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  • View in gallery

    A schematic figure showing a water-mass source spreading over a double basin. The PV contrast is larger over the basin where the source is located, compared with the end basin. Over the end basin, the water mass enters from across the equator and fills the basin with low PV

  • View in gallery

    Upper panel: a WOCE, hydrographic section P15 for potential density, σ4, in the Pacific along 170°W (displayed only from 1 km to the seafloor). Lower panel: the resulting meridional variation in large-scale potential vorticity, Q, (10−11 m−1 s−1) for σ4 = 45.75 and 45.87 surfaces (full and dashed lines respectively). The Q has a nearly uniform and a low magnitude for the denser surface (dashed line) over the North Pacific

  • View in gallery

    Climatological maps of Q (10−12 m−1 s−1) in the Pacific from O'Dwyer and Williams (1997): along σ4 = 45.75 (upper panel) and σ4 = 45.87 (lower panel) surfaces with Δσ4 = 0.02. Data in shaded areas are excluded from the contouring of the fields; they include topography, data-poor regions and shelf-sea basins. The maps reveal low Q extending over the denser surface for the North Pacific

  • View in gallery

    A schematic figure of the model domain used in the idealized experiments. Dense fluid enters the domain from a southern relaxation zone and is diapycnally transferred to lighter fluid in the interior through a combination of background and enhanced bottom mixing. In later experiments, wind stress forcing is incorporated to drive a double-gyre circulation and generate an active eddy circulation

  • View in gallery

    Meridional sections in the coarse-resolution, idealized experiment along 6°E. (a) The initial interfaces slope over the relaxation zone, but are flat elsewhere (dashed line). If there is no interior diapycnic diffusivity, an influx of dense water leads to the interfaces doming up over the interior, as shown by the dotted lines after 200 years. A steady solution is obtained if a constant, background diffusivity is incorporated (full lines) with the influx of dense fluid converted to lighter fluid. (b) Incorporating additional diapycnic mixing along the deepest interface leads to a poleward deepening of the interface and eventual grounding of the bottom layer. The volume flux (Sv) into and between each layer is indicated in the arrows

  • View in gallery

    Potential vorticity (10−12 m−1 s−1) of layer 3 for coarse-resolution integrations with (a) uniform background mixing and (b) enhanced bottom mixing along the deepest interface. The right panels shows the PV (full line) and planetary vorticity scaled by the mean layer thickness (dashed line) vs latitude. The enhanced bottom mixing leads to a weaker meridional contrast in PV, as shown in (b)

  • View in gallery

    Deep and bottom circulations for the coarse-resolution model with uniform mixing for layers 3 and 4 in (a) and (b) and for layer 4 with enhanced bottom mixing in (c). The contours are for Montgomery potential (105 N m−2) and the arrows represent the volume flux in the layer (plotted every second grid point). Note how in the bottom layer grounds in both basins (shaded) when there is enhanced bottom mixing in (c)

  • View in gallery

    Layer thickness (m) of the bottom layer (layer 4) for (a) coarse and (b) eddy-resolving integrations with enhanced bottom mixing and wind forcing. (c) The meridional transport in the bottom layer is included for the coarse (dashed line) and eddy-resolving (full line) integrations, which is shown over the entire domain and over the western boundary (0° to 6°E). Incorporating eddies inhibits the grounding of the bottom layer (shaded) and leads to a greater poleward transport

  • View in gallery

    Modeled maps of PV (10−12 m−1 s−1) of layer 3 for (a) coarse and (b) eddy-resolving integrations with enhanced bottom mixing and wind forcing. The right panels show the PV (full line) and planetary vorticity scaled by the mean layer thickness (dashed line), which are zonal averages from 0° to 12°E, vs latitude. The slight increase in the PV contrast over layer 3 for the eddy case is an indirect consequence of the eddies inhibiting grounding of the bottom layer (as shown in Fig. 8)

  • View in gallery

    Modeled meridional section for σ4 along 170°W through the Pacific. The model is integrated for 800 years with realistic topography at 1.4° resolution and enhanced bottom mixing. The initial and final states are marked by the dashed and full lines, respectively. The meridional transport and area-integrated diapycnic flux (Sv) are included for the final state. There is a northward deepening of the denser interface, which broadly resembles the idealised solution with enhanced bottom mixing (Fig. 5b)

  • View in gallery

    Model circulation in the bottom layer with realistic topography at 1.4° after 800 years of integration: (a) bottom velocity and (b) bottom transport. The vectors representing bottom velocity and transport are each scaled to 1 cm s−1 and 1 Sv (106 m3 s−1), respectively. The core of the deep inflow spreads along the western side of the deep channels. Dark and light shading represents depths less than 3 and 4 km, respectively. (b) The right panel shows bottom transport (full line) and a bar plot of zonally integrated diapycnal transfer across the deepest interface, scaled to give the area-integrated mean flux in Sv every 10° in latitude

  • View in gallery

    Modeled variations in diapycnic velocity wd (10−7 m s−1), buoyancy frequency N (10−3 s−1), and diapycnal diffusivity κ (10−4 m2 s−1) over the bottom layer. The plots are for a zonal average from 160°E to 130°W after 800 years of integration

  • View in gallery

    Modeled maps of PV (10−12 m−1 s−1) over the Pacific after 800 years of integration with realistic topography at 1.4° resolution: (a) meridional variation for σ4 = 45.75 and 45.87 surfaces (full and dashed lines respectively); (b) maps for σ4 = 45.76 and 45.87 surfaces (layers 3 and 4). The model solution reveals weaker meridional contrast in PV across the northern basin for the denser surface, which is broadly in accord with the diagnostics from the WOCE section and climatology (Figs. 2, 3)

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Formation of Low Potential Vorticity over the Deep Pacific

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  • 1 Oceanography Laboratories, Department of Earth Sciences, University of Liverpool, Liverpool, United Kingdom
  • | 2 Norwegian Polar Institute, Tromsø, Norway
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Abstract

Low potential vorticity extends over the deep waters of the North Pacific and, possibly, the bottom waters of the North Atlantic. Isopycnic model integrations are conducted to investigate how these potential vorticity distributions are controlled, first, for an idealized double-hemisphere and, second, for the Pacific with realistic topography. Dense water is released from a southern, high-latitude source and circulates over the domain with diapycnic mixing gradually reducing its stratification. The potential vorticity contrast is large over the Southern Hemisphere, but weak over the Northern Hemisphere where the meridional changes in planetary vorticity and layer thickness oppose each other. Including an active eddy field inhibits the grounding of dense water, which increases the potential vorticity contrast in the overlying layer. Incorporating realistic topography leads to the dense fluid spreading via deep channels with tight recirculations and jets bifurcating. The experiments suggest that extensive regions of low potential vorticity are formed whenever there is both enhanced bottom mixing and a basin is filled by a single water mass entering from across the equator.

Corresponding author address: Dr Richard G. Williams, Oceanography Laboratories, Department of Earth Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom. Email: ric@liv.ac.uk

Abstract

Low potential vorticity extends over the deep waters of the North Pacific and, possibly, the bottom waters of the North Atlantic. Isopycnic model integrations are conducted to investigate how these potential vorticity distributions are controlled, first, for an idealized double-hemisphere and, second, for the Pacific with realistic topography. Dense water is released from a southern, high-latitude source and circulates over the domain with diapycnic mixing gradually reducing its stratification. The potential vorticity contrast is large over the Southern Hemisphere, but weak over the Northern Hemisphere where the meridional changes in planetary vorticity and layer thickness oppose each other. Including an active eddy field inhibits the grounding of dense water, which increases the potential vorticity contrast in the overlying layer. Incorporating realistic topography leads to the dense fluid spreading via deep channels with tight recirculations and jets bifurcating. The experiments suggest that extensive regions of low potential vorticity are formed whenever there is both enhanced bottom mixing and a basin is filled by a single water mass entering from across the equator.

Corresponding author address: Dr Richard G. Williams, Oceanography Laboratories, Department of Earth Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom. Email: ric@liv.ac.uk

1. Introduction

Potential vorticity (PV) has been used as a diagnostic tool to identify different dynamical regimes in the upper ocean (McDowell et al. 1982; Keffer 1985). Ventilation has been associated with open contours of PV extending from the mixed layer into the main thermocline (Luyten et al. 1983). Conversely, eddy stirring and homogenization has been associated with extensive regions of nearly uniform PV over poorly ventilated parts of the main thermocline (Rhines and Young 1982a,b; Lozier 1997). Model studies suggest that the distinction between these processes becomes blurred though within the upper thermocline: ventilation sometimes provides weak contrasts in PV (Williams 1991) and eddy stirring smears out subducted mode waters and their contrasts in PV (Cox 1985; DYNAMO Group 1997).

In the deep and bottom waters, there are also different PV regimes even though the background flow is weaker. Potential vorticity contours are nearly zonal in some regions, such as at low latitudes over the middepths of the Atlantic and Pacific. Conversely, PV contours are strongly deformed by the circulation, as revealed by the spreading of mode waters (Talley and McCartney 1982). There are even regions of nearly uniform PV in the deep waters of the North Pacific and, perhaps, also the bottom waters of the North Atlantic (O'Dwyer and Williams 1997, henceforth referred to as OW).

These diagnostics raise the question of why regions of low and nearly uniform PV are formed within some density layers in deep basins and not others. There are a number of different possible explanations involving eddy stirring, diabatic mixing, the large-scale circulation, or an interplay of these processes.

Eddy stirring probably accounts for the homogenization of PV over the main thermocline of the North Pacific and, possibly, over the North Atlantic. However, it is unlikely that eddy stirring alone is the controlling process for the deep waters since the regions of nearly uniform PV in the main thermocline and deep water are separated by a middepth region where PV increases poleward. Eddy stirring might contribute toward this distribution if other processes, such as the background circulation or mixing, induce weaker PV contrasts in the bottom waters compared with the middepths.

The different PV distributions might partly reflect different patterns of diabatic mixing. For example, low stratification can be formed through enhanced mixing above rough topography (Polzin et al. 1997) and near boundaries (Armi 1978), as well as from geothermal heating of abyssal waters (Joyce et al. 1986; Talley 1988). However, the diapycnic mixing alone would form extensive regions of low stratification, rather than low PV unless the mixing varied in strength in a such a way to offset the northward increase in planetary vorticity.

The isolation of a basin and the number of water-mass sources are always important in determining tracer contrasts within a basin. For a tracer such as PV, there is an additional factor in that the planetary vorticity distinguishes a water-mass source located at low or high latitudes. There should be an influx of low PV whenever a water mass enters a basin from across the equator, which is then likely to dominate the PV distribution if there are no other water-mass sources (Fig. 1). This situation occurs in the deep and bottom waters of the North Pacific and the bottom water of the North Atlantic.

In this study, we examine the factors needed to obtain weak contrasts in PV in the deep and bottom waters. In section 2, we briefly describe the PV distribution in the Pacific using a meridional section from hydrographic data and climatological maps. In section 3, we conduct a series of isopycnic model experiments, which examine the PV distribution associated with an influx of dense water into a basin. The experiments examine the consequence of including enhanced diapycnic mixing near the seafloor and incorporating eddy stirring for an idealized domain. In section 4, the isopycnic model is integrated for a coarse resolution over the Pacific including realistic topography. Our realistic case complements the cartesian simulation of the abyssal circulation over the Pacific by Ishizaki (1994a,b). Finally, in section 5, the implications of the study are discussed.

2. Potential vorticity distribution in the deep Pacific

The potential vorticity variation in the Pacific is shown, first, for a hydrographic section along 170°W and, second, for climatological maps. The large-scale potential vorticity, Q, is evaluated as
i1520-0485-32-6-1811-e1
where f is planetary vorticity, σ is the potential density referenced to a depth of 4 km, z is the vertical coordinate, and ρ is a reference density.

a. Hydrographic section

The meridional variation of σ4, a potential density referenced to 4 km, from the WOCE hydrographic section P15 is shown in Fig. 2, upper panel. The northward deepening of isopycnals from 60°S to 40°S is associated with the eastward transport of the Antarctic Circumpolar Current. Surfaces lighter than σ4 = 45.8 become shallower farther north. Denser surfaces continue to deepen, with some surfaces grounding on the seafloor, and there is a consistent northward increase in the vertical spacing of the surfaces.

The meridional variation of Q along P15 for σ4 = 45.75 and 45.87 surfaces is shown in Fig. 2 (lower panel). There is a poleward increase in the magnitude of Q for both surfaces in the Southern Hemisphere and along the lighter surface in the Northern Hemisphere. However, along the denser surface, Q acquires a relatively low magnitude of less than 1 × 10−12 m−1 s−1, which extends over most of the northern basin (Fig. 2, dashed line).

b. Climatological maps

Climatological maps of Q along σ4 = 45.75 and 45.87 over the Pacific are shown in Fig. 3 from OW. The σ4 = 45.75 and 45.87 surfaces reach depths of 2800 and 4200 m in the North Pacific, respectively. On both surfaces, the Q contours are inclined to latitude circles over the South Pacific and become more zonal at low latitudes. For the lighter surface, Q contours continue to follow latitude circles over the North Pacific except for north of 40°N where some of the contours become distorted, perhaps, by the overlying gyre circulation. However, for the denser surface, Q acquires a low value of typically 2 × 10−12 m−1 s−1, which extends over much of the North Pacific; this result is also obtained when Q is evaluated using neutral surfaces (OW).

These maps of Q can be compared with the isopycnal maps of salinity, oxygen, and silica on the σ3 = 41.44 and σ4 = 45.87 surfaces, and geostrophic flow at the depths between 2500 and 5000 db calculated by Reid (1997). The Q distributions broadly resemble those of salinity, a conservative tracer. Here Q contours become zonal at low latitudes by definition, but this behavior is also seen in these other tracer fields, reflecting the zonal flow along the equator. North of the equator, both salinity and Q have stronger meridional gradients on the lighter surface. Oxygen and silica still have significant gradients over the denser surface for the North Pacific reflecting their nonconservation, which assists in revealing the large-scale circulation.

Reid (1997) argued that the wind forcing influences the circulation over the water column for much of the North Pacific. Flow is dominated by large anticyclonic gyres at midlatitudes in each hemisphere, which contract poleward at depth. In the deep and bottom water, a western boundary current transports high oxygen and low salinity from the Southern Ocean at least as far as the mid latitudes in the North Pacific. In the eastern interior, lower oxygen and higher silicate concentrations suggest a southward return flow from the Northeast Pacific. This anticyclonic circulation is the opposite direction to the interior abyssal flow predicted by Stommel and Arons (1960). Johnson and Toole (1993) suggest that this response might be an effect of the topography, caused by the slope of the East Pacific Rise. Alternatively, the anticyclonic circulation might arise from the horizontal divergence of fluid upwelling over a dome-shaped basin, called the “hypsometric effect” (Rhines and MacCready 1989).

The following modeling experiments are conducted to examine how the overturning circulation controls the potential vorticity distributions over the deep Pacific.

3. Mechanisms controlling the potential vorticity in deep waters

a. Formulation of model

The model experiments examine the influx of dense fluid into a basin using an isopycnic model (referred to as MICOM version 2.7; Bleck and Smith 1990). Idealized experiments are conducted for two different resolutions:

  1. a coarse 2° resolution integration over a flat bottom, 120° × 100° wide rectangular basin with four density layers of σ4 = 44.1, 45.8, 45.85, and 45.9;
  2. an eddy resolving integration at 0.125° resolution over a more limited, rectangular domain 120° × 25° wide with the same vertical resolution.

Since the experiments are focusing on the influx and modification of dense water, the buoyancy forcing is confined to a southern relaxation zone and interior diapycnic diffusion, and there is no surface buoyancy forcing (Fig. 4). Wind forcing is not included in the initial coarse-resolution experiment. However, wind forcing is added in later coarse-resolution experiments in order to generate sufficient available potential energy and initialize an eddy-resolving experiment.

The diapycnic diffusivity, κ, is chosen to consist of two parts: (i) a background value, κs, which is incorporated to allow a steady state to be reached, and (ii) an additional mixing along the bottom interface, κbot, which varies inversely with buoyancy frequency N. In our experiments, κbot is typically 0.5 × 10−4 m2 s−1 for N ∼ 10−3 s−1 in the deep water. In addition, isopycnic mixing and thickness diffusion is included with a diffusive velocity of 0.5 cm s−1 and with Laplacian and biharmonic forms respectively. The momentum mixing is deformation dependent with a background Laplacian mixing and a turbulent mixing velocity of 1 cm s−1.

b. Definition of potential vorticity

The potential vorticity is calculated in the isopycnal model in terms of the product of the absolute vortity and stratification:
i1520-0485-32-6-1811-e2
where ζ is the relative vorticity. The vertical gradient in potential density is evaluated from the ratio of the density difference across a layer Δσ and the layer thickness h or equivalently in terms of the bounding interfaces, σn+1 and σn, and their vertical positions, z(σn+1) and z(σn); the σ surfaces are again referenced to a depth of 4 km. This definition becomes unclear when the denser bounding interface, σn+1, has grounded.
If the potential vorticity is defined in terms of layer thickness, Q* = (ζ + f)/h, then a singularity in potential vorticity occurs whenever the layer thickness h vanishes. Instead, following our data diagnostics, we choose to diagnose the potential vorticity upon grounding by
i1520-0485-32-6-1811-e3
where σb and z(σb) is the potential density and vertical position of the seafloor, respectively. The potential density along the seafloor is chosen to vary between σn and σn+1 according to the overlying mass-weighted layers and the value of bottom pressure in the model (which are connected together via the hydrostatic balance). This approach leads to the PV always having a finite value using (3) rather than an artificial singularity implied by grounding.

Our choice of (3) is permitted since potential vorticity is a diagnostic quantity and is not solved for in MICOM. The model applies a flux form of the momentum and tracer equations, which for potential vorticity is equivalent to solving for absolute vorticity: uhQ* = u(ζ + f), where h is the layer thickness and Q* is the potential vorticity defined in terms of layer thickness. In the following diagnostics, this choice is only important for maps shown for the Pacific integration (see later Fig. 13), where an additional ring of high values would appear if a layer-thickness definition, Q*, is preferred.

c. Idealized, coarse-resolution experiment

The experiments include a southern source of dense water (Fig. 4), formed by relaxing the layer interface within a zone 1000 km wide at the southern boundary; the restoring timescale smoothly increases from 60 to 480 days. The experiments are initialized with flat interfaces in the interior, which shoal over the relaxation zone (Fig. 5a, dashed line). The deeper two interfaces are initially at 3500 and 4000 m in the interior, while the upper layer is 200 m thick.

If the model is integrated without diapycnic mixing over the interior, the basin fills up with dense water (Fig. 5a, dotted line) until eventually the southern source switches itself off.

1) Uniform background, diapycnic mixing

A downward diffusion of heat is incorporated in order to offset the dense water source and obtain a steady solution. The diffusive velocity is interactively calculated to compensate for the input of dense water from the restoring on the southern boundary. After 200 years, there is a steady solution with a northward volume flux of 11.4 Sv entering layer 4 (the bottom layer) and 0.6 Sv (Sv ≡ 106 m3 s−1) into layer 3 from the southern relaxation zone. This volume influx is diapycnally transferred into layer 2 and eventually returned to the southern relaxation zone; the effective background diffusivity is 1.1 × 10−4 m2 s−1 over the interior. The resulting meridional section shows the interface heights are broadly symmetric with similar variations in the Northern and Southern Hemispheres (outside of the relaxation zone: Fig. 5a, solid line).

The PV varies symmetrically over each hemisphere and is controlled by the planetary vorticity since the layer thickness changes are relatively small (Fig. 6a). The PV contours are generally zonal, apart from an equatorward advection along the western boundary.

In the spin up of the circulation, the dense water initially spreads through a Kelvin wave response, as described by Kawase (1987). At a steady state, the final solution is broadly in accord with Stommel and Arons (1960) since there is a flat bottom and no eddy-induced circulation. In the bottom layer, the western boundary layer feeds the poleward flow in the interior of each hemisphere and an eastward flow along the equator (Figs. 7a,b). In response, in the overlying layer, there is a westward return flow along the equator that broadens toward the eastern boundary. Elsewhere, there are recirculating gyres with a polewards interior flow.

2) Enhanced bottom mixing

The role of enhanced bottom mixing is now investigated, motivated by the observations of increased mixing towards the bottom and over rough topography (Polzin et al. 1997). Additional diapycnic mixing is included along the deepest layer interface that has not grounded. Consequently, there is increased diapycnal transfer from layer 4 to 3 and a northward deepening of the interface (Fig. 5b). For a choice of κbot = 0.5 × 10−7 m2 s−2/N (corresponding to κbot ∼ 0.5 × 10−4 m2 s−1 for a typical N ∼ 10−3 s−1), the interface grounds at 20°N. Incorporating a larger diffusivity leads to the grounding line retreating farther southward.

The steady state involves a balance between the influx of dense fluid in the bottom layer and the diapycnal transfer to lighter fluid. Incorporating this diapycnal transfer means that mass is only conserved globally, but not for an individual layer. A steady state is reached after 800 years of integration (continued from the previous uniform background mixing solution). The southern source provides a volume flux into layer 4 of 16.2 Sv, which is diapycnally transferred to lighter fluid; the background mixing and additional bottom mixing providing diapycnic transfers of 11.2 Sv and 5 Sv, respectively. Eventually, the upper circulation returns 2 Sv in layer 3 and 14.2 Sv in layer 2 back to the southern relaxation zone. The model takes longer to equilibrate with bottom mixing due to the mass transfer between layers.

The PV variation becomes asymmetrical with a larger PV contrast across the Southern Hemisphere, than across the Northern Hemisphere (Fig. 6b). Potential vorticity is lower in magnitude over the Northern Hemisphere and the circulation leads to closed off contours in the northwest part of the domain. The modeled density and PV variations (Figs. 5 and 6) become more similar to the observations (Figs. 2 and 3) when the enhanced bottom mixing is included.

The choice of bottom mixing only significantly alters the circulation over the bottom layer (Figs. 7b,c). When additional bottom mixing is incorporated, the extra diapycnic transfer leads to the bottom layer grounding over the center of the southern basin and much of the northern basin (Fig. 7c). Over the northern basin, the transport of dense water along the western boundary becomes exhausted and the dense fluid spreads poleward over the eastern side of the basin.

We now examine how the model solutions with enhanced bottom mixing are modified by, first, eddy stirring and, second, realistic topography for the Pacific (in section 4).

d. Idealized, eddy-resolving experiment

The idealized model experiments are repeated with an increased resolution of 0.125° and the same meridional extent of 120°, but a reduced zonal extent of 25°. First, a coarse-resolution model is integrated over the reduced domain with wind forcing applied for 200 years, which is initialized with output from the previous 800-yr integration with enhanced bottom mixing. Second, an eddy-resolving integration is conducted for 20 years with the same wind forcing and the output is shown from a time average for the last 2 years.

The imposed wind forcing includes a zonal variation following a double sine pattern over the basin plus a meridional periodic perturbation, which assists in making the ocean jets unstable; the perturbation represents a synoptic, cyclone–anticyclone dipole moving eastward across the domain. The wind forcing drives a surface, double gyre recirculation over each basin. The jets are unstable and generate a intense eddy field, particularly over the tropics and the boundary between the subtropical and subpolar gyres.

Compared with the coarse-resolution integrations, the eddy activity penetrates throughout the water column and redistributes the thickness of each layer (Figs. 8a,b). The eddies inhibit the grounding of dense water in the bottom layer, as revealed over the central part of the southern basin and the influx of dense fluid in the northwest corner of the domain. If a layer thickness definition, Q* = (ζ + f)/h, is employed, then eddies acting to oppose the grounding of the bottom layer is consistent with a downgradient transfer of Q*. This eddy-induced change in layer thickness is associated with an increase in meridional transport over the bottom layer carried over the entire domain and within the western boundary (Fig. 8c).

However, the eddy spreading of dense fluid leads to the PV contrast in layer 3 being slightly increased and closer to that implied from the planetary vorticity variation, compared with in the coarse-resolution integration (Fig. 9). Since the isopycnic gradient in PV is controlled by that of h over the large scale, a decrease in the h gradient for the bottom layer will lead to a compensating increase over an overlying layer. This process by which the bottom flow interactions control the PV distribution and can inhibit homogenization is in accord with model studies by Merryfield and Holloway (1999) and Adcock and Marshall (2000).

4. Pacific model with realistic topography

a. Model formulation

The model experiments are now extended to include a more realistic representation of the Pacific. The model resolution is 1.4° in the horizontal, five layers with σ4 = 43.7, 45.5, 45.7, 45.81, and 45.9, and topography based on a 5-min ETOP05 dataset (see later Fig. 11a). In the southern part of the domain, cyclic boundary conditions are included in order to simulate the Antarctic Circumpolar Current over the upper water column. The previous closed basin experiments for the deep flow are still relevant, since the deep southern Pacific is relatively isolated by the topographic barriers.

The model is initialized with flat isopycnals except within the southern relaxation zone (Fig. 10, dashed lines) and the diapycnic diffusive velocity again includes a background value and the enhanced diffusion across the bottom interface; the same values are chosen as in the previous idealized integrations. The model is integrated for 800 years and forced with a monthly mean, wind stress from the COADS climatology. Incorporating the additional bottom mixing again leads to a general northward deepening of the denser model interfaces (Fig. 10, full lines). The model interfaces undulate locally over the topography through the circulation induced there.

The wind forcing drives the expected pattern of recirculating gyres with a western boundary current transport of 85 Sv in the Kuroshio for the northward flow across 35°N between 136° and 144°E. The Circumpolar Current transport through Drake Passage reaches 115 Sv. The overturning circulation is at least an order of magnitude weaker than the horizontal transports in the gyres and circumpolar current.

The overturning circulation is broadly similar to the previous idealized solutions (Fig. 5b) with a northward volume flux of 12.4 Sv in the bottom layer now leaving the southern relaxation zone. This dense fluid is diapycnally transferred into the lighter, overlying layers through a combination of the background mixing (7.5 Sv) and the enhanced bottom mixing (4.9 Sv). This diapycnic transformation implies a diapycnal diffusivity of 1.25 × 10−4 m2 s−1 acting at the interface between layers 4 and 5, 0.72 × 10−4 m2 s−1 between layers 3 and 4, and 0.58 × 10−4 m2 s−1 between layers 2 and 3. The lighter fluid eventually is returned to the southern relaxation zone with 4.0 Sv in layer 4, 0.6 Sv in layer 3, and 7.8 Sv in layer 2.

b. Deep circulation

The bottom circulation is displayed in Fig. 11 with vectors denoting current velocities and transports in the upper and lower panel, respectively. Incorporating realistic topography leads to a much more complex bottom circulation including the formation of topographic jets, flow bifurcations, and tight recirculations.

The modeled northward transport of bottom water is carried principally by a deep western boundary current over the South Pacific, which reaches a maximum speed of 5 cm s−1. The boundary current bifurcates at 35°S with a branch separating from the coast and forming an intense anticyclonic gyre in the southern basin. However, most of the boundary current continues northward until again splitting at 15°S: the eastern branch transports 2 Sv around the Manihiki Plateau (10°S, 160°W), while the western branch transports 2.6 Sv around the Samoan Passage (10°S, 170°W). Both branches turn eastward at 5°S and recombine and form a western boundary current carrying 4 Sv across the equator at 178°E.

The western boundary current bifurcates at 10°N with the main branch extending northwestward and a weaker branch directed eastward. This bifurcation is consistent with observations along 10°N by Johnson and Toole (1993, see their schematic). However, we find that their prediction of a southward interior transport only occurs in our overlying layer (with 2.15 Sv of deep water transported southward across 10°N) since the bottom flow is blocked by topography. Farther north, there is a complex circulation with the transport carried by interior jets following deep channels. A portion of the bottom flow provides an eastward transport across 170°W with 1.3 Sv carried along the deep channels between 35° and 45°N, and 0.4 Sv at 15°N crossing the Clarion passage. While bottom currents reaching the northern rim of the North Pacific are returned westward.

The modeled circulation does not appear to be consistently cyclonic or anticyclonic over the large scale. For example, the eastwards flow along 15°N appears to be part of an anticyclonic circulation, while the flow along 30°N part of a cyclonic circulation. This response differs from the large-scale cyclonic circulation expected from Stommel and Arons (1960), which was seen in the previous flat-bottom integrations. Likewise, the model solution does not reveal the large-scale anticyclonic circulation expected from the “hypsometric effect” suggested by Rhines and MacCready (1989), which was found in the model study by Ishizaki (1994b) for the deep Pacific. Instead, in our solutions, the local changes in topography appear to mask and obscure any large-scale control of the sign of the horizontal circulation.

c. Diapycnal transfer

The diapycnal transfer controls the northward decrease in bottom transport over the Pacific (Fig. 11b, right panel). Here 12 Sv of bottom water is formed at the southern relaxation zone, which reduces to 8.5 Sv at 50°S, 4.6 Sv at 10°S, 3.5 Sv at 10°N, and 2.3 Sv at 24°N (Fig. 11, right panel). In comparison, the observations suggest that the northward transport should be at least twice as large: 12 Sv of bottom water at 12°S (Taft et al. 1991), 8.4–9.6 Sv at 10°N (Johnson 1990; Johnson and Toole 1993), and 4.9 Sv at 24°N (Bryden et al. 1991). However, there is a similar rate at which the dense water is converted to light water in the model and as implied from the observations. In the model, the percentages of dense water fluxed across 10°S that reach 10°N and 24°N are 76% and 50%, respectively. In comparison, in the observations, the percentages of dense water fluxed across 12°S that reaches 10°N and 24°N are 70%–83% and 48%, respectively. Our underestimate of bottom transport is probably due to a combination of the model forcing being too weak over the southern relaxation zone and having too poor a vertical resolution; Ishizaki (1994a) obtains a similar underestimate of bottom transport in a cartesian simulation.

The most intense diapycnal mixing and decrease in bottom transport in the model solution are found south of 40°S (Fig. 12). Elsewhere, there are similar diapycnal transfers of dense water over the domain; for example, the area-integrated diapycnal transfer is almost identical over the western and eastern halves of the North Pacific (1.8 Sv and 1.7 Sv, respectively).

The diapycnic velocity and diffusivity vary slightly in the model alter slightly through their dependence on layer thickness, h, and buoyancy frequency, N (Fig. 12). The diapycnic mixing coefficient, κ, includes a spatially variable component depending inversely on buoyancy frequency: κbot = 0.5 × 10−7 m2 s−2/N. Hence, there is an inverse variation between κ and N in Fig. 12. The diapycnal velocity wd depends on the diapycnic mixing coefficient and stratification with scale analysis suggesting wdκ/hκN2. Consequently, there is a slight decrease in wd over the central North Pacific following the increase in h and decrease in N there (Fig. 12). In reality, there might be much larger variations in the wd and κ if more realistic closures are chosen, which depend on the roughness of the topography and velocity shear.

d. Modeled potential vorticity

The modeled distribution of PV reflects the evolution of the circulation and density distribution. The model is initialized with flat isopycnals, but over the 800-yr integration, dense isopycnals deepen northward and eventually ground (Fig. 10). The resulting PV distribution is shown in Fig. 13 as a meridional section and maps along the σ4 = 45.75 and 45.87 surfaces in Fig. 13. There are strong meridional contrasts in PV over the Northern and Southern Hemispheres along σ4 = 45.75, but a much weaker contrast in the Northern Hemisphere along σ4 = 45.87. The main difference in the PV distributions from the model and diagnosed from data is over the South Pacific: at 40°S, the modeled PV is −1.5 × 10−11 m−1 s−1 compared with −3 × 10−11 m−1 s−1 in the data. This difference is due to the model restoring having been chosen to sloping isopycnals with a constant vertical spacing (as in the previous idealized experiments). These isopycnic slopes are steeper in the more realistic ocean, as seen by comparing Figs. 2a and 10. Elsewhere, there is reasonable agreement between the PV distributions from the model and diagnosed from observations, as shown in Figs. 2b and 3. Given that the model was initialized with flat isopycnals, this broad agreement is achieved through the combination of the overturning circulation and enhanced bottom mixing.

5. Discussion

There are extensive regions of low and nearly uniform PV over the deep waters of the North Pacific and, possibly, the bottom waters of the North Atlantic. These signals are restricted to the deep waters with a meridional increase in PV occurring at mid depths. The model experiments suggest that the extensive regions of low PV over the deep waters are formed through (i) a single water mass entering a basin from across the equator and providing an influx of low PV as well as (ii) an enhanced bottom mixing leading to isopycnals grounding, which reduces the meridional contrast in PV within the overlying layer.

In the model experiments, the dense water initially has relatively large stratification at the high-latitude source, which is gradually weakened by the diapycnic mixing throughout its journey around the domain. Consequently, the PV has a large contrast over the basin where the source is located, where the changes in planetary vorticity and layer thickness reinforce each other. However, over the end basin, there is a relatively weak contrast in PV across the basin through the poleward changes in planetary vorticity and layer thickness opposing each other.

In practice, the extensive regions of low and nearly uniform PV only occur over the northern basins. This asymmetry is due to the importance of the Southern Ocean in ventilating deep and abyssal waters with most dense isopycnals outcropping there. The enhanced bottom mixing acts to weaken the stratification so that the lowest stratification is generally in the oldest bottom waters away from the southern source and, hence, in the Northern Hemisphere.

While eddy stirring probably accounts for much of the nearly uniform PV in the main thermocline, this mechanism is not required to explain the deep PV distributions. Eddy stirring might subsequently weaken the PV contrasts within particular layers. In our experiments, the eddies inhibit the grounding of dense water in the bottom layer (and reduces the PV contrast over the bottom layer if defined in terms of layer thickness), but increases the PV contrast in the overlying layer. This response is consistent with other studies emphasising how the response of the bottom flow to topography can inhibit eddy homogenization of PV (Merryfield and Holloway 1999; Adcock and Marshall 2000).

Incorporating realistic topography leads to dense fluid spreading via deep channels, as well as the deep jets separating from the coast and bifurcating. In our model solutions, the basin-scale variations in PV are controlled by the overturning circulation and the enhanced bottom mixing. The PV over the interior might perhaps be further altered through the lateral injection from boundary sources, as suggested by Hallberg and Rhines (2000), involving separated boundary currents and eddy transfers from solid boundaries. In addition, there might be further variations in the PV, perhaps on a more local scale, if the diabatic mixing varied more realistically with the roughness of the topography and strength of bottom flow.

Acknowledgments

The work was supported by Research Grant GR3/119/55 and supercomputing time from GR9/03418 from the UK Natural Environment Research Council. We are grateful to Mike Spall and an anonymous reviewer for providing thoughtful and constructive comments that improved the study.

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Fig. 1.
Fig. 1.

A schematic figure showing a water-mass source spreading over a double basin. The PV contrast is larger over the basin where the source is located, compared with the end basin. Over the end basin, the water mass enters from across the equator and fills the basin with low PV

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 2.
Fig. 2.

Upper panel: a WOCE, hydrographic section P15 for potential density, σ4, in the Pacific along 170°W (displayed only from 1 km to the seafloor). Lower panel: the resulting meridional variation in large-scale potential vorticity, Q, (10−11 m−1 s−1) for σ4 = 45.75 and 45.87 surfaces (full and dashed lines respectively). The Q has a nearly uniform and a low magnitude for the denser surface (dashed line) over the North Pacific

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 3.
Fig. 3.

Climatological maps of Q (10−12 m−1 s−1) in the Pacific from O'Dwyer and Williams (1997): along σ4 = 45.75 (upper panel) and σ4 = 45.87 (lower panel) surfaces with Δσ4 = 0.02. Data in shaded areas are excluded from the contouring of the fields; they include topography, data-poor regions and shelf-sea basins. The maps reveal low Q extending over the denser surface for the North Pacific

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 4.
Fig. 4.

A schematic figure of the model domain used in the idealized experiments. Dense fluid enters the domain from a southern relaxation zone and is diapycnally transferred to lighter fluid in the interior through a combination of background and enhanced bottom mixing. In later experiments, wind stress forcing is incorporated to drive a double-gyre circulation and generate an active eddy circulation

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 5.
Fig. 5.

Meridional sections in the coarse-resolution, idealized experiment along 6°E. (a) The initial interfaces slope over the relaxation zone, but are flat elsewhere (dashed line). If there is no interior diapycnic diffusivity, an influx of dense water leads to the interfaces doming up over the interior, as shown by the dotted lines after 200 years. A steady solution is obtained if a constant, background diffusivity is incorporated (full lines) with the influx of dense fluid converted to lighter fluid. (b) Incorporating additional diapycnic mixing along the deepest interface leads to a poleward deepening of the interface and eventual grounding of the bottom layer. The volume flux (Sv) into and between each layer is indicated in the arrows

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 6.
Fig. 6.

Potential vorticity (10−12 m−1 s−1) of layer 3 for coarse-resolution integrations with (a) uniform background mixing and (b) enhanced bottom mixing along the deepest interface. The right panels shows the PV (full line) and planetary vorticity scaled by the mean layer thickness (dashed line) vs latitude. The enhanced bottom mixing leads to a weaker meridional contrast in PV, as shown in (b)

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 7.
Fig. 7.

Deep and bottom circulations for the coarse-resolution model with uniform mixing for layers 3 and 4 in (a) and (b) and for layer 4 with enhanced bottom mixing in (c). The contours are for Montgomery potential (105 N m−2) and the arrows represent the volume flux in the layer (plotted every second grid point). Note how in the bottom layer grounds in both basins (shaded) when there is enhanced bottom mixing in (c)

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 8.
Fig. 8.

Layer thickness (m) of the bottom layer (layer 4) for (a) coarse and (b) eddy-resolving integrations with enhanced bottom mixing and wind forcing. (c) The meridional transport in the bottom layer is included for the coarse (dashed line) and eddy-resolving (full line) integrations, which is shown over the entire domain and over the western boundary (0° to 6°E). Incorporating eddies inhibits the grounding of the bottom layer (shaded) and leads to a greater poleward transport

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 9.
Fig. 9.

Modeled maps of PV (10−12 m−1 s−1) of layer 3 for (a) coarse and (b) eddy-resolving integrations with enhanced bottom mixing and wind forcing. The right panels show the PV (full line) and planetary vorticity scaled by the mean layer thickness (dashed line), which are zonal averages from 0° to 12°E, vs latitude. The slight increase in the PV contrast over layer 3 for the eddy case is an indirect consequence of the eddies inhibiting grounding of the bottom layer (as shown in Fig. 8)

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 10.
Fig. 10.

Modeled meridional section for σ4 along 170°W through the Pacific. The model is integrated for 800 years with realistic topography at 1.4° resolution and enhanced bottom mixing. The initial and final states are marked by the dashed and full lines, respectively. The meridional transport and area-integrated diapycnic flux (Sv) are included for the final state. There is a northward deepening of the denser interface, which broadly resembles the idealised solution with enhanced bottom mixing (Fig. 5b)

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 11.
Fig. 11.

Model circulation in the bottom layer with realistic topography at 1.4° after 800 years of integration: (a) bottom velocity and (b) bottom transport. The vectors representing bottom velocity and transport are each scaled to 1 cm s−1 and 1 Sv (106 m3 s−1), respectively. The core of the deep inflow spreads along the western side of the deep channels. Dark and light shading represents depths less than 3 and 4 km, respectively. (b) The right panel shows bottom transport (full line) and a bar plot of zonally integrated diapycnal transfer across the deepest interface, scaled to give the area-integrated mean flux in Sv every 10° in latitude

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 12.
Fig. 12.

Modeled variations in diapycnic velocity wd (10−7 m s−1), buoyancy frequency N (10−3 s−1), and diapycnal diffusivity κ (10−4 m2 s−1) over the bottom layer. The plots are for a zonal average from 160°E to 130°W after 800 years of integration

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

Fig. 13.
Fig. 13.

Modeled maps of PV (10−12 m−1 s−1) over the Pacific after 800 years of integration with realistic topography at 1.4° resolution: (a) meridional variation for σ4 = 45.75 and 45.87 surfaces (full and dashed lines respectively); (b) maps for σ4 = 45.76 and 45.87 surfaces (layers 3 and 4). The model solution reveals weaker meridional contrast in PV across the northern basin for the denser surface, which is broadly in accord with the diagnostics from the WOCE section and climatology (Figs. 2, 3)

Citation: Journal of Physical Oceanography 32, 6; 10.1175/1520-0485(2002)032<1811:FOLPVO>2.0.CO;2

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