated that these unsteady inshore regions are produced by instability caused by an outcrop of the upper isopycnal, which is led by a large baroclinic volume transport.
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Todd, Robert E., W. Brechner Owens, and Daniel L. Rudnick. "Potential Vorticity Structure in the North Atlantic Western Boundary Current from Underwater Glider Observations." Journal of Physical Oceanography 46, no. 1 (January 2016): 327–48. http://dx.doi.org/10.1175/jpo-d-15-0112.1.
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AbstractPotential vorticity structure in two segments of the North Atlantic’s western boundary current is examined using concurrent, high-resolution measurements of hydrography and velocity from gliders. Spray gliders occupied 40 transects across the Loop Current in the Gulf of Mexico and 11 transects across the Gulf Stream downstream of Cape Hatteras. Cross-stream distributions of the Ertel potential vorticity and its components are calculated for each transect under the assumptions that all flow is in the direction of measured vertically averaged currents and that the flow is geostrophic. Mean cross-stream distributions of hydrographic properties, potential vorticity, and alongstream velocity are calculated for both the Loop Current and the detached Gulf Stream in both depth and density coordinates. Differences between these mean transects highlight the downstream changes in western boundary current structure. As the current increases its transport downstream, upper-layer potential vorticity is generally reduced because of the combined effects of increased anticyclonic relative vorticity, reduced stratification, and increased cross-stream density gradients. The only exception is within the 20-km-wide cyclonic flank of the Gulf Stream, where intense cyclonic relative vorticity results in more positive potential vorticity than in the Loop Current. Cross-stream gradients of mean potential vorticity satisfy necessary conditions for both barotropic and baroclinic instability within the western boundary current. Instances of very low or negative potential vorticity, which predispose the flow to various overturning instabilities, are observed in individual transects across both the Loop Current and the Gulf Stream.
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Napolitano, Dante C., Ilson C. A. da Silveira, Cesar B. Rocha, Glenn R. Flierl, Paulo H. R. Calil, and Renato P. Martins. "On the Steadiness and Instability of the Intermediate Western Boundary Current between 24° and 18°S." Journal of Physical Oceanography 49, no. 12 (December 2019): 3127–43. http://dx.doi.org/10.1175/jpo-d-19-0011.1.
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AbstractThe Intermediate Western Boundary Current (IWBC) transports Antarctic Intermediate Water across the Vitória–Trindade Ridge (VTR), a seamount chain at ~20°S off Brazil. Recent studies suggest that the IWBC develops a strong cyclonic recirculation in Tubarão Bight, upstream of the VTR, with weak time dependency. We herein use new quasi-synoptic observations, data from the Argo array, and a regional numerical model to describe the structure and variability of the IWBC and to investigate its dynamics. Both shipboard acoustic Doppler current profiler (ADCP) data and trajectories of Argo floats confirm the existence of the IWBC recirculation, which is also captured by our Regional Oceanic Modeling System (ROMS) simulation. An “intermediate-layer” quasigeostrophic (QG) model indicates that the ROMS time-mean flow is a good proxy for the IWBC steady state, as revealed by largely parallel isolines of streamfunction and potential vorticity ; a scatter diagram also shows that the IWBC is potentially unstable. Further analysis of the ROMS simulation reveals that remotely generated, westward-propagating nonlinear eddies are the main source of variability in the region. These eddies enter the domain through the Tubarão Bight eastern edge and strongly interact with the IWBC. As they are advected downstream and negotiate the local topography, the eddies grow explosively through horizontal shear production.
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GRIFFITHS, ROSS W., and ANDREW E. KISS. "Flow regimes in a wide ‘sliced-cylinder’ model of homogeneous beta-plane circulation." Journal of Fluid Mechanics 399 (November 25, 1999): 205–36. http://dx.doi.org/10.1017/s0022112099006370.
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We report new experiments with the ‘sliced-cylinder’ β-plane model of Pedlosky & Greenspan (1967) and Beardsley (1969), but with a much wider basin such that the western boundary current and its eddies occupy a small fraction of the basin width. These experiments provide new insights into nonlinear aspects of the flow: the critical conditions for boundary current separation and the transition from stable to unstable flow are redefined, and a further transition from periodic to chaotic eddy shedding under strong anticyclonic forcing is also found. In the nonlinear regimes the western boundary current separates from the western wall and shoots into the interior as a narrow jet that undergoes a rapid adjustment to join with the broad slow interior flow. In the unstable regimes this adjustment involves eddy shedding. Each transition occurs at a fixed critical value of a Reynolds number Reγ based on the velocity and width scales for a purely viscous boundary current: the flow is unstable for Reγ > 123±4 and aperiodic for Reγ > 231±5. The results provide evidence that the mechanism causing instability is shear in the separated jet rather than the breaking of a large-amplitude Rossby wave. A quasi-geostrophic numerical model applied to the laboratory conditions yields a stability boundary and detailed characteristics of the flow largely consistent with those determined from the experiments. It also reveals a strong dependence of the circulation pattern on basin aspect ratio, and shows that an adverse higher-order pressure gradient is responsible for western boundary current separation in this model. Eddy–eddy interactions and feedback of fluctuations from the eddy formation region to upstream parts of the boundary current contribute to aperiodic behaviour. As a result of eddy shedding, passive tracer from each streamline in the boundary current can be stirred across much of the width of the basin.
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Spall, Michael A., Robert S. Pickart, Paula S. Fratantoni, and Albert J. Plueddemann. "Western Arctic Shelfbreak Eddies: Formation and Transport." Journal of Physical Oceanography 38, no. 8 (August 1, 2008): 1644–68. http://dx.doi.org/10.1175/2007jpo3829.1.
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Abstract The mean structure and time-dependent behavior of the shelfbreak jet along the southern Beaufort Sea, and its ability to transport properties into the basin interior via eddies are explored using high-resolution mooring data and an idealized numerical model. The analysis focuses on springtime, when weakly stratified winter-transformed Pacific water is being advected out of the Chukchi Sea. When winds are weak, the observed jet is bottom trapped with a low potential vorticity core and has maximum mean velocities of O(25 cm s−1) and an eastward transport of 0.42 Sv (1 Sv ≡ 106 m3 s−1). Despite the absence of winds, the current is highly time dependent, with relative vorticity and twisting vorticity often important components of the Ertel potential vorticity. An idealized primitive equation model forced by dense, weakly stratified waters flowing off a shelf produces a mean middepth boundary current similar in structure to that observed at the mooring site. The model boundary current is also highly variable, and produces numerous strong, small anticyclonic eddies that transport the shelf water into the basin interior. Analysis of the energy conversion terms in both the mooring data and the numerical model indicates that the eddies are formed via baroclinic instability of the boundary current. The structure of the eddies in the basin interior compares well with observations from drifting ice platforms. The results suggest that eddies shed from the shelfbreak jet contribute significantly to the offshore flux of heat, salt, and other properties, and are likely important for the ventilation of the halocline in the western Arctic Ocean. Interaction with an anticyclonic basin-scale circulation, meant to represent the Beaufort gyre, enhances the offshore transport of shelf water and results in a loss of mass transport from the shelfbreak jet.
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Edwards, Christopher A., and Joseph Pedlosky. "Dynamics of Nonlinear Cross-Equatorial Flow. Part II: The Tropically Enhanced Instability of the Western Boundary Current." Journal of Physical Oceanography 28, no. 12 (December 1998): 2407–17. http://dx.doi.org/10.1175/1520-0485(1998)028<2407:doncef>2.0.co;2.
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Yan, Xiaomei, Dujuan Kang, Enrique N. Curchitser, and Chongguang Pang. "Energetics of Eddy–Mean Flow Interactions along the Western Boundary Currents in the North Pacific." Journal of Physical Oceanography 49, no. 3 (March 2019): 789–810. http://dx.doi.org/10.1175/jpo-d-18-0201.1.
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AbstractThe energetics of eddy–mean flow interactions along two western boundary currents of the North Pacific, the Kuroshio and Ryukyu Currents, are systematically investigated using 22 years of numerical data from the Ocean General Circulation Model for the Earth Simulator (OFES). For the time-mean and time-varying flow fields, all the energy components and conversions exhibit inhomogeneous spatial distributions. In the two currents, complex cross-stream and along-stream variations are seen in the eddy–mean flow energy conversions. East of Taiwan, the kinetic energy is mainly transferred from the mean flow to the eddy field through barotropic instability, whereas the baroclinic energy conversions form a meridional dipole structure caused by the topographic constraint. In the northern area, particularly, the eddy field drains 2.25 × 108 W of kinetic energy and releases 2.82 × 108 W of available potential energy when interacting with the mean flow, indicating that mesoscale eddies impinging on the Kuroshio decay with baroclinic inverse energy cascades. In the Ryukyu Current, inverse energy conversions from the eddy field to the mean flow also dominate the power transfer in the subsurface layer. The eddy field transfers 0.16 × 108 W of kinetic energy and 1.89 × 108 W of available potential energy to the mean flow, suggesting that meososcale eddies play an important role in maintaining the velocity and hydrographic structure of the current. In other areas, both barotropic and baroclinic instabilities contribute to the generation of eddy kinetic energy with the latter one providing more than 3 times as much power as the former one.
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Feng, Ming, Susan Wijffels, Stuart Godfrey, and Gary Meyers. "Do Eddies Play a Role in the Momentum Balance of the Leeuwin Current?" Journal of Physical Oceanography 35, no. 6 (June 1, 2005): 964–75. http://dx.doi.org/10.1175/jpo2730.1.
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Abstract The Leeuwin Current is a poleward-flowing eastern boundary current off the western Australian coast, and alongshore momentum balance in the current has been hypothesized to comprise a southward pressure gradient force balanced by northward wind and bottom stresses. This alongshore momentum balance is revisited using a high-resolution upper-ocean climatology to determine the alongshore pressure gradient and altimeter and mooring observations to derive an eddy-induced Reynolds stress. Results show that north of the Abrolhos Islands (situated near the shelf break between 28.2° and 29.3°S), the alongshore momentum balance is between the pressure gradient and wind stress. South of the Abrolhos Islands, the Leeuwin Current is highly unstable and strong eddy kinetic energy is observed offshore of the current axis. The alongshore momentum balance on the offshore side of the current reveals an increased alongshore pressure gradient, weakened alongshore wind stress, and a significant Reynolds stress exerted by mesoscale eddies. The eddy Reynolds stress has a −0.5 Sv (Sv ≡ 106 m3 s−1) correction to the Indonesian Throughflow transport estimate from Godfrey’s island rule. The mesoscale eddies draw energy from the mean current through mixed barotropic and baroclinic instability, and the pressure gradient work overcomes the negative wind work to supply energy for the instability process. Hence the anomalous large-scale pressure gradient in the eastern Indian Ocean drives the strongest eddy kinetic energy level among all the midlatitude eastern boundary currents.
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Biló, Tiago Carrilho, and William E. Johns. "The Deep Western Boundary Current and Adjacent Interior Circulation at 24°–30°N: Mean Structure and Mesoscale Variability." Journal of Physical Oceanography 50, no. 9 (September 1, 2020): 2735–58. http://dx.doi.org/10.1175/jpo-d-20-0094.1.
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AbstractThe mean North Atlantic Deep Water (NADW, 1000 < z < 5000 m) circulation and deep western boundary current (DWBC) variability offshore of Abaco, Bahamas, at 26.5°N are investigated from nearly two decades of velocity and hydrographic observations, and outputs from a 30-yr-long eddy-resolving global simulation. Observations at 26.5°N and Argo-derived geostrophic velocities show the presence of a mean Abaco Gyre spanning the NADW layer, consisting of a closed cyclonic circulation between approximately 24° and 30°N and 72° and 77°W. The southward-flowing portion of this gyre (the DWBC) is constrained to within ~150 km of the western boundary with a mean transport of ~30 Sv (1 Sv ≡ 106 m3 s−1). Offshore of the DWBC, the data show a consistent northward recirculation with net transports varying from 6.5 to 16 Sv. Current meter records spanning 2008–17 supported by the numerical simulation indicate that the DWBC transport variability is dominated by two distinct types of fluctuations: 1) periods of 250–280 days that occur regularly throughout the time series and 2) energetic oscillations with periods between 400 and 700 days that occur sporadically every 5–6 years and force the DWBC to meander far offshore for several months. The shorter-period variations are related to DWBC meandering caused by eddies propagating southward along the continental slope at 24°–30°N, while the longer-period oscillations appear to be related to large anticyclonic eddies that slowly propagate northwestward counter to the DWBC flow between ~20° and 26.5°N. Observational and theoretical evidence suggest that these two types of variability might be generated, respectively, by DWBC instability processes and Rossby waves reflecting from the western boundary.
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Heath, RA. "Large-scale influence of the New Zealand seafloor topography on western boundary currents of the South Pacific Ocean." Marine and Freshwater Research 36, no. 1 (1985): 1. http://dx.doi.org/10.1071/mf9850001.
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The extensive New Zealand submarine platform lying approximately 1600 km east of Australia has a strong influence on the South Pacific circulation. Together with the Kermadec Ridge, it is the western boundary of the deep South Pacific Ocean with an associated deep western boundary current. Although New Zealand probably influences where the East Australian Current separates from the east Australian coast, at the latitude of northernmost New Zealand, the sloping seafloor on the New Zealand west coast does allow for a meridional flow there. However, the decrease in current speed with depth does decrease the influence of the bottom topography. The net result is that there is both an intensification of the zonal flow across the Tasman Sea at the latitude of northernmost New Zealand, the speed of which is enhanced by the flow over the extensive ridge system, and a general eastwards flow in the Tasman Sea over the latitudinal range of New Zealand, which feeds meridional flows on the New Zealand west coast. It is suggested that the general west to east flow past New Zealand restricts the westward propagation of second- and higher-order baroclinic Rossby waves with the result that, whereas the East Australian Current has rapid near-surface flow which decreases rapidly with depth in the upper 500 m, the surface flow on the east coast of New Zealand is less rapid and decreases more uniformly with depth. One possible consequence of the current speed change with depth is that the flow and eddies on the New Zealand east coast appear to be influenced by the bathymetry whereas the East Australian Current eddies are more a primary component of the current linked to instability in the current system.
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Chien, Fang-Ching, Jing-Shan Hong, and Ying-Hwa Kuo. "The Marine Boundary Layer Height over the Western North Pacific Based on GPS Radio Occultation, Island Soundings, and Numerical Models." Sensors 19, no. 1 (January 4, 2019): 155. http://dx.doi.org/10.3390/s19010155.
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This paper estimates marine boundary layer height (MBLH) over the western North Pacific (WNP) based on Global Positioning System Radio Occultation (GPS-RO) profiles from the Formosa Satellite Mission 3 (FORMOSAT-3)/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites, island soundings, and numerical models. The seasonally-averaged MBLHs computed from nine years (2007–2015) of GPS-RO data are inter-compared with those obtained from sounding observations at 15 island stations and from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-Interim) and National Centers for Environmental Prediction Global Forecast System (NCEP GFS) data over the WNP from 2012 to 2015. It is found that the MBLH using nine years of GPS-RO data is smoother and more consistent with that obtained from sounding observations than is the MBLH using four years of GPS-RO data in a previous study. In winter, higher MBLHs are found around the subtropical latitudes and over oceans east of Japan, which are approximately located within the paths of the North Equatorial Current and the Kuroshio Current. The MBLH is also significantly higher in winter than in summer over the WNP. The above MBLH pattern is generally similar to those obtained from the analysis data of the ERA-Interim and NCEP GFS, but the heights are about 200 m higher. The verification with soundings suggests that the ERA-Interim has a better MBLH estimation than the NCEP GFS. Thus, the MBLH distributions obtained from both the nine-year GPS-RO and the ERA-Interim data can represent well the climatological MBLH over the WNP, but the heights should be adjusted about 30 m lower for the former and ~200 m higher for the latter. A positive correlation between the MBLH and the instability of the lower atmosphere exists over large near-shore areas of the WNP, where cold air can move over warm oceans from the land in winter, resulting in an increase in lower-atmospheric instability and providing favorable conditions for convection to yield a higher MBLH. During summer, the lower-atmospheric instability becomes smaller and the MBLH is thus lower over near-shore oceans.
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Hochet, Antoine, Thierry Huck, and Alain Colin de Verdière. "Large-Scale Baroclinic Instability of the Mean Oceanic Circulation: A Local Approach." Journal of Physical Oceanography 45, no. 11 (November 2015): 2738–54. http://dx.doi.org/10.1175/jpo-d-15-0084.1.
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AbstractLarge-scale baroclinic instability is investigated as a potential source of Rossby waves and large-scale variability in the ocean. This baroclinic instability is first reviewed in a 2.5-layer model. As already noticed by several authors, the instability arises in westward surface mean flow when the phase velocities of the two vertical modes are made equal by mean flow influence. This large-scale instability is stronger at low latitudes and thus is likely to happen in the westward return flow of the subtropical gyres. Further investigations with a continuous stratification quasigeostrophic model show that the instability is stronger where the mean flow projects negatively on the second baroclinic mode (imposing positive vertical modes at the surface). The linear stability calculation is then performed on Argo-derived mean flow along with mean stratification data. The results show that the unstable regions are situated at low latitudes in every oceanic basin, in western boundary currents, and in some part of the Antarctic Circumpolar Current. The location of these unstable regions is well correlated with the region of negative projection of the mean flow on the second baroclinic mode. Given that the unstable mode growth times are generally smaller than 6 months at low latitudes, these unstable modes are likely to be observable in satellite altimetry. Therefore, results of the present article suggest that the large-scale instability is indeed a source of large-scale variability at low latitudes.
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Solodoch, Aviv, Andrew L. Stewart, and James C. McWilliams. "Baroclinic instability of axially symmetric flow over sloping bathymetry." Journal of Fluid Mechanics 799 (June 22, 2016): 265–96. http://dx.doi.org/10.1017/jfm.2016.376.
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Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical two-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Non-zero barotropic flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.
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Polito, Paulo S., and Olga T. Sato. "Global Interannual Trends and Amplitude Modulations of the Sea Surface Height Anomaly from the TOPEX/Jason-1 Altimeters." Journal of Climate 21, no. 12 (June 15, 2008): 2824–34. http://dx.doi.org/10.1175/2007jcli1924.1.
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Abstract This study uses the global Ocean Topography Experiment (TOPEX)/Jason-1 altimeters’ time series to estimate the 13-yr trend in sea surface height anomaly. These trends are estimated at each grid point by two methods: one fits a straight line to the time series and the other is based on the difference between the average height between the two halves of the time series. In both cases the trend shows large regional variability, mostly where the intense western boundary currents turn. The authors hypothesize that the regional variability of the sea surface height trends leads to changes in the local geostrophic transport. This in turn affects the instability-related processes that generate mesoscale eddies and enhances the Rossby wave signals. This hypothesis is verified by estimates of the trend of the amplitude of the filtered sea surface height anomaly that contains the spectral bands associated with Rossby waves and mesoscale eddies. The authors found predominantly positive tendency in the amplitude of Rossby waves and eddies, which suggests that, on average, these events are becoming more energetic. In some regions, the variation in amplitude over 13 yr is comparable to the standard deviation of the data and is statistically significant according to both methods employed in this study. It is plausible that in this case, the energy is transferred from the mean currents to the waves and eddies through barotropic and baroclinic instability processes that are more pronounced in the western boundary current extension regions. If these heat storage patterns and trends are confirmed on longer time series, then it will be justified to argue that the warming trend of the last century provides the energy that amplifies both Rossby waves and mesoscale eddies.
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Hogg, Andrew Mc C., William K. Dewar, Pavel Berloff, Sergey Kravtsov, and David K. Hutchinson. "The Effects of Mesoscale Ocean–Atmosphere Coupling on the Large-Scale Ocean Circulation." Journal of Climate 22, no. 15 (August 1, 2009): 4066–82. http://dx.doi.org/10.1175/2009jcli2629.1.
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Abstract Small-scale variation in wind stress due to ocean–atmosphere interaction within the atmospheric boundary layer alters the temporal and spatial scale of Ekman pumping driving the double-gyre circulation of the ocean. A high-resolution quasigeostrophic (QG) ocean model, coupled to a dynamic atmospheric mixed layer, is used to demonstrate that, despite the small spatial scale of the Ekman-pumping anomalies, this phenomenon significantly modifies the large-scale ocean circulation. The primary effect is to decrease the strength of the nonlinear component of the gyre circulation by approximately 30%–40%. This result is due to the highest transient Ekman-pumping anomalies destabilizing the flow in a dynamically sensitive region close to the western boundary current separation. The instability of the jet produces a flux of potential vorticity between the two gyres that acts to weaken both gyres.
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Furue, Ryo, Julian P. McCreary, and Zuojun Yu. "Dynamics of the Northern Tsuchiya Jet*." Journal of Physical Oceanography 39, no. 9 (September 1, 2009): 2024–51. http://dx.doi.org/10.1175/2009jpo4065.1.
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Abstract The Tsuchiya jets (TJs) are narrow eastward currents located along thermal fronts at the poleward edges of thermostad water in the Pacific Ocean. In this study, an oceanic general circulation model (OGCM) is used to explore the dynamics of the northern TJ. Solutions are found in a rectangular basin, extending 100° zonally and from 40°S to 40°N. They are forced by three idealized forcings: several patches of idealized wind fields, including one that simulates the strong Ekman pumping region in the vicinity of the Costa Rica Dome (CRD); surface heating that warms the ocean in the tropics; and a prescribed interocean circulation (IOC) that enters the basin through the southern boundary and exits through the western boundary from 2° to 6°N (the model’s Indonesian passages). Solutions forced by all the aforementioned processes and with minimal diffusion resemble the observed flow field in the tropical North Pacific. A narrow eastward current, the model’s northern TJ, flows across the basin along the northern edge of a thick equatorial thermostad. Part of the TJ water upwells at the CRD upwelling region and the rest returns westward in the lower part of the North Equatorial Current. The deeper part of the TJ is supplied by water that leaves the western boundary current somewhat north of the equator. Its shallower part originates from water that diverges from the deep portion of the Equatorial Undercurrent (EUC); as a result, the TJ transport increases to the east and the TJ warms as it flows across the basin. These and other properties suggest that the dynamics of the model’s TJ are those of an arrested front, which in a 2½-layer model are generated when characteristics of the flow converge strongly or intersect. Eddy form stress, due to instability waves generated at the CRD region, extends the TJ circulation to deeper levels. When diffusivity is increased to commonly used values, the thermostad is less well defined and the TJ is weak. In a solution without the IOC, the TJ is shifted to higher temperatures with its water supplied by the subtropical cell. When horizontal viscosity is reduced, the TJ becomes narrower and is flanked by a westward current on its equatorward side.
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Aoki, Kunihiro, Shoshiro Minobe, Youichi Tanimoto, and Yoshikazu Sasai. "Southward Eddy Heat Transport Occurring along Southern Flanks of the Kuroshio Extension and the Gulf Stream in a 1/10° Global Ocean General Circulation Model." Journal of Physical Oceanography 43, no. 9 (September 1, 2013): 1899–910. http://dx.doi.org/10.1175/jpo-d-12-0223.1.
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Abstract The present study investigates meridional heat transport induced by oceanic mesoscale variability in the World Ocean using a ° global ocean general circulation model (OGCM) running on the Earth Simulator. The results indicate prominent poleward eddy heat transport around the western boundary currents and the Antarctic Circumpolar Current, and equatorward eddy heat transport in the equatorial region, consistent with the previous studies using coarse-resolution OGCMs. Such poleward eddy heat transport in midlatitude oceans suggests that the eddies act to reduce meridional background temperature gradients across the currents, as would be expected based on baroclinic instability. Interestingly, however, along the southern flanks of the eastward jets of the Kuroshio Extension and the Gulf Stream, southward eddy heat transport occurs in subsurface layers. This is likely due to the southward migration of warm water cores originating from southern areas adjacent to these currents. Southward movement of these cores is caused by interactions with unsteady meanders and cold eddies detaching from the meanders. The potential impact on biological production in the subtropical surface layers of these southward-traveling warm water cores is also discussed.
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Zhai, Ping, Larry J. Pratt, and Amy Bower. "On the Crossover of Boundary Currents in an Idealized Model of the Red Sea." Journal of Physical Oceanography 45, no. 5 (May 2015): 1410–25. http://dx.doi.org/10.1175/jpo-d-14-0192.1.
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AbstractThe west-to-east crossover of boundary currents has been seen in mean circulation schemes from several past models of the Red Sea. This study investigates the mechanisms that produce and control the crossover in an idealized, eddy-resolving numerical model of the Red Sea. The authors also review the observational evidence and derive an analytical estimate for the crossover latitude. The surface buoyancy loss increases northward in the idealized model, and the resultant mean circulation consists of an anticyclonic gyre in the south and a cyclonic gyre in the north. In the midbasin, the northward surface flow crosses from the western boundary to the eastern boundary. Numerical experiments with different parameters indicate that the crossover latitude of the boundary currents changes with f0, β, and the meridional gradient of surface buoyancy forcing. In the analytical estimate, which is based on quasigeostrophic, β-plane dynamics, the crossover is predicted to lie at the latitude where the net potential vorticity advection (including an eddy component) is zero. Various terms in the potential vorticity budget can be estimated using a buoyancy budget, a thermal wind balance, and a parameterization of baroclinic instability.
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Mathias, Luca, Patrick Ludwig, and Joaquim G. Pinto. "Synoptic-scale conditions and convection-resolving hindcast experiments of a cold-season derecho on 3 January 2014 in western Europe." Natural Hazards and Earth System Sciences 19, no. 5 (May 15, 2019): 1023–40. http://dx.doi.org/10.5194/nhess-19-1023-2019.
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Abstract. A major linear mesoscale convective system caused severe weather over northern France, Belgium, the Netherlands and northwestern Germany on 3 January 2014. The storm was classified as a cold-season derecho with widespread wind gusts exceeding 25 m s−1. While such derechos occasionally develop along cold fronts of extratropical cyclones, this system formed in a postfrontal air mass along a baroclinic surface pressure trough and was favoured by a strong large-scale air ascent induced by an intense mid-level jet. The lower-tropospheric environment was characterised by weak latent instability and strong vertical wind shear. Given the poor operational forecast of the storm, we analyse the role of initial and lateral boundary conditions to the storm's development by performing convection-resolving limited-area simulations with operational analysis and reanalysis datasets. The storm is best represented in simulations with high temporally and spatially resolved initial and lateral boundary conditions derived from ERA5, which provide the most realistic development of the essential surface pressure trough. Moreover, simulations at convection-resolving resolution enable a better representation of the observed derecho intensity. This case study is testimony to the usefulness of ensembles of convection-resolving simulations in overcoming the current shortcomings of forecasting cold-season convective storms, particularly for cases not associated with a cold front.
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Mano, Manlio F., Afonso M. Paiva, Audalio R. Torres, and Alvaro L. G. A. Coutinho. "Energy Flux to a Cyclonic Eddy off Cabo Frio, Brazil." Journal of Physical Oceanography 39, no. 11 (November 1, 2009): 2999–3010. http://dx.doi.org/10.1175/2009jpo4026.1.
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Abstract To evaluate the energy flux from the mean flow of South Atlantic western boundary currents toward typical Cabo Frio eddies (at Brazilian southeast coast), the southwestern Atlantic circulation was simulated with the Princeton Ocean Model. Throughout the study period, the vertical profile of eddy available potential energy direction was monitored. The results indicated that baroclinic instability eddies first appear in intermediate depths and then its signal propagates upward, draining energy from the Brazil Current (BC), until it reaches the surface, 30 days after its formation. The depth of eddy formation is related to the vertical profile of the mean potential vorticity cross-current gradient (∂q/∂s). The beginning of the potential energy flux toward the perturbation and the origin of the eddy occurred at a similar depth and time. The observed pattern suggests the following cycle: 1) a well-defined southwestward-flowing BC in the beginning of the period, with a baroclinically unstable profile of ∂q/∂s; 2) energy flux from the mean flow toward perturbation at intermediate depth; 3) current destabilization and meandering; 4) formation and growth of the cyclonic eddy; 5) potential energy flux progressively shallower; 6) propagation of the eddy signal upward; and 7) stabilization of the water column.
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Liu, F., S. Tang, and C. Chen. "Satellite observations of the small-scale cyclonic eddies in the western South China Sea." Biogeosciences 12, no. 2 (January 16, 2015): 299–305. http://dx.doi.org/10.5194/bg-12-299-2015.
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Abstract. High-resolution ocean color observations offer an opportunity to investigate the oceanic small-scale processes. In this study, the Medium Resolution Imaging Spectrometer (MERIS) daily 300 m data were used to study small-scale processes in the western South China Sea. It is indicated that the cyclonic eddies with horizontal scales of 10 km are frequently observed during the upwelling season of each year over the 2004–2009 period. These small-scale eddies were generated in the vicinity of the southern front of the cold tongue, and then propagated eastward with a speed of approximately 12 cm s−1. This propagation speed was consistent with the velocity of the western boundary current. As a result, the small-scale eddies kept the high levels of phytoplankton rotating away from the coastal areas, resulting in the accumulation of phytoplankton in the interior of the eddies. The generation of the small-scale eddies may be associated with strengthening of the relative movement between the rotation speed of the anticyclonic mesoscale eddies and the offshore transport. With the increases of the normalized rotation speed of the anticyclonic mesoscale eddies relative to the offshore transport, the offshore current became a meander under the impacts of the anticyclonic mesoscale eddies. The meandered cold tongue and instability front may stimulate the generation of the small-scale eddies. Unidirectional uniform wind along the cold tongue may also contribute to the formation of the small-scale eddies.
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Liu, F., S. Tang, and C. Chen. "Satellite observations of the small-scale cyclonic eddies in the western South China Sea." Biogeosciences Discussions 11, no. 9 (September 19, 2014): 13515–32. http://dx.doi.org/10.5194/bgd-11-13515-2014.
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Abstract. High-resolution ocean color observation offers an opportunity to investigate the oceanic small-scale processes. In this study, The Medium Resolution Imaging Spectrometer (MERIS) daily 300 m data are used to study small-scale processes in the western South China Sea. It is indicated that the cyclonic eddies with horizontal scales of the order of 10 km are frequently observed during upwelling season of each year over 2004–2009. These small-scale eddies are generated in the vicinity of the southern front of the cold tongue, and then propagate eastward with a speed of approximately 12 cm s−1. This propagation speed is consistent with the velocity of the western boundary current. As a result, the small-scale eddies keep rotating high levels of the phytoplankton away from the coastal areas, resulting in the accumulation of phytoplankton in the interior of the eddies. The generation of the small-scale eddies may be associated with strengthening of the relative movement between the rotation speed of the anticylconic mesoscale eddies and the offshore transport. With the increases of the normalized rotation speed of the anticyclonic mesoscale eddies relative to the offshore transport, the offshore current become meander under the impacts of the anticyclonic mesoscale eddies. The meandered cold tongue and instability front may stimulate the generation of the small-scale eddies. Unidirectional uniform wind along cold tongue may also contribute to the formation of the small-scale eddies.
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Arzel, Olivier, Thierry Huck, and Alain Colin de Verdière. "The Different Nature of the Interdecadal Variability of the Thermohaline Circulation under Mixed and Flux Boundary Conditions." Journal of Physical Oceanography 36, no. 9 (September 1, 2006): 1703–18. http://dx.doi.org/10.1175/jpo2938.1.
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Abstract The differences between the interdecadal variability under mixed and constant flux boundary conditions are investigated using a coarse-resolution ocean model in an idealized flat-bottom single-hemisphere basin. Objective features are determined that allow one type of oscillation to be distinguished versus the other. First, by performing a linear stability analysis of the steady state obtained under restoring boundary conditions, it is shown that the interdecadal variability under constant flux and mixed boundary conditions arises, respectively, from the instability of a linear mode around the mean stratification and circulation and from departure from the initial state. Based on the budgets of density variance, it is shown next that the two types of oscillations have different energy sources: Under the constant-flux boundary condition (the thermal mode), the downgradient meridional eddy heat flux in the western boundary current regions sustains interdecadal variability, whereas under mixed boundary conditions (the salinity mode), a positive feedback between convective adjustment and restoring surface heat flux is at the heart of the existence of the decadal oscillation. Furthermore, the positive correlations between temperature and salinity anomalies in the forcing layer are shown to dominate the forcing of density variance. In addition, the vertical structure of perturbations reveals vertical phase lags at different depths in all tracer fields under constant flux, while under mixed boundary conditions only the temperature anomalies show a strong dipolar structure. The authors propose that these differences will allow one to identify which type of oscillation, if any, is at play in the more exhaustive climate models.
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Swaters, Gordon E. "The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part I: Model Development and Dynamical Properties." Journal of Physical Oceanography 36, no. 3 (March 1, 2006): 335–55. http://dx.doi.org/10.1175/jpo2855.1.
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Abstract The equatorward flow of source-driven grounded deep western boundary currents within a stratified basin with variable topography is examined. The model is the two-layer quasigeostrophic (QG) equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic (PG) equations, describing the abyssal layer, on a midlatitude β plane. The model retains subapproximations such as classical Stommel–Arons theory, the Nof abyssal dynamical balance, the so-called planetary shock wave balance (describing the finite-amplitude β-induced westward propagation of abyssal anomalies), and baroclinic instability. The abyssal height field can possess groundings. In the reduced gravity limit, a new nonlinear steady-state balance is identified that connects source-driven equatorward abyssal flow (as predicted by Stommel–Arons theory) and the inertial topographically steered deep flow described by Nof dynamics. This model is solved explicitly, and the meridional structure of the predicted grounded abyssal flow is described. In the fully baroclinic limit, a variational principle is established and is exploited to obtain general stability conditions for meridional abyssal flow over variable topography on a β plane. The baroclinic coupling of the PG abyssal layer with the QG overlying ocean eliminates the ultraviolet catastrophe known to occur in inviscid PG reduced gravity models. The baroclinic instability problem for a constant-velocity meridional abyssal current flowing over sloping topography with β present is solved and the stability characteristics are described.
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Dawe, Jordan T., and Lu Anne Thompson. "Viscosity-Dependent Internal Variability in a Model of the North Pacific." Journal of Physical Oceanography 35, no. 5 (May 1, 2005): 747–56. http://dx.doi.org/10.1175/jpo2707.1.
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Abstract A 2°-resolution isopycnal model of the North Pacific Ocean is shown to produce anomalies that propagate around the subtropical gyre on the decadal time scale that do not appear in a 1°-resolution version of the same model. A principal oscillation pattern (POP) analysis of the isopycnal interface anomaly is performed to examine the dynamics responsible for the anomaly generation. The POPs show a coherent oscillation around the entire subtropical gyre with two centers of action, one in the Central Mode Water (CMW) region, the other in the Subtropical Countercurrent (STCC). Lead–lag covariances between the subduction rate in the CMW and the layer thickness along the oscillation path indicate that anomalous subduction events are not the driving mechanism for the oscillation. A linearized quasigeostrophic mode analysis shows that the anomalies are generated by flow instability in the region of the STCC. The instability disappears in the 1° model because of changes in the horizontal viscosity, which is set in each model to the minimum value necessary to resolve the western boundary current and preserve numerical stability. A criterion for model resolution of an instability of a given length and time scale damped by biharmonic viscosity is derived. The enhancement of the large-scale instabilities in the low-resolution model emphasizes the importance of achieving mesoscale resolution in ocean models used for climate studies.
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Schubert, René, Arne Biastoch, Meghan F. Cronin, and Richard J. Greatbatch. "Instability-Driven Benthic Storms below the Separated Gulf Stream and the North Atlantic Current in a High-Resolution Ocean Model." Journal of Physical Oceanography 48, no. 10 (October 2018): 2283–303. http://dx.doi.org/10.1175/jpo-d-17-0261.1.
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AbstractBenthic storms are important for both the energy budget of the ocean and for sediment resuspension and transport. Using 30 years of output from a high-resolution model of the North Atlantic, it is found that most of the benthic storms in the model occur near the western boundary in association with the Gulf Stream and the North Atlantic Current, in regions that are generally collocated with the peak near-bottom eddy kinetic energy. A common feature is meander troughs in the near-surface jets that are accompanied by deep low pressure anomalies spinning up deep cyclones with near-bottom velocities of up to more than 0.5 m s−1. A case study of one of these events shows the importance of both baroclinic and barotropic instability of the jet, with energy being extracted from the jet in the upstream part of the meander trough and partly returned to the jet in the downstream part of the meander trough. This motivates examining the 30-yr time mean of the energy transfer from the (annual mean) background flow into the eddy kinetic energy. This quantity is shown to be collocated well with the region in which benthic storms and large increases in deep cyclonic relative vorticity occur most frequently, suggesting an important role for mixed barotropic–baroclinic instability-driven cyclogenesis in generating benthic storms throughout the model simulation. Regions of the largest energy transfer and most frequent benthic storms are found to be the Gulf Stream west of the New England Seamounts and the North Atlantic Current near Flemish Cap.
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Delman, Andrew, and Tong Lee. "Global contributions of mesoscale dynamics to meridional heat transport." Ocean Science 17, no. 4 (August 5, 2021): 1031–52. http://dx.doi.org/10.5194/os-17-1031-2021.
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Abstract. Mesoscale ocean processes are prevalent in many parts of the global oceans and may contribute substantially to the meridional movement of heat. Yet earlier global surveys of meridional temperature fluxes and heat transport (HT) have not formally distinguished between mesoscale and large-scale contributions, or they have defined eddy contributions based on temporal rather than spatial characteristics. This work uses spatial filtering methods to separate large-scale (gyre and planetary wave) contributions from mesoscale (eddy, recirculation, and tropical instability wave) contributions to meridional HT. Overall, the mesoscale temperature flux (MTF) produces a net poleward meridional HT at midlatitudes and equatorward meridional HT in the tropics, thereby resulting in a net divergence of heat from the subtropics. In addition to MTF generated by propagating eddies and tropical instability waves, MTF is also produced by stationary recirculations near energetic western boundary currents, where the temperature difference between the boundary current and its recirculation produces the MTF. The mesoscale contribution to meridional HT yields substantially different results from temporally based “eddy” contributions to meridional HT, with the latter including large-scale gyre and planetary wave motions at low latitudes. Mesoscale temperature fluxes contribute the most to interannual and decadal variability of meridional HT in the Southern Ocean, the tropical Indo-Pacific, and the North Atlantic. Surface eddy kinetic energy (EKE) is not a good proxy for MTF variability in regions with the highest time-mean EKE, though it does explain much of the temperature flux variability in regions of modest time-mean EKE. This approach to quantifying mesoscale fluxes can be used to improve parameterizations of mesoscale effects in coarse-resolution models and assess regional impacts of mesoscale eddies and recirculations on tracer fluxes.
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Jing, Zhao, Shengpeng Wang, Lixin Wu, Ping Chang, Qiuying Zhang, Bingrong Sun, Xiaohui Ma, et al. "Maintenance of mid-latitude oceanic fronts by mesoscale eddies." Science Advances 6, no. 31 (July 2020): eaba7880. http://dx.doi.org/10.1126/sciadv.aba7880.
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Oceanic fronts associated with strong western boundary current extensions vent a vast amount of heat into the atmosphere, anchoring mid-latitude storm tracks and facilitating ocean carbon sequestration. However, it remains unclear how the surface heat reservoir is replenished by ocean processes to sustain the atmospheric heat uptake. Using high-resolution climate simulations, we find that the vertical heat transport by ocean mesoscale eddies acts as an important heat supplier to the surface ocean in frontal regions. This vertical eddy heat transport is not accounted for by the prevailing inviscid and adiabatic ocean dynamical theories such as baroclinic instability and frontogenesis but is tightly related to the atmospheric forcing. Strong surface cooling associated with intense winds in winter promotes turbulent mixing in the mixed layer, destructing the vertical shear of mesoscale eddies. The restoring of vertical shear induces an ageostrophic secondary circulation transporting heat from the subsurface to surface ocean.
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Sun, Shantong, Lixin Wu, and Bo Qiu. "Response of the Inertial Recirculation to Intensified Stratification in a Two-Layer Quasigeostrophic Ocean Circulation Model." Journal of Physical Oceanography 43, no. 7 (July 1, 2013): 1254–69. http://dx.doi.org/10.1175/jpo-d-12-0111.1.
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Abstract Previous observation and model studies show that the upper-ocean stratification is enhanced under global warming (Capotondi et al.; Cravatte et al.; Deser et al., etc.). The response of the recirculation, which is associated with the western boundary current (WBC) jet extension and significantly increases its transport, to the intensified stratification, is studied in a two-layer quasigeostrophic ocean circulation model. It is found that the barotropic transport of the circulation first increases with stratification but then decreases as a result of saturation of the surface-layer circulation intensity when the stratification exceeds a threshold. PV budget analysis indicates that the saturation is caused by the increased intergyre transport of relative potential vorticity resulting from the intensified variability of the jet location. Both the barotropic instability and bifurcation mechanisms contribute to the intensified variability of the jet location. Because of barotropic instability, eddies are generated in the confluence region of the WBCs and advected eastward, causing the variability of the jet location. With increased stratification, the surface-layer circulation is strengthened and the barotropic instability is intensified. As a result, the surface flow becomes more variable with excessive eddies and intense variability of the jet. With the increasing stratification, three regimes, each marked by its own variation of the jet location, emerge owing to the successive system bifurcations. In the last two regimes, variability of the jet location is further enhanced by frequent switches among the different dynamic states on multidecadal time scales.
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Sayanagi, Kunio M., Raúl Morales-Juberías, and Andrew P. Ingersoll. "Saturn’s Northern Hemisphere Ribbon: Simulations and Comparison with the Meandering Gulf Stream." Journal of the Atmospheric Sciences 67, no. 8 (August 1, 2010): 2658–78. http://dx.doi.org/10.1175/2010jas3315.1.
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Abstract Voyager observations of Saturn in 1980–81 discovered a wavy feature engirdling the planet at 47°N planetographic latitude. Its latitude coincides with that of an eastward jet stream, which is the second fastest on Saturn after the equatorial jet. The 47°N jet’s wavy morphology is unique among the known atmospheric jets on the gas giant planets. Since the Voyagers, it has been seen in every high-resolution image of this latitude for over 25 years and has been termed the Ribbon. The Ribbon has been interpreted as a dynamic instability in the jet stream. This study tests this interpretation and uses forward modeling to explore the observed zonal wind profile’s stability properties. Unforced, initial-value numerical experiments are performed to examine the nonlinear evolution of the jet stream. Parameter variations show that an instability occurs when the 47°N jet causes reversals in the potential vorticity (PV) gradient, which constitutes a violation of the Charney–Stern stability criterion. After the initial instability development, the simulations demonstrate that the instability’s amplitude nonlinearly saturates to a constant when the eddy generation by the instability is balanced by the destruction of the eddies. When the instability saturates, the zonal wind profile approaches neutral stability according to Arnol’d’s second criterion, and the jet’s path meanders in a Ribbon-like manner. It is demonstrated that the meandering of the 47°N jet occurs over a range of tropospheric static stability and background wind speed. The results here show that a nonlinearly saturated shear instability in the 47°N jet is a viable mechanism to produce the Ribbon morphology. Observations do not yet have the temporal coverage to confirm the creation and destruction of eddies, but these simulations predict that this is actively occurring in the Ribbon region. Similarities exist between the behaviors found in this model and the dynamics of PV fronts studied in the context of meandering western boundary currents in Earth’s oceans. In addition, the simulations capture the nonlinear aspects of a new feature discovered by the Cassini Visual and Infrared Mapping Spectrometer (VIMS), the String of Pearls, which resides in the equatorward tip of the 47°N jet. The Explicit Planetary Isentropic Coordinate (EPIC) model is used herein.
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Swaters, Gordon E. "The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part II: Numerical Simulation." Journal of Physical Oceanography 36, no. 3 (March 1, 2006): 356–75. http://dx.doi.org/10.1175/jpo2868.1.
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Abstract A numerical simulation is described for source-driven abyssal currents in a 3660 km × 3660 km stratified Northern Hemisphere basin with zonally varying topography. The model is the two-layer quasigeostrophic equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic equations, describing the abyssal layer, on a midlatitude β plane. The source region is a fixed 75 km × 150 km area located in the northwestern sector of the basin with a steady downward volume transport of about 5.6 Sv (Sv ≡ 106 m3 s−1) corresponding to an average downwelling velocity of about 0.05 cm s−1. The other parameter values are characteristic of the North Atlantic Ocean. It takes about 3.2 yr for the abyssal water mass to reach the southern boundary and about 25 yr for a statistical state to develop. Time-averaged and instantaneous fields at a late time are described. The time-averaged fields show an equatorward-flowing abyssal current with distinct up- and downslope groundings with decreasing height in the equatorward direction. The average equatorward abyssal transport is about 8 Sv, and the average abyssal current thickness is about 500 m and is about 400 km wide. The circulation in the upper layers is mostly cyclonic and is western intensified, with current speeds about 0.6 cm s−1. The upper layer cyclonic circulation intensifies in the source region with speeds about 4 cm s−1, and there is an anticyclonic circulation region immediately adjacent to the western boundary giving rise to a weak barotropic poleward current in the upper layers with a speed of about 0.6 cm s−1. The instantaneous fields are highly variable. Even though the source is steady, there is a pronounced spectral peak at the period of about 54 days. The frequency associated with the spectral peak is an increasing function of the downwelling volume flux. The periodicity is associated with the formation of transient cyclonic eddies in the overlying ocean in the source region and downslope propagating plumes and boluses in the abyssal water mass. The cyclonic eddies have a radii about 100–150 km and propagation speeds about 5–10 cm s−1. The eddies are formed initially because of stretching associated with the downwelling in the source region. Once detached from the source region, the cyclonic eddies are phase locked with the boluses or plumes that form on the downslope grounding of the abyssal current, which themselves form because of baroclinic instability. Eventually, the background vorticity gradients associated with β and the sloping bottom arrest the downslope (eastward) motion, the abyssal boluses diminish in amplitude, the abyssal current flows preferentially equatorward, the upper layer eddies disperse and diminish in amplitude, and westward intensification develops.
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Berloff, P., W. Dewar, S. Kravtsov, and J. McWilliams. "Ocean Eddy Dynamics in a Coupled Ocean–Atmosphere Model*." Journal of Physical Oceanography 37, no. 5 (May 1, 2007): 1103–21. http://dx.doi.org/10.1175/jpo3041.1.
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Abstract The role of mesoscale oceanic eddies is analyzed in a quasigeostrophic coupled ocean–atmosphere model operating at a large Reynolds number. The model dynamics are characterized by decadal variability that involves nonlinear adjustment of the ocean to coherent north–south shifts of the atmosphere. The oceanic eddy effects are diagnosed by the dynamical decomposition method adapted for nonstationary external forcing. The main effects of the eddies are an enhancement of the oceanic eastward jet separating the subpolar and subtropical gyres and a weakening of the gyres. The flow-enhancing effect is due to nonlinear rectification driven by fluctuations of the eddy forcing. This is a nonlocal process involving generation of the eddies by the flow instabilities in the western boundary current and the upstream part of the eastward jet. The eddies are advected by the mean current to the east, where they backscatter into the rectified enhancement of the eastward jet. The gyre-weakening effect, which is due to the time-mean buoyancy component of the eddy forcing, is a result of the baroclinic instability of the westward return currents. The diagnosed eddy forcing is parameterized in a non-eddy-resolving ocean model, as a nonstationary random process, in which the corresponding parameters are derived from the control coupled simulation. The key parameter of the random process—its variance—is related to the large-scale flow baroclinicity index. It is shown that the coupled model with the non-eddy-resolving ocean component and the parameterized eddies correctly simulates climatology and low-frequency variability of the control eddy-resolving coupled solution.
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Qiu, Bo, Shuiming Chen, Patrice Klein, Jinbo Wang, Hector Torres, Lee-Lueng Fu, and Dimitris Menemenlis. "Seasonality in Transition Scale from Balanced to Unbalanced Motions in the World Ocean." Journal of Physical Oceanography 48, no. 3 (March 2018): 591–605. http://dx.doi.org/10.1175/jpo-d-17-0169.1.
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AbstractThe transition scale Lt from balanced geostrophic motions to unbalanced wave motions, including near-inertial flows, internal tides, and inertia–gravity wave continuum, is explored using the output from a global 1/48° horizontal resolution Massachusetts Institute of Technology general circulation model (MITgcm) simulation. Defined as the wavelength with equal balanced and unbalanced motion kinetic energy (KE) spectral density, Lt is detected to be geographically highly inhomogeneous: it falls below 40 km in the western boundary current and Antarctic Circumpolar Current regions, increases to 40–100 km in the interior subtropical and subpolar gyres, and exceeds, in general, 200 km in the tropical oceans. With the exception of the Pacific and Indian sectors of the Southern Ocean, the seasonal KE fluctuations of the surface balanced and unbalanced motions are out of phase because of the occurrence of mixed layer instability in winter and trapping of unbalanced motion KE in shallow mixed layer in summer. The combined effect of these seasonal changes renders Lt to be 20 km during winter in 80% of the Northern Hemisphere oceans between 25° and 45°N and all of the Southern Hemisphere oceans south of 25°S. The transition scale’s geographical and seasonal changes are highly relevant to the forthcoming Surface Water and Ocean Topography (SWOT) mission. To improve the detection of balanced submesoscale signals from SWOT, especially in the tropical oceans, efforts to remove stationary internal tidal signals are called for.
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Waterman, Stephanie, Nelson G. Hogg, and Steven R. Jayne. "Eddy–Mean Flow Interaction in the Kuroshio Extension Region." Journal of Physical Oceanography 41, no. 6 (June 1, 2011): 1182–208. http://dx.doi.org/10.1175/2010jpo4564.1.
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Abstract The authors use data collected by a line of tall current meter moorings deployed across the axis of the Kuroshio Extension (KE) jet at the location of maximum time-mean eddy kinetic energy to characterize the mean jet structure, the eddy variability, and the nature of eddy–mean flow interactions observed during the Kuroshio Extension System Study (KESS). A picture of the 2-yr record mean jet structure is presented in both geographical and stream coordinates, revealing important contrasts in jet strength, width, vertical structure, and flanking recirculation structure. Eddy variability observed is discussed in the context of some of its various sources: jet meandering, rings, waves, and jet instability. Finally, various scenarios for eddy–mean flow interaction consistent with the observations are explored. It is shown that the observed cross-jet distributions of Reynolds stresses at the KESS location are consistent with wave radiation away from the jet, with the sense of the eddy feedback effect on the mean consistent with eddy driving of the observed recirculations. The authors consider these results in the context of a broader description of eddy–mean flow interactions in the larger KE region using KESS data in combination with in situ measurements from past programs in the region and satellite altimetry. This demonstrates important consistencies in the along-stream development of time-mean and eddy properties in the KE with features of an idealized model of a western boundary current (WBC) jet used to understand the nature and importance of eddy–mean flow interactions in WBC jet systems.
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Uchida, Takaya, Bruno Deremble, and Thierry Penduff. "The Seasonal Variability of the Ocean Energy Cycle from a Quasi-Geostrophic Double Gyre Ensemble." Fluids 6, no. 6 (June 2, 2021): 206. http://dx.doi.org/10.3390/fluids6060206.
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With the advent of submesoscale O(1km) permitting basin-scale ocean simulations, the seasonality of mesoscale O(50km) eddies with kinetic energies peaking in summer has been commonly attributed to submesoscale eddies feeding back onto the mesoscale via an inverse energy cascade under the constraint of stratification and Earth’s rotation. In contrast, by running a 101-member, seasonally forced, three-layer quasi-geostrophic (QG) ensemble configured to represent an idealized double-gyre system of the subtropical and subpolar basin, we find that the mesoscale kinetic energy shows a seasonality consistent with the summer peak without resolving the submesoscales; by definition, a QG model only resolves small Rossby and Froude number dynamics (O(Ro)≪1,O(Fr)≪1) while submesoscale dynamics are associated with O(Ro)∼1,O(Fr)≳1. Here, by quantifying the Lorenz cycle of the mean and eddy energy, defined as the ensemble mean and fluctuations about the mean, respectively, we propose a different mechanism from the inverse energy cascade. During summer, when the Western Boundary Current is stabilized and strengthened due to increased stratification, stronger mesoscale eddies are shed from the separated jet. Conversely, the opposite occurs during the winter; the separated jet destablizes and results in overall lower mean and eddy kinetic energies despite the domain being more susceptible to baroclinic instability from weaker stratification.
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Yang, Peiran, Zhao Jing, Bingrong Sun, Lixin Wu, Bo Qiu, Ping Chang, and Sanjiv Ramachandran. "On the Upper-Ocean Vertical Eddy Heat Transport in the Kuroshio Extension. Part I: Variability and Dynamics." Journal of Physical Oceanography 51, no. 1 (January 2021): 229–46. http://dx.doi.org/10.1175/jpo-d-20-0068.1.
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AbstractOceanic eddies play a crucial role in transporting heat from the subsurface to surface ocean. However, dynamics responsible for the vertical eddy heat transport QT have not been systematically understood, especially in the mixed layer of western boundary current extensions characterized by the coincidence of strong eddy activities and air–sea interactions. In this paper, the winter (December–March) QT in the Kuroshio Extension is simulated using a 1-km regional ocean model. An omega equation based on the geostrophic momentum approximation and generalized to include the viscous and diabatic effects is derived and used to decompose the contribution of QT from different dynamics. The simulated QT exhibits a pronounced positive peak around the center of the mixed layer (~60 m). The value of QT there exhibits multi-time-scale variations with irregularly occurring extreme events superimposed on a slowly varying seasonal cycle. The proposed omega equation shows good skills in reproducing QT, capturing its spatial and temporal variations. Geostrophic deformation and vertical mixing of momentum are found to be the two major processes generating QT in the mixed layer with the former and the latter accounting for its seasonal variation and extreme events, respectively. The mixed layer instability and the net effect of frontogenesis/frontolysis contribute comparably to the geostrophic deformation induced QT. The contribution of QT from vertical mixing of momentum can be understood on the basis of turbulent thermal wind balance.
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Saenko, Oleg A. "Influence of Global Warming on Baroclinic Rossby Radius in the Ocean: A Model Intercomparison." Journal of Climate 19, no. 7 (April 1, 2006): 1354–60. http://dx.doi.org/10.1175/jcli3683.1.
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Abstract Results from eight ocean–atmosphere general circulation models are used to evaluate the influence of the projected changes in the oceanic stratification on the first baroclinic Rossby radius of deformation in the ocean, associated with atmospheric CO2 increase. For each of the models, an oceanic state corresponding to the A1B stabilization experiment (with atmospheric CO2 concentration of 720 ppm) is compared to a state corresponding to the preindustrial control experiment (with atmospheric CO2 concentration of 280 ppm). In all of the models, the first baroclinic Rossby radius increases with increasing oceanic stratification in the warmer climate. There is, however, a considerable range among the models in the magnitude of the increase. At the latitudes of intense eddy activity associated with instability of western boundary currents (around 35°–40°), the increase reaches 4 km on average, or about 15% of the local baroclinic Rossby radius. Some of the models predict an increase of the baroclinic Rossby radius by more than 20% at these latitudes under the applied forcing. It is therefore suggested that in a plausible future warmer climate, the characteristic length scale of mesoscale eddies, as well as boundary currents and fronts, may increase. In addition, since the speed of long baroclinic Rossby waves is proportional to the squared baroclinic Rossby radius of deformation, the results suggest that the time scale for large-scale dynamical oceanic adjustment may decrease in the warmer climate, thereby increasing the frequency of long-term climate variability where the oceanic Rossby wave dynamics set the dominant period. Finally, the speed of equatorial Kelvin waves and Rossby waves, carrying signals along the equator, including those related to ENSO, is projected to increase.
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Meijers, A. J., N. L. Bindoff, and J. L. Roberts. "On the Total, Mean, and Eddy Heat and Freshwater Transports in the Southern Hemisphere of a ⅛° × ⅛° Global Ocean Model." Journal of Physical Oceanography 37, no. 2 (February 1, 2007): 277–95. http://dx.doi.org/10.1175/jpo3012.1.
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Abstract The large-scale volume, heat, and freshwater ocean transports in the Southern Hemisphere are investigated using time-averaged output from a seasonless, high-resolution general circulation model. The ocean circulation is realistic, and property transports are comparable to observations. The Antarctic Circumpolar Current (ACC) carries 144 Sv (Sv ≡ 106 m3 s−1) of water eastward across Drake Passage, increasing to 155 Sv south of Australia because of the Indonesian Throughflow (ITF). There is a clear Indo-Pacific gyre around Australia exchanging −10 Sv, 0.9 PW of heat, and 0.2 Sv of freshwater through the ITF, and there is a 9-Sv leakage from the Tasman Sea to the Indian Ocean. The transport of heat and freshwater by eddies is localized to the upper 1000 m of the water column and specific regions, such as western boundary currents, confluences, and the subantarctic front (SAF). Eddy transport of heat and freshwater is negligible in gyre interiors and south of the SAF but is vital across the northern edge of the ACC, in particular at the Agulhas Retroflection where eddies accomplish almost 100% of the net ocean heat and 60% of the southward freshwater transport. The eddy transport is almost zero across the latitude of Drake Passage while in a quasi-Lagrangian frame eddy transports are significant across the ACC but surprisingly are still smaller than the mean transport of heat. Mean and eddy property transport divergences are found to be strongly compensating in areas of high eddy activity. This is caused by increased baroclinic instability in strong mean flows, which induces an opposing eddy transport. This relationship is observed to be stronger in the case of horizontal heat transport than in corresponding horizontal freshwater transports.
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Booth, James F., Young-Oh Kwon, Stanley Ko, R. Justin Small, and Rym Msadek. "Spatial Patterns and Intensity of the Surface Storm Tracks in CMIP5 Models." Journal of Climate 30, no. 13 (July 2017): 4965–81. http://dx.doi.org/10.1175/jcli-d-16-0228.1.
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To improve the understanding of storm tracks and western boundary current (WBC) interactions, surface storm tracks in 12 CMIP5 models are examined against ERA-Interim. All models capture an equatorward displacement toward the WBCs in the locations of the surface storm tracks’ maxima relative to those at 850 hPa. An estimated storm-track metric is developed to analyze the location of the surface storm track. It shows that the equatorward shift is influenced by both the lower-tropospheric instability and the baroclinicity. Basin-scale spatial correlations between models and ERA-Interim for the storm tracks, near-surface stability, SST gradient, and baroclinicity are calculated to test the ability of the GCMs’ match reanalysis. An intermodel comparison of the spatial correlations suggests that differences (relative to ERA-Interim) in the position of the storm track aloft have the strongest influence on differences in the surface storm-track position. However, in the North Atlantic, biases in the surface storm track north of the Gulf Stream are related to biases in the SST. An analysis of the strength of the storm tracks shows that most models generate a weaker storm track at the surface than 850 hPa, consistent with observations, although some outliers are found. A linear relationship exists among the models between storm-track amplitudes at 500 and 850 hPa, but not between 850 hPa and the surface. In total, the work reveals a dual role in forcing the surface storm track from aloft and from the ocean surface in CMIP5 models, with the atmosphere having the larger relative influence.
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Kim, Seung-Bum, Tong Lee, and Ichiro Fukumori. "Mechanisms Controlling the Interannual Variation of Mixed Layer Temperature Averaged over the Niño-3 Region." Journal of Climate 20, no. 15 (August 1, 2007): 3822–43. http://dx.doi.org/10.1175/jcli4206.1.
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Abstract Processes controlling the interannual variation of mixed layer temperature (MLT) averaged over the Niño-3 domain (5°N–5°S, 150°–90°W) are studied using an ocean data assimilation product that covers the period of 1993–2003. The overall balance is such that surface heat flux opposes the MLT change but horizontal advection and subsurface processes assist the change. Advective tendencies are estimated here as the temperature fluxes through the domain’s boundaries, with the boundary temperature referenced to the domain-averaged temperature to remove the dependence on temperature scale. This allows the authors to characterize external advective processes that warm or cool the water within the domain as a whole. The zonal advective tendency is caused primarily by large-scale advection of warm-pool water through the western boundary of the domain. The meridional advective tendency is contributed to mostly by Ekman current advecting large-scale temperature anomalies through the southern boundary of the domain. Unlike many previous studies, the subsurface processes that consist of vertical mixing and entrainment are explicitly evaluated. In particular, a rigorous method to estimate entrainment allows an exact budget closure. The vertical mixing across the mixed layer (ML) base has a contribution in phase with the MLT change. The entrainment tendency due to the temporal change in ML depth is negligible compared to other subsurface processes. The entrainment tendency by vertical advection across the ML base is dominated by large-scale changes in upwelling and the temperature of upwelling water. Tropical instability waves (TIWs) result in smaller-scale vertical advection that warms the domain during La Niña cooling events. However, such a warming tendency is overwhelmed by the cooling tendency associated with the large-scale upwelling by a factor of 2. In summary, all the balance terms are important in the MLT budget except the entrainment due to lateral induction and temporal variation in ML depth. All three advective tendencies are primarily caused by large-scale and low-frequency processes, and they assist the Niño-3 MLT change. When the advective tendencies are evaluated by spatially averaging the conventional local advection of temperature, the apparent effects of currents with spatial scales smaller than the domain (such as TIWs) become very important as they redistribute heat within the Niño-3 domain. As a result, for example, the averaged zonal advective tendency counteracts rather than assists the Niño-3 MLT change. However, such internal redistribution of heat does not represent external processes that control the domain-averaged MLT.
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Su, Zhan, and Andrew P. Ingersoll. "On the Minimum Potential Energy State and the Eddy Size–Constrained APE Density." Journal of Physical Oceanography 46, no. 9 (September 2016): 2663–74. http://dx.doi.org/10.1175/jpo-d-16-0074.1.
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AbstractExactly solving the absolute minimum potential energy state (Lorenz reference state) is a difficult problem because of the nonlinear nature of the equation of state of seawater. This problem has been solved recently but the algorithm comes at a high computational cost. As the first part of this study, the authors develop an algorithm that is ~103–105 times faster, making it useful for energy diagnosis in ocean models. The second part of this study shows that the global patterns of Lorenz available potential energy (APE) density are distinct from those of eddy kinetic energy (EKE). This is because the Lorenz APE density is based on the entire domainwide parcel rearrangement, while mesoscale eddies, if related to baroclinic instability, are typically generated through local parcel rearrangement approximately around the eddy size. Inspired by this contrast, this study develops a locally defined APE framework: the eddy size–constrained APE density based on the strong constraint that the parcel rearrangement/displacement to achieve the minimum potential energy state should not exceed the local eddy size horizontally. This concept typically identifies baroclinically unstable regions. It is shown to be helpful to detect individual eddies/vortices and local EKE patterns, for example, around the Southern Ocean fronts and subtropical western boundary currents. This is consistent with the physical picture that mesoscale eddies are associated with a strong signature in both the velocity field (i.e., EKE) and the stratification (i.e., local APE). The new APE concept may be useful in parameterizing mesoscale eddies in ocean models.
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Kunze, Eric. "Internal-Wave-Driven Mixing: Global Geography and Budgets." Journal of Physical Oceanography 47, no. 6 (June 2017): 1325–45. http://dx.doi.org/10.1175/jpo-d-16-0141.1.
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AbstractInternal-wave-driven dissipation rates ε and diapycnal diffusivities K are inferred globally using a finescale parameterization based on vertical strain applied to ~30 000 hydrographic casts. Global dissipations are 2.0 ± 0.6 TW, consistent with internal wave power sources of 2.1 ± 0.7 TW from tides and wind. Vertically integrated dissipation rates vary by three to four orders of magnitude with elevated values over abrupt topography in the western Indian and Pacific as well as midocean slow spreading ridges, consistent with internal tide sources. But dependence on bottom forcing is much weaker than linear wave generation theory, pointing to horizontal dispersion by internal waves and relatively little local dissipation when forcing is strong. Stratified turbulent bottom boundary layer thickness variability is not consistent with OGCM parameterizations of tidal mixing. Average diffusivities K = (0.3–0.4) × 10−4 m2 s−1 depend only weakly on depth, indicating that ε = KN2/γ scales as N2 such that the bulk of the dissipation is in the pycnocline and less than 0.08-TW dissipation below 2000-m depth. Average diffusivities K approach 10−4 m2 s−1 in the bottom 500 meters above bottom (mab) in height above bottom coordinates with a 2000-m e-folding scale. Average dissipation rates ε are 10−9 W kg−1 within 500 mab then diminish to background deep values of 0.15 × 10−9 W kg−1 by 1000 mab. No incontrovertible support is found for high dissipation rates in Antarctic Circumpolar Currents or parametric subharmonic instability being a significant pathway to elevated dissipation rates for semidiurnal or diurnal internal tides equatorward of 28° and 14° latitudes, respectively, although elevated K is found about 30° latitude in the North and South Pacific.
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Ribbe, Joachim, and Daniel Brieva. "A western boundary current eddy characterisation study." Estuarine, Coastal and Shelf Science 183 (December 2016): 203–12. http://dx.doi.org/10.1016/j.ecss.2016.10.036.
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Berloff, Pavel S., and James C. McWilliams. "Quasigeostrophic Dynamics of the Western Boundary Current." Journal of Physical Oceanography 29, no. 10 (October 1999): 2607–34. http://dx.doi.org/10.1175/1520-0485(1999)029<2607:qdotwb>2.0.co;2.
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Ribbe, Joachim, Liv Toaspern, Jörg-Olaf Wolff, and Mochamad Furqon Azis Ismail. "Frontal eddies along a western boundary current." Continental Shelf Research 165 (August 2018): 51–59. http://dx.doi.org/10.1016/j.csr.2018.06.007.
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