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John R. Taylor and Raffaele Ferrari

Abstract

In this study, the influence of a geostrophically balanced horizontal density gradient on turbulent convection in the ocean is examined using numerical simulations and a theoretical scaling analysis. Starting with uniform horizontal and vertical buoyancy gradients, convection is driven by imposing a heat loss or a destabilizing wind stress at the upper boundary, and a turbulent layer soon develops. For weak lateral fronts, turbulent convection results in a nearly homogeneous mixed layer (ML) whose depth grows in time. For strong fronts, a turbulent layer develops, but this layer is not an ML in the traditional sense because it is characterized by persistent horizontal and vertical gradients in density. The turbulent layer is, however, nearly homogeneous in potential vorticity (PV), with a value near zero. Using the PV budget, a scaling for the depth of the turbulent low PV layer and its time dependence is derived that compares well with numerical simulations. Two dynamical regimes are identified. In a convective layer near the surface, turbulence is generated by the buoyancy loss at the surface; below this layer, turbulence is generated by a symmetric instability of the lateral density gradient. This work extends classical scalings for the depth of turbulent boundary layers to account for the ubiquitous presence of lateral density gradients in the ocean. The new results indicate that a lateral density gradient, in addition to the surface forcing, can affect the stratification and the rate of growth of the surface boundary layer.

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R. Alan Plumb and Raffaele Ferrari

Abstract

A theoretical formalism for nongeostrophic eddy transport in zonal-mean flows, using a transformed Eulerian-mean (TEM) approach in z coordinates, is discussed. By using Andrews and McIntyre’s coordinate-independent definition of the “quasi-Stokes streamfunction,” it is argued that the surface boundary condition can be dealt with more readily than when the widely used quasigeostrophic definition is adopted. Along with the “residual mean circulation,” the concept of “residual eddy flux” arises naturally within the TEM framework, and it is argued that it is this residual eddy flux, and not the “raw” eddy flux, that might reasonably be expected to be downgradient. This distinction is shown to be especially important for Ertel potential vorticity (PV). The authors show how a closed set of transformed mean equations can be generated, and how the eddy forcing appears in the TEM momentum equations. Under adiabatic conditions, the “eddy drag” is just proportional to the residual eddy flux of PV along the mean isopycnals; in the diabatic layer close to the surface, it is more complicated, but becomes very simple for small Rossby number (without any assumption of small isopycnal slope).

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R. Ferrari and K. L. Polzin

Abstract

Distributions of temperature (T) and salinity (S) and their relationship in the oceans are the result of a balance between TS variability generated at the surface by air–sea fluxes and its removal by molecular dissipation. In this paper the role of different motions in setting the cascade of TS variance to dissipation scales is quantified using data from the North Atlantic Tracer Release Experiment (NATRE). The NATRE observational programs include fine- and microscale measurements and provide a snapshot of TS variability across a wide range of scales from basin to molecular. It is found that microscale turbulence controls the rate of thermal dissipation in the thermocline. At this level the TS relation is established through a balance between large-scale advection by the gyre circulation and small-scale turbulence. Further down, at the level of intermediate and Mediterranean waters, mesoscale eddies are the rate-controlling process. The transition between the two regimes is related to the presence of a strong salinity gradient along density surfaces associated with the outflow of Mediterranean waters. Mesoscale eddies stir this gradient and produce a rich filamentation and salinity-compensated temperature inversions: isopycnal stirring and diapycnal mixing are both required to explain the TS relation at depth.

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Matthew R. Mazloff, Raffaele Ferrari, and Tapio Schneider

Abstract

The Southern Ocean (SO) limb of the meridional overturning circulation (MOC) is characterized by three vertically stacked cells, each with a transport of about 10 Sv (Sv ≡ 106 m3 s−1). The buoyancy transport in the SO is dominated by the upper and middle MOC cells, with the middle cell accounting for most of the buoyancy transport across the Antarctic Circumpolar Current. A Southern Ocean state estimate for the years 2005 and 2006 with ⅙° resolution is used to determine the forces balancing this MOC. Diagnosing the zonal momentum budget in density space allows an exact determination of the adiabatic and diapycnal components balancing the thickness-weighted (residual) meridional transport. It is found that, to lowest order, the transport consists of an eddy component, a directly wind-driven component, and a component in balance with mean pressure gradients. Nonvanishing time-mean pressure gradients arise because isopycnal layers intersect topography or the surface in a circumpolar integral, leading to a largely geostrophic MOC even in the latitude band of Drake Passage. It is the geostrophic water mass transport in the surface layer where isopycnals outcrop that accomplishes the poleward buoyancy transport.

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A. Mashayek, R. Ferrari, M. Nikurashin, and W. R. Peltier

Abstract

The meridional overturning circulation (MOC) is composed of interconnected overturning cells that transport cold dense abyssal waters formed at high latitudes back to the surface. Turbulent diapycnal mixing plays a primary role in setting the rate and patterns of the various overturning cells that constitute the MOC. The focus of the analyses in this paper will be on the influence of sharp vertical variations in mixing on the MOC and ocean stratification. Mixing is enhanced close to the ocean bottom topography where internal waves generated by the interaction of tides and geostrophic motions with topography break. It is shown that the sharp vertical variations in mixing lead to the formation of three layers with different dynamical balances governing meridional flow. Specifically, an abyssal bottom boundary layer forms above the ocean floor where mixing is largest and hosts the northward transport of the heaviest waters from the southern channel to the closed basins. A deep layer forms above the bottom layer in which the upwelled waters return south. A third adiabatic layer lies above the other two. While the adiabatic layer has been studied in detail in recent years, the deep and bottom layers are less appreciated. It is shown that the bottom layer, which is not resolved or allowed for in most idealized models, must be present to satisfy the no flux boundary condition at the ocean floor and that its thickness is set by the vertical profile of mixing. The deep layer spans a considerable depth range of the ocean within which the stratification scale is set by mixing, in line with the classic view of Munk in 1966.

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Madeleine K. Youngs, Glenn R. Flierl, and Raffaele Ferrari

Abstract

The Antarctic Circumpolar Current plays a central role in the ventilation of heat and carbon in the global ocean. In particular, the isopycnal slopes determine where each water mass outcrops and thus how the ocean interacts with the atmosphere. The region-integrated isopycnal slopes have been suggested to be eddy saturated, that is, stay relatively constant as the wind forcing changes, but whether or not the flow is saturated in realistic present day and future parameter regimes is unknown. This study analyzes an idealized two-layer quasigeostrophic channel model forced by a wind stress and a residual overturning generated by a mass flux across the interface between the two layers, with and without a blocking ridge. The sign and strength of the residual overturning set which way the isopycnal slopes change with the wind forcing, leading to an increase in slope with an increase in wind forcing for a positive overturning and a decrease in slope for a negative overturning, following the usual conventions; this behavior is caused by the dominant standing meander weakening as the wind stress weakens causing the isopycnal slopes to become more sensitive to changes in the wind stress and converge with the slopes of a flat-bottomed simulation. Eddy saturation only appears once the wind forcing passes a critical level. These results show that theories for saturation must have both topography and residual overturning in order to be complete and provide a framework for understanding how the isopycnal slopes in the Southern Ocean may change in response to future changes in wind forcing.

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J. H. LaCasce, R. Ferrari, J. Marshall, R. Tulloch, D. Balwada, and K. Speer

Abstract

As part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), 210 subsurface floats were deployed west of the Drake Passage on two targeted density surfaces. Absolute (single particle) diffusivities are calculated for the floats. The focus is on the meridional component, which is less affected by the mean shear. The diffusivities are estimated in several ways, including a novel method based on the probability density function of the meridional displacements. This allows the determination of the range of possible lateral diffusivities, as well as the period over which the spreading can be said to be diffusive. The method is applied to the float data and to synthetic trajectories generated with the Massachusetts Institute of Technology General Circulation Model (MITgcm). Because of ballasting problems, many of the floats did not remain on their targeted density surface. However, the float temperature records suggest that most occupied a small range of densities, so the floats were grouped together for the analysis. The latter focuses on a subset of 109 of the floats, launched near 105°W. The different methods yield a consistent estimate for the diffusivity of 800 ± 200 m2 s−1. The same calculations were made with model particles deployed on 20 different density surfaces and the result for the particles deployed on the neutral density surface γ = 27.7 surface was the same within the errors. The model was then used to map the variation of the diffusivity in the vertical, near the core of the Antarctic Circumpolar Current (ACC). The results suggest mixing is intensified at middepths, between 1500 and 2000 m, consistent with several previous studies.

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A. M. Thurnherr, L. Clément, L. St. Laurent, R. Ferrari, and T. Ijichi

Abstract

Closing the overturning circulation of bottom water requires abyssal transformation to lighter densities and upwelling. Where and how buoyancy is gained and water is transported upward remain topics of debate, not least because the available observations generally show downward-increasing turbulence levels in the abyss, apparently implying mean vertical turbulent buoyancy-flux divergence (densification). Here, we synthesize available observations indicating that bottom water is made less dense and upwelled in fracture zone valleys on the flanks of slow-spreading midocean ridges, which cover more than one-half of the seafloor area in some regions. The fracture zones are filled almost completely with water flowing up-valley and gaining buoyancy. Locally, valley water is transformed to lighter densities both in thin boundary layers that are in contact with the seafloor, where the buoyancy flux must vanish to match the no-flux boundary condition, and in thicker layers associated with downward-decreasing turbulence levels below interior maxima associated with hydraulic overflows and critical-layer interactions. Integrated across the valley, the turbulent buoyancy fluxes show maxima near the sidewall crests, consistent with net convergence below, with little sensitivity of this pattern to the vertical structure of the turbulence profiles, which implies that buoyancy flux convergence in the layers with downward-decreasing turbulence levels dominates over the divergence elsewhere, accounting for the net transformation to lighter densities in fracture zone valleys. We conclude that fracture zone topography likely exerts a controlling influence on the transformation and upwelling of bottom water in many areas of the global ocean.

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E. Kunze, J. M. Klymak, R.-C. Lien, R. Ferrari, C. M. Lee, M. A. Sundermeyer, and L. Goodman

Abstract

Submesoscale stirring contributes to the cascade of tracer variance from large to small scales. Multiple nested surveys in the summer Sargasso Sea with tow-yo and autonomous platforms captured submesoscale water-mass variability in the seasonal pycnocline at 20–60-m depths. To filter out internal waves that dominate dynamic signals on these scales, spectra for salinity anomalies on isopycnals were formed. Salinity-gradient spectra are approximately flat with slopes of −0.2 ± 0.2 over horizontal wavelengths of 0.03–10 km. While the two to three realizations presented here might be biased, more representative measurements in the literature are consistent with a nearly flat submesoscale passive tracer gradient spectrum for horizontal wavelengths in excess of 1 km. A review of mechanisms that could be responsible for a flat passive tracer gradient spectrum rules out (i) quasigeostrophic eddy stirring, (ii) atmospheric forcing through a relict submesoscale winter mixed layer structure or nocturnal mixed layer deepening, (iii) a downscale vortical-mode cascade, and (iv) horizontal diffusion because of shear dispersion of diapycnal mixing. Internal-wave horizontal strain appears to be able to explain horizontal wavenumbers of 0.1–7 cycles per kilometer (cpkm) but not the highest resolved wavenumbers (7–30 cpkm). Submesoscale subduction cannot be ruled out at these depths, though previous observations observe a flat spectrum well below subduction depths, so this seems unlikely. Primitive equation numerical modeling suggests that nonquasigeostrophic subinertial horizontal stirring can produce a flat spectrum. The last need not be limited to mode-one interior or surface Rossby wavenumbers of quasigeostrophic theory but may have a broaderband spectrum extending to smaller horizontal scales associated with frontogenesis and frontal instabilities as well as internal waves.

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Ross Tulloch, Raffaele Ferrari, Oliver Jahn, Andreas Klocker, Joseph LaCasce, James R. Ledwell, John Marshall, Marie-Jose Messias, Kevin Speer, and Andrew Watson

Abstract

The first direct estimate of the rate at which geostrophic turbulence mixes tracers across the Antarctic Circumpolar Current is presented. The estimate is computed from the spreading of a tracer released upstream of Drake Passage as part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). The meridional eddy diffusivity, a measure of the rate at which the area of the tracer spreads along an isopycnal across the Antarctic Circumpolar Current, is 710 ± 260 m2 s−1 at 1500-m depth. The estimate is based on an extrapolation of the tracer-based diffusivity using output from numerical tracers released in a one-twentieth of a degree model simulation of the circulation and turbulence in the Drake Passage region. The model is shown to reproduce the observed spreading rate of the DIMES tracer and suggests that the meridional eddy diffusivity is weak in the upper kilometer of the water column with values below 500 m2 s−1 and peaks at the steering level, near 2 km, where the eddy phase speed is equal to the mean flow speed. These vertical variations are not captured by ocean models presently used for climate studies, but they significantly affect the ventilation of different water masses.

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