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Christopher L. Wolfe
and
Paola Cessi

Abstract

The effect of the pole-to-pole surface temperature difference on the deep stratification and the strength of the global meridional overturning circulation (MOC) is examined in an eddy-resolving ocean model configured in an idealized domain roughly representing the Atlantic sector. Mesoscale eddies lead to qualitative differences in the mean stratification and the MOC compared to laminar (i.e., eddy free) models. For example, the spreading of fluid across the model’s representation of the Antarctic Circumpolar Current (ACC) no longer relies on the existence of a sill in the ACC. In addition, the deep- and bottom-water masses—roughly representing North Atlantic Deep Water (NADW) and Antarctic Bottom Water (ABW), respectively—are eroded by the eddies so that their zonal and meridional extents are much smaller than in the laminar case. It is found that if the north pole temperature is sufficiently warm, the formation of northern deep water is suppressed and the middepth cell is small and weak while the deep cell is large and vigorous. In contrast, if the north pole temperature is in the range of the southern channel temperatures, the middepth cell is large and strong while the deep cell has a reduced amplitude. This result is consistent with the predictions of the laminar theory of the MOC. In contrast to the laminar theory, realistically strong deep stratification is formed even if the temperature at the northern sinking site is warmer than any temperature found in the channel. Indeed, middepth stratification is actually stronger in the latter case than the former case.

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Paola Cessi
and
Christopher L. Wolfe

Abstract

It is demonstrated that eddy fluxes of buoyancy at the eastern and western boundaries maintain alongshore buoyancy gradients along the coast. Eddy fluxes arise near the eastern and western boundaries because on both coasts buoyancy gradients normal to the boundary are strong. The eddy fluxes are accompanied by mean vertical flows that take place in narrow boundary layers next to the coast where the geostrophic constraint is broken. These ageostrophic cells have a velocity component normal to the coast that balances the geostrophic mean velocity. It is shown that the dynamics in these thin ageostrophic boundary layers can be replaced by effective boundary conditions for the interior flow, relating the eddy flux of buoyancy at the seaward edge of the boundary layers to the buoyancy gradient along the coast. These effective boundary conditions are applied to a model of the thermocline linearized around a mean stratification and a state of rest. The linear model parameterizes the eddy fluxes of buoyancy as isopycnal diffusion. The linear model produces horizontal gradients of buoyancy along the eastern coast on a vertical scale that depends on both the vertical diffusivity and the eddy diffusivity. The buoyancy field of the linear model agrees very well with the mean state of an eddy-resolving computation. Because the east–west difference in buoyancy is related to the zonally integrated meridional velocity, the linear model successfully predicts the meridional overturning circulation.

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C. S. Jones
and
Paola Cessi

Abstract

The salt transport by the wind-driven gyres and the meridional overturning circulation (MOC) is studied in an idealized-geometry primitive equation ocean model. Two narrow continents, running along meridians, divide the model domain into two basins of different widths connected by a re-entrant channel south of 52.5°S. One of the continents, representing the Americas, is longer than the other, representing Europe/Africa. Two different configurations of the model are used: the “standard” one, in which the short continent is west of the wide basin, and the “exchanged” one, in which the short continent is west of the narrow basin. In both cases, deep water is formed in the basin to the west of the short continent. Most residual transport of the MOC’s upper branch enters this basin by flowing along open streamlines that pass westward south of the short continent before proceeding northward. The meridional salt transport in the upper ocean of the sinking basin is decomposed into two portions: transport along open streamlines and transport by closed streamlines (gyres). In the Northern Hemisphere of the basin in which deep water is formed, the total northward salt transport per unit width along open streamlines is larger in the standard configuration than in the exchanged configuration. This larger salt transport is caused by two factors: a larger northward advection of salt by the interbasin transport and a larger cross-streamline salt transport out of the subpolar gyre. It is concluded that increasing interbasin flow south of Africa would likely bring more salt into the Atlantic Ocean.

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Paola Cessi
and
C. S. Jones

Abstract

The interbasin exchange of the meridional overturning circulation (MOC) is studied in an idealized domain with two basins connected by a circumpolar channel in the southernmost region. Gnanadesikan’s conceptual model for the upper branch of the MOC is extended to include two basins of different widths connected by a reentrant channel at the southern edge and separated by two continents of different meridional extents. Its analysis illustrates the basic processes of interbasin flow exchange either through the connection at the southern tip of the long continent (cold route) or through the connection at the southern tip of the short continent (warm route). A cold-route exchange occurs when the short continent is poleward of the latitude separating the subpolar and subtropical gyre in the Southern Hemisphere (the zero Ekman pumping line); otherwise, there is warm-route exchange. The predictions of the conceptual model are compared to primitive equation computations in a domain with the same idealized geometry forced by wind stress, surface temperature relaxation, and surface salinity flux. Visualizations of the horizontal structure of the upper branch of the MOC illustrate the cold and warm routes of interbasin exchange flows. Diagnostics of the primitive equation computations show that the warm-route exchange flow is responsible for a substantial salinification of the basin where sinking occurs. This salinification is larger when the interbasin exchange is via the warm route, and it is more pronounced when the warm-route exchange flows from the wide to the narrow basin.

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C. S. Jones
and
Paola Cessi

Abstract

The surface salinity in the North Atlantic controls the position of the sinking branch of the meridional overturning circulation (MOC); the North Atlantic has higher salinity, so deep-water formation occurs there rather than in the North Pacific. Here, it is shown that in a 3D primitive equation model of two basins of different widths connected by a reentrant channel, there is a preference for sinking in the narrow basin even under zonally uniform surface forcing. This preference is linked to the details of the velocity and salinity fields in the “sinking” basin. The southward western boundary current associated with the wind-driven subpolar gyre has higher velocity in the wide basin than in the narrow basin. It overwhelms the northward western boundary current associated with the MOC for wide-basin sinking, so freshwater is brought from the far north of the domain southward and forms a pool on the western boundary in the wide basin. The fresh pool suppresses local convection and spreads eastward, leading to low salinities in the north of the wide basin for wide-basin sinking. This pool of freshwater is much less prominent in the narrow basin for narrow-basin sinking, where the northward MOC western boundary current overcomes the southward western boundary current associated with the wind-driven subpolar gyre, bringing salty water from lower latitudes northward and enabling deep-water mass formation.

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Paola Cessi
and
Glenn R. Ierley

Abstract

Viscous shear instability is proposed as a primary mechanism for generating time-dependent eddies at western boundaries. Thus, the authors examine the stability of the Munk flow with constant transport flowing along a straight coast, tilted at an angle with respect to the north-south direction. Various properties of the marginally unstable wave are calculated as a function of the tilting angle, such as the critical Reynolds number and the phase and group velocities. The effects of weak nonlinearity are also examined, and the authors find that the instability is supercritical for the whole range of tilting angles examined. Thus, the marginally unstable mode can equilibrate at a small finite amplitude, and we derive the equation governing its slow evolution. The flow that results after the disturbance has equilibrated to finite amplitude is in agreement with the eddying boundary currents obtained in many wind-driven general circulation models.

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Paola Cessi
and
Lu Anne Thompson

Abstract

In this paper we discuss the conditions under which a free solution of the steady, one-layer, quasi-geostrophic equation on a β-plane is realized in the inviscid limit. We restrict attention to the case where no body force is applied and the fluid moves under a stress prescribed at the boundary of the closed domain. We show that, depending on the geometrical configuration of the boundary where the stress is prescribed, either a frictional solution or a free inertial solution is found in the limit of infinitesimal dissipation.

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Paola Cessi
and
Glenn R. Ierley

Abstract

The classical Munk problem of barotropic flow driven by an antisymmetric wind stress exhibits multiple steady solutions in the range of moderate to high forcing and moderate to low dissipation. Everywhere in the parameter space a perfectly antisymmetric solution exists in which the strength of the cyclonic gyre is equal and opposite to that of the anticyclonic gyre. This kind of solution has been well documented in the literature.

In a subset of the parameter a pair of nonsymmetric stationary solutions coexists with the antisymmetric solution. For one member of the pair the amplitude of the cyclonic circulation exceeds that of the anticyclonic flow. The other member of the pair is obtained from the quasigeostrophic symmetry y&minusy and ψ→−ψ. As a result, the point at which the western boundary current separates from the coast can be either south or north of the latitude at which the antisymmetric Ekman pumping changes sign. This is the first oceanogrphic example of spontaneous breaking of the quasigeostrophic symmetry.

Within the region of parameter space where three solutions are found, a second pair of nonsymmetric stationary solutions emerges, bringing the total number of stationary solutions to five. This last pair of nonsymmetric solutions is characterized by basin-filling gyres with amplitudes much above the Sverdrup prediction. Once again, the separation point is displaced from the latitude of vanishing wind stress curl.

The existence of nonsymmetric double gyres in an antisymmetrically forced basin shows that there can be no general rule for determining the point of separation of the boundary current in terms of the relative strength of the subtropical and subpolar forcings.

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Paola Cessi
,
Glenn Ierley
, and
William Young

Abstract

Some essential features of a recirculating inertial gyre (the “recirculation”) can be analyzed with a very simple, analytically tractable model. In wind-driven eddy-resolving general circulation models the recirculation appears as a strong sub-basin-scale inertial flow with homogeneous potential vorticity. The constant value of potential vorticity decreases with increasing forcing/dissipation ratio while the size and the strength of the recirculating gyre increases. In the subtropical gyre the recirculating gyre might be driven by anomalous values of low potential vorticity carried northward by the western boundary current. We have modeled this process using a barotropic model and prescribing the values of potential vorticity at the edge of the gyre. Our model gyre is contained in a rectangular box in an attempt to simplify the geometry as much as possible and to isolate the processes occurring in the recirculating region.

With weak diffusion the prescribed boundary forcing induces a flow with constant potential vorticity. We show how to calculate the homogenized value of potential vorticity in the interior without explicitly solving for the flow. We also numerically solve our model and so obtain explicit solutions. Two distinct cases arise: 1) For strong boundary forcing the gyre fills the whole box. Therefore the homogenized value of potential vorticity can be determined but the extent of the recirculation is prescribed. 2) For weak boundary forcing the recirculation fills only part of the basin and the size of the gyre must be determined as well as the homogenized value of potential vorticity within it. The latter case is the most relevant to the wind-driven, numerical experiments, because in these calculations the recirculating flow is confined to a sub-basin-scale region. Also in this case the homogenized value of potential vorticity decreases with increasing forcing, while the size and the strength of the gyre increase.

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Blanca Gallego
,
Paola Cessi
, and
James C. McWilliams

Abstract

A simple channel-flow model is used to examine the equilibrium upper-ocean dynamics and thermodynamics of the Antarctic Circumpolar Current (ACC). The model consists of two zonally averaged, variable-temperature layers—a surface boundary layer and a thermocline layer—separated by a turbulent interface. Weak air–sea heat flux, determined by relaxation to a prescribed atmospheric temperature, determines the leading-order temperature structure in the oceanic surface layer. The equilibrium thermal structure in the interior is mostly determined by a dominant balance between the meridional transport due to the wind-driven Eulerian mean circulation and the heat flux due to the baroclinic eddies. The resulting latitudinal temperature gradient depends on both the wind and the atmospheric temperature forcing and sustains the geostrophic zonal flow. Consideration of the next-order balance for the oceanic surface temperature results in an air–sea heat flux proportional to the magnitude of the residual flow. The residual meridional circulation (Eulerian mean plus eddy-induced) is necessary to balance small diabatic sources and sinks of heat. Therefore, it depends on the processes of vertical diffusion, boundary layer entrainment/detrainment, and, on the polar flank, convection. In the absence of substantial lateral diffusion, the leading-order balance of weak residual circulation implies a very weak meridional heat transport across the ACC and a correspondingly weak differential heat exchange to the atmosphere. This limitation can be eased if the lateral diffusive flux of temperature in the surface layer becomes as large as the adiabatic eddy transport.

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