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Trevor J. McDougall and Raffaele Ferrari

Abstract

A buoyancy and volume budget analysis of bottom-intensified mixing in the abyssal ocean reveals simple expressions for the strong upwelling in very thin continental boundary layers and the interior near-boundary downwelling in the stratified ocean interior. For a given amount of Antarctic Bottom Water that is upwelled through neutral density surfaces in the abyssal ocean (between 2000 and 5000 m), up to 5 times this volume flux is upwelled in narrow, turbulent, sloping bottom boundary layers, while up to 4 times the net upward volume transport of Bottom Water flows downward across isopycnals in the near-boundary stratified ocean interior. These ratios are a direct result of a buoyancy budget with respect to buoyancy surfaces, and these ratios are calculated from knowledge of the stratification in the abyss along with the assumed e-folding height that characterizes the decrease of the magnitude of the turbulent diapycnal buoyancy flux away from the seafloor. These strong diapycnal upward and downward volume transports are confined to a few hundred kilometers of the continental boundaries, with no appreciable diapycnal motion in the bulk of the interior ocean.

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John R. Taylor and Raffaele Ferrari

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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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Baylor Fox-Kemper and Raffaele Ferrari

Abstract

The time-mean effects of eddies are studied in a model based on the Parsons–Veronis–Huang–Flierl models of the wind-driven gyre. Much of the analysis used for the steady solutions carries over if the model is cast in terms of the thickness-weighted mean velocity, because then mass transport is nondivergent in the absence of diabatic forcing. The model exemplifies the use of residual mean theory to simplify analysis.

A result of the analysis is a boundary layer width in the case of a rapid upper-layer flow and weak lower-layer flow. This boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed.

Further analysis of the model illustrates important aspects of eddy behavior, model sensitivity to eddy fluxes, and model sensitivity to frictional parameters.

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R. Alan Plumb and Raffaele Ferrari

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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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Jörn Callies, Oliver Bühler, and Raffaele Ferrari

Abstract

Spectral analysis is applied to infer the dynamics of mesoscale winds from aircraft observations in the upper troposphere and lower stratosphere. Two datasets are analyzed: one collected aboard commercial aircraft and one collected using a dedicated research aircraft. A recently developed wave–vortex decomposition is used to test the observations’ consistency with linear inertia–gravity wave dynamics. The decomposition method is shown to be robust in the vicinity of the tropopause if flight tracks vary sufficiently in altitude. For the lower stratosphere, the decompositions of both datasets confirm a recent result that mesoscale winds are consistent with the polarization and dispersion relations of inertia–gravity waves. For the upper troposphere, however, the two datasets disagree: only the research aircraft data indicate consistency with linear wave dynamics at mesoscales. The source of the inconsistency is a difference in mesoscale variance of the measured along-track wind component. To further test the observed flow’s consistency with linear wave dynamics, the ratio between tropospheric and stratospheric mesoscale energy levels is compared to a simple model of upward-propagating waves that are partially reflected at the tropopause. For both datasets, the observed energy ratio is roughly consistent with the simple wave model, but wave frequencies diagnosed from the data draw into question the applicability of the monochromatic theory at wavelengths smaller than 10 km.

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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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Henri F. Drake, Raffaele Ferrari, and Jörn Callies

Abstract

The emerging view of the abyssal circulation is that it is associated with bottom-enhanced mixing, which results in downwelling in the stratified ocean interior and upwelling in a bottom boundary layer along the insulating and sloping seafloor. In the limit of slowly varying vertical stratification and topography, however, boundary layer theory predicts that these upslope and downslope flows largely compensate, such that net water mass transformations along the slope are vanishingly small. Using a planetary geostrophic circulation model that resolves both the boundary layer dynamics and the large-scale overturning in an idealized basin with bottom-enhanced mixing along a midocean ridge, we show that vertical variations in stratification become sufficiently large at equilibrium to reduce the degree of compensation along the midocean ridge flanks. The resulting large net transformations are similar to estimates for the abyssal ocean and span the vertical extent of the ridge. These results suggest that boundary flows generated by mixing play a crucial role in setting the global ocean stratification and overturning circulation, requiring a revision of abyssal ocean theories.

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Andreas Klocker, Raffaele Ferrari, and Joseph H. LaCasce

Abstract

Particle- and tracer-based estimates of lateral diffusivities are used to estimate the suppression of eddy mixing across strong currents. Particles and tracers are advected using a velocity field derived from sea surface height measurements from the South Pacific, in a region west of Drake Passage. This velocity field has been used in a companion paper to show that both particle- and tracer-based estimates of eddy diffusivities are equivalent, despite recent claims to the contrary. These estimates of eddy diffusivities are here analyzed to show 1) that the degree of suppression of mixing across the strong Antarctic Circumpolar Current is correctly predicted by mixing length theory modified to include eddy propagation along the mean flow and 2) that the suppression can be inferred from particle trajectories by studying the structure of the autocorrelation function of the particle velocities beyond the first zero crossing. These results are then used to discuss how to compute lateral and vertical variations in eddy diffusivities using floats and drifters in the real ocean.

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Baylor Fox-Kemper, Raffaele Ferrari, and Joseph Pedlosky

Abstract

The decomposition of an eddy flux into a divergent flux component and a rotational flux component is not unique in a bounded or singly periodic domain. Therefore, assertions made under the assumption of uniqueness, implicit or explicit, may be meaningless. Nondivergent, irrotational perturbations are allowed to any decomposition that may affect naive interpretation of the flux field. These perturbations are restricted, however, so that unique diagnostics can be formed from the flux field.

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Gokhan Danabasoglu, Raffaele Ferrari, and James C. McWilliams

Abstract

A simplified version of the near-boundary eddy flux parameterization developed recently by Ferrari et al. has been implemented in the NCAR Community Climate System Model (CCSM3) ocean component for the surface boundary only. This scheme includes the effects of diabatic mesoscale fluxes within the surface layer. The experiments with the new parameterization show significant improvements compared to a control integration that tapers the effects of the eddies as the surface is approached. Such surface tapering is typical of present implementations of eddy transport in some current ocean models. The comparison is also promising versus available observations and results from an eddy-resolving model. These improvements include the elimination of strong, near-surface, eddy-induced circulations and a better heat transport profile in the upper ocean. The experiments with the new scheme also show reduced abyssal cooling and diminished trends in the potential temperature drifts. Furthermore, the need for any ad hoc, near-surface taper functions is eliminated. The impact of the new parameterization is mostly associated with the modified eddy-induced velocity treatment near the surface. The new parameterization acts in the depth range exposed to enhanced turbulent mixing at the ocean surface. This depth range includes the actively turbulent boundary layer and a transition layer underneath, composed of waters intermittently exposed to mixing. The mixed layer, that is, the regions of weak stratification at the ocean surface, is found to be a good proxy for the sum of the boundary layer depth and transition layer thickness.

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