Remote forcing of the Antarctic Circumpolar Current by diapycnal mixing

Authors


Abstract

[1] We show that diapycnal mixing can drive a significant Antarctic Circumpolar Current (ACC) volume transport, even when the mixing is located remotely in northern-hemisphere ocean basins. In the case of remote forcing, the globally-averaged diapycnal mixing coefficient is the important parameter. This result is anticipated from theoretical arguments and demonstrated in a global ocean circulation model. The impact of enhanced diapycnal mixing on the ACC during glacial periods is discussed.

1. Introduction

[2] The transport of the Antarctic Circumpolar Current (ACC) is dominated by the thermal wind relative to the sea floor. Integrating the thermal wind relation across the ACC, assuming no flow at the sea floor, and neglecting variations in the Coriolis parameter, the ACC transport is:

equation image

Here g is the gravitational acceleration, ρ0 is a reference density, fACC is a typical value of the Coriolis parameter at the ACC latitude, z is depth with z = 0 at the surface and z = −H at the sea floor, and ρn and ρs are the densities evaluated along the sloping boundaries to the north and south of Drake Passage. To the extent that isopycnals outcrop to the south, the baroclinic ACC transport is connected with the stratification to the north.

[3] Traditionally it has been assumed that the density contrast across the ACC is maintained by Southern Ocean wind and buoyancy forcing. Air-sea heat and freshwater fluxes create the density contrast and the surface wind stress generates the overturning “Deacon cell” that steepens the isopycnals. In equilibrium, this is arrested by baroclinic instability, the eddy-driven transport opposing the Deacon cell [Danabasoglu et al., 1994] with the residual overturning circulation being set by surface buoyancy forcing [Marshall, 1997].

[4] However, the stratification to the north of the ACC is also affected by non-local processes that set the depth of the global pycnocline; these include deep water formation in the North Atlantic and diapycnal upwelling throughout the global ocean [Gnanadesikan, 1999; Gnanadesikan and Hallberg, 2000]. The link between North Atlantic deep water formation and the transport of the ACC has recently been investigated by Fučkar and Vallis [2007]. In this paper we explore the impact of diapycnal upwelling on the ACC transport.

[5] The idea that the ACC transport is affected by both local wind forcing over the Southern Ocean and remote diapycnal mixing is consistent with the mechanical energy budget of the ocean [Munk and Wunsch, 1998]. Most of the global input of wind energy (∼1 TW [Wunsch, 2010]) occurs over the Southern Ocean. In contrast, surface buoyancy forcing provides a small global energy sink [Wunsch and Ferrari, 2004] (note that alternative definitions of available potential energy can lead to different conclusions [e.g., Hughes et al., 2009; Tailleux, 2009]). Satellite altimetry suggests much of the remaining mechanical energy input (∼1 TW) may be supplied by tidal dissipation in the deep ocean [Egbert and Ray, 2000]. To the extent that diapycnal mixing provides energy for the meridional overturning circulation of the oceans, it may also contribute to setting the ACC transport.

2. Theory

[6] A simple model of the processes that set the isopycnal slope in the Southern Ocean is that developed by Gnanadesikan [1999] for the global pycnocline depth. The global ocean is represented by a buoyant surface layer overlying an abyssal layer, separated by a pycnocline of depth h (Figure 1). The pycnocline depth is set by the sources and sinks of water to the surface layer:

equation image

where

equation image

are the parameterizations suggested by Gnanadesikan [1999]. Thus the pycnocline depth is increased by equatorward Ekman transport in the Southern Ocean (TEk) and diapycnal upwelling (TU) and decreased by poleward eddy bolus transport in the Southern Ocean (TEddies) and northern deep water formation (TN). Here τACC is the wind stress over the ACC, Lx is the circumpolar length of the ACC, κGM is the eddy diffusivity (following Gent and McWilliams [1990]), Ly is the meridional extent of the ACC, κv is the diapycnal diffusivity and A is the area of the ocean basins to the north of the ACC. Both τACC and Ly should be calculated as integrals over the ACC as described by Allison et al. [2010].

Figure 1.

Schematic of the processes setting the global pycnocline depth and hence ACC transport [Gnanadesikan, 1999].

[7] Gnanadesikan [1999] further suggests parameterizing TN as proportional to h2. However, northern sinking also depends on subtle thermohaline feedbacks that control the meridional density gradient along the western boundary of the North Atlantic [Johnson et al., 2007; Schewe and Levermann, 2010; Levermann and Fürst, 2010; also see de Boer et al., 2010]. Here we sidestep these complications by treating TN as constant.

[8] Assuming that the ACC is in geostrophic balance and that the pycnocline outcrops to the south, the ACC transport is given by

equation image

where g′ is the reduced gravity, analogous to (1). Thus, any process that influences the pycnocline depth will also affect the volume transport of the ACC.

[9] In order to interpret the numerical experiments described below, it is useful to consider the limiting case of no wind forcing and no deep water formation, i.e., TEk = TN = 0. In this limit, the pycnocline is set by diapycnal mixing and eddies, and the ACC transport scales, through (2) and (3), as:

equation image

i.e., the ACC transport is linearly dependent on the amount of diapycnal mixing integrated over the basins to the north of the ACC.

[10] More generally, differentiating (2) and (3) with respect to h for fixed values of TEk and κGM, but keeping TN = 0:

equation image

This ratio asymptotes to one when diapycnal upwelling dominates over the Ekman transport and to zero when the Ekman transport dominates over diapycnal upwelling.

3. Numerical Experiments

[11] To explore the relationship between diapycnal upwelling and the ACC transport in a more realistic setting, we now describe a series of numerical experiments with a global ocean model (MITgcm [Marshall et al., 1997]). The model has horizontal grid spacing of 4° and 15 vertical levels. Mesoscale eddies are parameterized following Gent and McWilliams [1990] with constant isopycnal and thickness diffusivities of 1000 m2 s−1. Surface temperature and salinity are restored to climatology [Levitus and Boyer, 1994] over time scales of 2 and 6 months respectively, and climatological surface wind stress [Trenberth et al., 1990] is applied in some experiments, each as annually-repeating seasonal cycles.

[12] Three sets of experiments are performed, each with and without surface wind stress forcing. In the first set, the diapycnal mixing coefficient (κv) is set to uniform values between 1 × 10−5 m2 s−1 and 3.0 × 10−4 m2 s−1. In the second set, κv is held at 10−5 m2 s−1 in the Southern Ocean and Atlantic, but enhanced to 10−4 m2 s−1 in the Indian and Pacific north of: (a) 32°S, (b) the equator, and (c) 24°N. Finally, in the third set, κv is held at 10−5 m2 s−1 in the Southern Ocean, Indian, and Pacific, but enhanced to 3 × 10−5 m2 s−1 and 10−4 m2 s−1 in the Atlantic north of (a) 32°S and (b) the equator.

[13] In Figure 2 we show the barotropic streamfunction at equilibrium for a subset of our experiments. Each of the calculations is presented with and without wind forcing. A comparison of Figures 2a and 2b illustrates that there is an order of magnitude increase in ACC transport due to the presence of wind forcing at the lowest, background value of κv. Without wind forcing, the depth-integrated gyres are absent in each of the basins but there is still a weak ACC (13 Sv).

Figure 2.

Depth-integrated streamfunction (Sv) at equilibrium. The ACC transport through Drake Passage is indicated in each panel. (a, b) spatially uniform low mixing of 10−5 m2 s−1; (c, d) enhanced mixing of 10−4 m2 s−1 north of 32°S in the Atlantic; (e, f) enhanced mixing of 10−4 m2 s−1 north of 32°S in the Pacific and Indian basins. (left) With and (right) without wind forcing.

[14] Figures 2c2f show that enhancing diapycnal mixing by an order of magnitude in the northern basins enhances the ACC transport. When mixing is enhanced in the Atlantic, with wind forcing, the ACC transport is increased from 110 Sv to 119 Sv; enhanced mixing in the Indian and Pacific increases the ACC transport to 144 Sv.

[15] Plotted in Figure 3a is the volume transport of the ACC at Drake Passage, as a function of the area-weighted diapycnal mixing coefficient,

equation image

To enable comparison with the theoretical prediction (5), logarithmic scales are used for both axes; the solid grey lines correspond to slopes of 0 and 1. In the absence of wind, the ACC transport varies linearly with equation image, as predicted by (5); this dependence weakens as equation image increases due to an increase in TN, not accounted for in the theory. In the presence of wind, the ACC transport is independent of κv for small values of the latter, as also predicted by (5).

Figure 3.

(a) ACC transport through Drake Passage as a function of the area-weighted diapycnal mixing coefficient equation image. Experiments with a spatially uniform κv are plotted in blue, those with enhanced mixing in the Atlantic in green, and those with enhanced mixing in the Pacific and Indian in red. Squares represent experiments with wind forcing and circles without. (b) Meridional cross-section of potential density (kgm−3) in the Pacific basin at 206°E for the experiments in Figures 2a (uniform low mixing, blue) and 2e (enhanced mixing in the Pacific and Indian, red).

[16] The dependence of ACC transport on diapycnal mixing has been noted by other authors [e.g., Cai, 1994; Cai and Baines, 1996], but attributed to interactions between baroclinicity and topography in the Southern Ocean. Saenko et al. [2002] also obtain a strong circumpolar transport in a coupled ocean-atmosphere model in which wind stress is not transmitted to the ocean. Figure 3b shows the model density field in the Pacific for the experiments in Figures 2a and 2e, confirming that it is the adjustment of the basinwide pycnocline that is responsible for the increase in ACC transport.

[17] In the case of altered wind forcing, the change in TN additionally increases TACC by warming the abyss and increasing thermal shear across the ACC [Gnanadesikan and Hallberg, 2000]. A thermal wind calculation based on abyssal density differences (see Figures S1–S3 of the auxiliary material) suggests this effect is non-negligible, but always smaller than the values of TACC reported in Figure 3a.

4. Discussion

[18] Our results suggest that diapycnal mixing, even when located in regions remote from the Southern Ocean, can drive a significant ACC transport. This is a consequence of the impact of enhanced diapycnal mixing on the global pycnocline depth, and hence on the slope of isopycnals across the ACC. Since diapycnal mixing in the deep ocean results from the dissipation of tidal energy, this implies a low-order lunar influence on the ACC transport.

[19] While the mechanical energy for an ACC forced by remote diapycnal mixing comes from tidal (and wind-driven) mixing, the momentum source is less obvious. Consider a thought experiment in which diapycnal mixing is instantaneously enhanced north of the ACC. Increased diapycnal mixing deepens the pycnocline, which is communicated globally via eastern boundary waves [Johnson and Marshall, 2004]. Assuming isopycnals remain pinned to the surface around Antarctica, the density gradient attempts to slump, with southward surface flow and northward flow at depth. However, the Coriolis acceleration causes these density currents to turn to their left, resulting in eastward flow at the surface and westward at depth. Finally, bottom form stress decelerates the abyssal limb, leaving an eastward ACC at the surface.

[20] During the Last Glacial Maximum (LGM), lower sea level may have led to enhanced diapycnal mixing in the abyssal ocean [Wunsch, 2003; Green et al., 2009]. Differences are likely to have been most pronounced in the North Atlantic, where below 1000 m tidal energy dissipation may have been 3 times larger than present day [Egbert et al., 2004]. Figures 2a and 2c indicate that the increase in ACC transport in our model is of order 10% when the diapycnal mixing coefficient is increased by an order of magnitude north of 32°S in the Atlantic. However, if mixing is enhanced in the Pacific and Indian basins, then the ACC transport increases by ∼30%. Palaeoclimate proxy data [e.g., Pudsey and Howe, 1998] suggests that the ACC was indeed stronger during the LGM.

[21] The results presented in this paper are subject to the important caveat that the mesoscale eddy field in our model simulations is parameterized. Significant differences occur in model simulations when resolution is increased beyond the eddy-resolving threshold [Hallberg and Gnanadesikan, 2006; Meredith and Hogg, 2006]. On the much longer time-scales required to equilibrate the deep ocean, these differences may be more substantial. The conceptual model in Section 2 gives an indication of the competition between diapycnal mixing and mesoscale eddies. While we expect the relationship between diapycnal mixing and ACC transport to be more complicated in the presence of a fully-resolved eddy field, the basic idea that the ACC transport is sensitive to globally integrated rates of diapycnal mixing is likely to be robust.

Acknowledgments

[22] This study is funded by the UK Natural Environment Research Council. HLJ is supported by a Royal Society University Research Fellowship. DPM acknowledges additional support from the Oxford Martin School.

[23] The authors and Editor thank two anonymous reviewers for their assistance in evaluating this paper.

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