1. Introduction
By removing heat from surface to subsurface layers, ocean dynamics play a key role in mitigating climate change in response to enhanced radiative forcing. Indeed, a substantial contribution to the observed ocean heat uptake (OHU) comes from the warming of subsurface layers (Levitus et al. 2012). The processes that transport heat vertically in the ocean include small-scale turbulence, convection, mesoscale and submesoscale eddy effects, and large-scale circulation [e.g., Ekman pumping and meridional overturning circulation (MOC)]. Some of these are only partly resolved in coupled atmosphere–ocean general circulation models (AOGCMs) employed for long-term climate simulations. Some are not resolved at all; instead, they are parameterized. The formulations and/or parameters used to represent ocean unresolved or partly resolved processes often differ between the models, contributing to the differences in the simulated OHU (Exarchou et al. 2015). Even such a global-scale feature as the Atlantic MOC (AMOC) shows a considerable range across AOGCMs in terms of its strength and depth. This contributes to the spread in the ocean heat uptake efficiency (OHUE; i.e., OHU per unit increase in surface warming) in climate change simulations (e.g., Kostov et al. 2014; Winton et al. 2014; J. M. Gregory et al. 2017, unpublished manuscript). The spread in the OHUE across AOGCMs is quite large, being a factor of 2 in the AOGCMs that participated in phase 3 of the Coupled Model Intercomparison Project (CMIP3) and phase 5 of the Coupled Model Intercomparison Project (CMIP5; Kuhlbrodt and Gregory 2012). How the AMOC is related to OHUE and why there is a correlation between the AMOC strength and OHUE in climate simulations based on AOGCMs (e.g., Kostov et al. 2014; Winton et al. 2014; J. M. Gregory et al. 2017, unpublished manuscript) has not as yet been comprehensively explained. One of the purposes here is to provide some insight on this important subject.
Uncertainties in the formulations and/or parameters used to represent unresolved ocean processes can contribute to the uncertainties in the simulated OHU/OHUE not only directly, through affecting the associated heat fluxes, but also indirectly. The latter can arise because of the influence of parameterized processes on the large-scale ocean circulation, with one familiar example being the impact of vertical diffusivity on the MOC (e.g., Wunsch and Ferrari 2004). Another example is the representation of mesoscale eddy transfer, which is our focus here. Studies where ocean mesoscale eddy effects have been resolved to some extent (Wolfe et al. 2008; Morrison et al. 2013; Kuhlbrodt et al. 2015; Griffies et al. 2015) confirmed an earlier result of Gregory (2000) that eddies play a major part in the vertical transport of heat in the ocean. The indirect effects associated with representation of ocean mesoscale eddies on the simulated OHU have been studied somewhat less extensively. Here, we aim to investigate further the apparent link between the mesoscale eddy transfer coefficient in the Gent and McWilliams (1990) scheme (see section 2), which is often employed for representing eddy-induced ocean transport, and the AMOC and OHU. This is motivated by several studies that showed relationships 1) between the mesoscale eddy transfer coefficient and OHUE/OHU (Kuhlbrodt and Gregory 2012; Marshall and Zanna 2014), 2) between OHUE and AMOC (e.g., Kostov et al. 2014; Winton et al. 2014; J. M. Gregory et al. 2017, unpublished manuscript), and 3) between the AMOC and mesoscale eddy transfer (e.g., Gnanadesikan 1999; Marshall et al. 2017). Combined, these previous studies suggest that some of the apparent correlation between the OHUE and AMOC strength could arise because of the influence of the ocean mesoscale eddy transfer on both these quantities. Here, we aim to provide a further support for this suggestion. However, to present our main finding in a systematic way, we feel that it is essential to demonstrate that the main pieces of our argument, if considered separately, are consistent with these previous results. We try to ensure this throughout the paper.
To analyze a range of numerical experiments, some of which require running a model to near-steady state, we adopt an ocean-only modeling approach. This is certainly a simplification compared to the use of AOGCMs. Nevertheless, employing ocean-only models to study OHU processes can be quite insightful (e.g., Xie and Vallis 2012; Marshall et al. 2015). To simulate OHU, we force our model with sea surface temperature (SST) anomalies that are meant to mimic the impact of CO2 increase in the atmosphere. Section 2 provides more details on the experimental design and employed model, including on the formulation for the mesoscale eddy transfer. Unlike in some previous studies where a horizontally uniform mesoscale eddy transfer coefficient was used in relation with the AMOC (e.g., Gnanadesikan 1999; Marshall et al. 2017), we employ a density-dependent formulation. This allows for a feedback between the simulated density field and the mesoscale eddy transfer. Section 3 begins with a discussion of different components of the global ocean MOC and how they are influenced by the mesoscale eddy transfer in a set of 1000-yr control simulations. In particular, it is found that with the decrease of the eddy transfer coefficient, the strength of the AMOC increases. This is in general agreement with Gnanadesikan (1999) and Marshall et al. (2017), whose scaling relations are employed to interpret our results. This is followed by a discussion of sensitivity experiments where the simulated control ocean states are perturbed by imposing SST anomalies. It is shown that the associated OHU correlates with the AMOC strength and, hence, anticorrelates with the mesoscale eddy transfer. Simulations with a surface-forced passive tracer are used to argue that OHUE is linked to the ocean mesoscale eddy transfer and to the eddy energy generated from the mean state. In section 4, a special consideration is given to the ocean overturning in depth–temperature space, which represents the advective vertical heat transport (e.g., Nycander et al. 2007; Zika et al. 2013, 2015), and to its connection to the AMOC. Conclusions are summarized in section 5.
2. Model and experimental design
The employed model is a low-resolution configuration of the Nucleus for European Modelling of the Ocean, version 3.4 (NEMO; Madec et al. 2012). The model uses a free-surface formulation and is configured on the global tripolar ORCA1 grid with 46 z-coordinate vertical levels. The horizontal resolution is 1°, varying with the cosine of latitude, with a refinement of the meridional grid spacing to ⅓° near the equator. Momentum and tracers are mixed vertically using a TKE scheme based on the model of Gaspar et al. (1990). Base values of vertical diffusivity and viscosity are 1.5 × 10−5 and 1.5 × 10−4 m2 s−1, respectively. Tidal mixing is parameterized following Simmons et al. (2004). Lateral viscosity is parameterized by a horizontal Laplacian operator with eddy viscosity coefficient of 104 m2 s−1 in the tropics, decreasing with latitude as the grid spacing decreases. Lateral mixing of tracers (Redi 1982) is parameterized by an isoneutral Laplacian operator with eddy diffusivity coefficient of














Meridional profiles of observational estimate of eddy scale based on altimetry data (solid) and
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
The spatial structure of
(left) The spatial structure of time-mean
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
The model restores SST













(a) Meridional structure of annual-mean SST anomalies
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
One of the purposes of running two sets of sensitivity experiments was to find out if using a highly idealized
Vertically integrated ocean heat uptake (GJ m−2) in (a) Simple and (b) Complex sensitivity experiments with the scaling-factor γ in
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
The AMOC strength, defined as the mean of the AMOC maximum values between 20° and 30°N in the Atlantic, decreases in both sets of sensitivity experiments (Fig. 5). The largest AMOC decrease, by 1.5–2 Sv (1 Sv ≡ 106 m3 s−1), is during the first two decades, followed by some recovery. [If both
Time series of the AMOC anomalies (Sv) in the (a) Simple and (b) Complex sets of sensitivity experiments for the different values of the scale-factor γ in the calculation of
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
In what follows, we shall often compare and correlate relative variations of different quantities and parameters (AMOC strength,
3. Linking mesoscale eddy transfer to AMOC and OHU
a. Control simulations
Figure 6a presents the relative variations in some major components of the global ocean MOC (illustrated schematically in Fig. 6b) in the control runs, plotted against the variations in
(a) Relative variations in the strength of the major overturning cells in the five control experiments, plotted against the relative variations in the eddy transfer coefficient
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1

































The strength of the lower southern cell
b. Response to SST perturbations
Introducing the perturbations discussed in section 2 to the control SSTs leads to OHU, which positively correlates with the control AMOC strength (Fig. 7a) and, hence, anticorrelates with the mesoscale eddy transfer (Fig. 6a). The warming penetrates deeper (i.e., D80% is larger) under the smaller
Relative variations in the (a) OHU and (b) depth above which 80% of the total OHU is confined D80% in the two sets of SST-perturbation experiments (Simple in red and Complex in green), plotted against relative variations in the corresponding control AMOC strength
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
Thus, in our eddy-parameterizing ocean model, the values of
Change in ocean temperature (K), averaged (top) zonally and (bottom) within the 1000–2000-m-depth layer and corresponding to the models with (left) the smallest
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
We next consider the main mechanisms causing the differences in vertical penetration of heat in the Simple experiments with the smallest and largest
Time evolution of the global ocean temperature profile changes (K) in the Simple experiments with (left) the smallest
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
Change in ocean temperature within the 100–2000-m layer of the ocean after 50 years [K (50 yr)−1] since the SST perturbation in Simple relative to Control (total), and contributions to it due to the model resolved advection (resolved adv), eddy advection (eddy adv), and all the parameterized mixing effects (mixing) for the global ocean (global), the Southern Ocean (south of 30°S), and northern North Atlantic (40°–70°N, 75°W–5°E). The upper numbers correspond to the case with the smallest
Much of the above discussion of the global OHU mechanisms under the two extreme
In the northern North Atlantic, the subsurface temperature changes are residuals of large in magnitude and opposite in sign changes in the net advection and mixing (Table 1). The decrease of advective heat convergence tends to make the subsurface North Atlantic colder (more so in the larger
c. Using passive tracers to test the OHUE–eddy transfer link
The anticorrelation between OHU and
To test this hypothesis, we introduce a passive tracer. The tracer evolution is meant to represent the process of OHU. This is justified since much of the OHU process in AOGCMs can be simulated with a passive tracer forced at the surface (Gregory et al. 2016). Following Banks and Gregory (2006), we call it the passive anomaly temperature (PAT). PAT is initialized with a zero field and is transported within the model like potential temperature in the corresponding control run. Banks and Gregory (2006) found the vertical distribution of ocean temperature anomaly in their climate change simulation to be very similar to that of PAT. Given the same global-mean PAT, such as in the experiments described below, higher PAT in the upper ocean is meant to represent enhanced surface warming.
To obtain a preliminary insight, PAT is first forced with a constant and uniform surface flux of 2 W m−2. This flux value roughly corresponds to the global-mean heat flux anomaly in the flux-anomaly-forced (faf) passive-heat experiment of the Flux-Anomaly-Forced Model Intercomparison Project (FAFMIP) described in Gregory et al. (2016). Figure 10 (top left) shows zonally averaged PAT at the end of the 50-yr-long control run with the smallest
PAT tracer forced with a uniform flux of 2 W m−2 (K), averaged (top) zonally and (bottom) within the 1000–2000-m-depth layer, corresponding to the control cases with (left) the smallest
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
To test our hypothesis under less idealized forcing, PAT is next forced with a nonuniform surface flux presented in Fig. 11a. This is the mean heat flux anomaly corresponding to the 1% yr−1 CO2-increase experiment, averaged around the time of CO2 doubling (years 61–80) and between 13 CMIP5 models. Its global-mean value is 1.86 W m−2. It has been adopted as the surface perturbation in some of the FAFMIP experiments [see Gregory et al. (2016) for more details]. The PAT forced with this flux is introduced in all five control experiments and run for 70 years (for consistency with the FAFMIP experimental design). The mean PAT in the upper 100 m of the ocean, which represents here the quantity inversely proportional to the OHUE, negatively correlates with the AMOC strength (Fig. 11b). This further supports our hypothesis that at least some of the correlation between OHUE and AMOC in climate simulations based on AOGCMs could be explained by the influence of the mesoscale eddy transfer coefficient on both OHUE and AMOC.
(a) Nonuniform surface heat flux (W m−2) used to force PAT in the second set of passive tracer experiments. It corresponds to CO2 doubling in the 1% yr−1 CO2-increase experiment, averaged between 13 CMIP5 models and adopted as one of the surface perturbations in FAFMIP [see Gregory et al. (2016) for more details]. (b)–(d) The corresponding relative variations of the global-mean PAT in the upper 0–100-m layer plotted against relative variations of the AMOC strength
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
The upper-ocean PAT also scales with the global
4. Linking vertical advective heat flux to OHU and AMOC














(a) Relative variations in the OHU in the two sets of SST-perturbation experiments (Simple in red and Complex in green), plotted against relative variations in the net downward advective (resolved plus eddy) heat transport across about 100-m depth in the five control runs
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
The direction of the vertical heat transport associated with
From Figs. 7a and 12a, it is clear that















Global ocean overturning circulation (Sv) in depth–temperature coordinates (positive clockwise), corresponding to the (top) net (resolved plus eddy induced) velocity, (middle) the resolved velocity, and (bottom) eddy-induced velocity in the control runs with (left) the smallest
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
We next investigate the contributions to
The net (resolved plus eddy) ocean overturning circulations (Sv) in depth–temperature coordinates corresponding to the top panels in Fig. 12, but separated into contributions from (top) the ocean north of 30°S and south of 30°S and (bottom) the Atlantic north of 40°N and the rest of the ocean. The plots correspond to the control runs with (left) the smallest
Citation: Journal of Climate 31, 20; 10.1175/JCLI-D-18-0186.1
As a final remark here, we note that the negative part of
5. Discussion and conclusions
AOGCM-based studies show a correlation between the AMOC and OHUE (Kostov et al. 2014; Winton et al. 2014; J. M. Gregory et al. 2017, unpublished manuscript) and an anticorrelation between the mesoscale eddy transfer coefficient and OHUE (Kuhlbrodt and Gregory 2012). However, how the AMOC is related to OHUE and why there is a correlation between the AMOC strength and OHUE in climate simulations based on AOGCMs had not been comprehensively explained. Here, we argue that at least some of the AMOC–OHUE correlation in AOGCMs could be explained by the influence of the mesoscale eddy transfer in the Gent and McWilliams (1990) parameterization on both OHUE and AMOC. Our arguments are based, in part, on the finding (e.g., Gregory et al. 2016) that much of the OHU in AOGCMs can be modeled with a passive tracer forced at the surface. We show that given the same prescribed surface flux, the tracer values decrease near the surface and increase in the deep ocean with the decrease of
In addition, we show that the OHU in our SST-perturbation experiments correlates with the net downward advective transport of heat in the control model runs (or with the net upward heat flux by all other processes combined). Thus, changes in the net downward heat advection, at least if induced by changes in the mesoscale eddy transfer, scale with changes in the AMOC strength. To show that the AMOC in our model does add to the net global downward advective transport of heat, we use overturning streamfunction in depth–temperature coordinates and separate it into contributions from several regions. That the AMOC transports heat downward can also be inferred from the finding of Gregory et al. (2016) that the change in heat redistribution in their faf-heat experiment, arising mainly from the weakening of the AMOC, causes cooling at all depths in the north (their Fig. 11i), leading to a net cooling below about 1500 m (their Fig. 11g).
The link between the net downward heat advection and the AMOC strength may hold in other models, too, and not necessarily only in those that explicitly parameterize mesoscale eddy effects. For example, in the suite of the GFDL climate models analyzed by Griffies et al. (2015) the net (mean plus eddy) downward advective heat flux decreases with the increase of resolution from 1° to 0.1° (their Fig. 12) and so does the AMOC strength. Some of our other results, such the decrease of OHUE with the increase of eddy energy generation by baroclinic instability, may also find applicability when interpreting climate change simulations with high-resolution ocean components.
Acknowledgments
The authors thank the NEMO development team for providing the model and continuous guidance. We also thank Dudley Chelton for providing the eddy-scale data used in Fig. 1. We are grateful to the ocean group at the Canadian Centre for Climate Modelling and Analysis and to Laure Zanna for discussions. Special thanks to Neil Swart for helping with the passive tracer and to Bill Merryfield and Andrew Shao for providing internal reviews. We also thank three anonymous reviewers for very constructive comments. The nonuniform surface heat flux data, used in the passive tracer experiments, are available online (http://www.fafmip.org).
REFERENCES
Banks, H. T., and J. M. Gregory, 2006: Mechanisms of ocean heat uptake in a coupled climate model and the implications for tracer based predictions of ocean heat uptake. Geophys. Res. Lett., 33, L07608, https://doi.org/10.1029/2005GL025352.
Bryan, K., J. K. Dukowicz, and R. D. Smith, 1999: On the mixing coefficient in the parameterization of bolus velocity. J. Phys. Oceanogr., 29, 2442–2456, https://doi.org/10.1175/1520-0485(1999)029<2442:OTMCIT>2.0.CO;2.
Cessi, P., 2008: An energy-constrained parameterization of eddy buoyancy flux. J. Phys. Oceanogr., 38, 1807–1819, https://doi.org/10.1175/2007JPO3812.1.
Chelton, D. B., M. G. Schlax, and R. M. Samelson, 2011: Global observations of nonlinear mesoscale eddies. Prog. Oceanogr., 91, 167–216, https://doi.org/10.1016/j.pocean.2011.01.002.
Cummins, P. F., D. Masson, and O. A. Saenko, 2016: Vertical heat flux in the ocean: Estimates from observations and from a coupled general circulation model. J. Geophys. Res. Oceans, 121, 3790–3802, https://doi.org/10.1002/2016JC011647.
Exarchou, E., T. Kuhlbrodt, J. M. Gregory, and R. S. Smith, 2015: Ocean heat uptake processes: A model intercomparison. J. Climate, 28, 887–908, https://doi.org/10.1175/JCLI-D-14-00235.1.
Gaspar, P., Y. Grégoris, and J.-M. Lefevre, 1990: A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station Papa and long-term upper ocean study site. J. Geophys. Res., 95, 16179–16193, https://doi.org/10.1029/JC095iC09p16179.
Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean general circulation models. J. Phys. Oceanogr., 20, 150–155, https://doi.org/10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.
Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25, 463–474, https://doi.org/10.1175/1520-0485(1995)025<0463:PEITTI>2.0.CO;2; Corrigendum, 25, 1365, https://doi.org/10.1175/1520-0485(1995)025<1365:>2.0.CO;2.
Gnanadesikan, A., 1999: A simple predictive model for the structure of the oceanic pycnocline. Science, 283, 2077–2079, https://doi.org/10.1126/science.283.5410.2077.
Gnanadesikan, A., R. D. Slater, P. S. Swathi, and G. K. Vallis, 2005: The energetics of ocean heat transport. J. Climate, 18, 2604–2616, https://doi.org/10.1175/JCLI3436.1.
Gnanadesikan, A., M.-A. Pradal, and R. Abernathey, 2015: Isopycnal mixing by mesoscale eddies significantly impacts oceanic anthropogenic carbon uptake. Geophys. Res. Lett., 42, 4249–4255, https://doi.org/10.1002/2015GL064100.
Gregory, J. M., 2000: Vertical heat transports in the ocean and their effect on time-dependent climate change. Climate Dyn., 16, 501–515, https://doi.org/10.1007/s003820000059.
Gregory, J. M., and R. Tailleux, 2011: Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change. Climate Dyn., 37, 893–914, https://doi.org/10.1007/s00382-010-0847-6.
Gregory, J. M., and Coauthors, 2005: A model intercomparison of changes in the Atlantic thermohaline circulation in response to increasing atmospheric CO2 concentration. Geophys. Res. Lett., 32, L12703, https://doi.org/10.1029/2005GL023209.
Gregory, J. M., and Coauthors, 2016: The Flux-Anomaly-Forced Model Intercomparison Project (FAFMIP) contribution to CMIP6: Investigation of sea-level and ocean climate change in response to CO2 forcing. Geosci. Model Dev., 9, 3993–4017, https://doi.org/10.5194/gmd-9-3993-2016.
Griffies, S. M., and Coauthors, 2015: Impacts on ocean heat from transient mesoscale eddies in a hierarchy of climate models. J. Climate, 28, 952–977, https://doi.org/10.1175/JCLI-D-14-00353.1.
Hogg, A. M., P. Spence, O. A. Saenko, and S. M. Downes, 2017: The energetics of Southern Ocean upwelling. J. Phys. Oceanogr., 47, 135–153, https://doi.org/10.1175/JPO-D-16-0176.1.
Huber, M. B., and L. Zanna, 2017: Drivers of uncertainty in simulated ocean circulation and heat uptake. Geophys. Res. Lett., 44, 1402–1413, https://doi.org/10.1002/2016GL071587.
Ito, T., and J. Marshall, 2008: Control of lower-limb overturning circulation in the Southern Ocean by diapycnal mixing and mesoscale eddy transfer. J. Phys. Oceanogr., 38, 2832–2845, https://doi.org/10.1175/2008JPO3878.1.
Kostov, Y., K. C. Armour, and J. Marshall, 2014: Impact of the Atlantic meridional overturning circulation on ocean heat storage and transient climate change. Geophys. Res. Lett., 41, 2108–2116, https://doi.org/10.1002/2013GL058998.
Kuhlbrodt, T., and J. M. Gregory, 2012: Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change. Geophys. Res. Lett., 39, L18608, https://doi.org/10.1029/2012GL052952.
Kuhlbrodt, T., J. M. Gregory, and L. C. Shaffrey, 2015: A process-based analysis of ocean heat uptake in an AOGCM with an eddy-permitting ocean component. Climate Dyn., 45, 3205–3226, https://doi.org/10.1007/s00382-015-2534-0.
Levitus, S., and Coauthors, 2012: World ocean heats content and thermosteric sea level change (0–2000 m), 1955–2010. Geophys. Res. Lett., 39, L10603, https://doi.org/10.1029/2012GL051106.
Madec, G., and Coauthors, 2012: NEMO ocean engine, version 3.4. Institut Pierre-Simon Laplace Note du Pole de Modélisation 27, 367 pp.
Marshall, D. P., and L. Zanna, 2014: A conceptual model of ocean heat uptake under climate change. J. Climate, 27, 8444–8465, https://doi.org/10.1175/JCLI-D-13-00344.1.
Marshall, J., J. R. Scott, K. C. Armour, J.-M. Campin, M. Kelley, and A. Romanou, 2015: The ocean’s role in the transient response of climate to abrupt greenhouse gas forcing. Climate Dyn., 44, 2287–2299, https://doi.org/10.1007/s00382-014-2308-0.
Marshall, J., J. R. Scott, A. Romanou, M. Kelley, and A. Leboissetier, 2017: The dependence of the ocean’s MOC on mesoscale eddy diffusivities: A model study. Ocean Modell., 111, 1–8, https://doi.org/10.1016/j.ocemod.2017.01.001.
Morrison, A. K., O. A. Saenko, A. M. Hogg, and P. Spence, 2013: The role of vertical eddy flux in Southern Ocean heat uptake. Geophys. Res. Lett., 40, 5445–5450, https://doi.org/10.1002/2013GL057706.
Morrison, A. K., S. M. Griffies, M. Winton, W. G. Anderson, and J. L. Sarmiento, 2016: Mechanisms of Southern Ocean heat uptake and transport in a global eddying climate model. J. Climate, 29, 2059–2075, https://doi.org/10.1175/JCLI-D-15-0579.1.
Nycander, J., J. Nilsson, K. Döös, and G. Broström, 2007: Thermodynamic analysis of ocean circulation. J. Phys. Oceanogr., 37, 2038–2052, https://doi.org/10.1175/JPO3113.1.
Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12, 1154–1158, https://doi.org/10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2.
Simmons, H. L., S. R. Jayne, L. C. St. Laurent, and A. J. Weaver, 2004: Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modell., 6, 245–263, https://doi.org/10.1016/S1463-5003(03)00011-8.
Stanley, G. J., and O. A. Saenko, 2014: Bottom-enhanced diapycnal mixing driven by mesoscale eddies: Sensitivity to wind energy supply. J. Phys. Oceanogr., 44, 68–85, https://doi.org/10.1175/JPO-D-13-0116.1.
Visbeck, M., J. Marshall, T. Haine, and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27, 381–402, https://doi.org/10.1175/1520-0485(1997)027<0381:SOETCI>2.0.CO;2.
Winton, M., W. G. Anderson, T. L. Delworth, S. M. Griffies, W. J. Hurlin, and A. Rosati, 2014: Has coarse ocean resolution biased simulations of transient climate sensitivity? Geophys. Res. Lett., 41, 8522–8529, https://doi.org/10.1002/2014GL061523.
Wolfe, C. L., P. Cessi, J. L. McClean, and M. E. Maltrud, 2008: Vertical heat transport in eddying ocean models. Geophys. Res. Lett., 33, L19708, https://doi.org/10.1029/2008GL036138.
Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314, https://doi.org/10.1146/annurev.fluid.36.050802.122121.
Xie, P., and G. K. Vallis, 2012: The passive and active nature of ocean heat uptake in idealized climate change experiments. Climate Dyn., 38, 667–684, https://doi.org/10.1007/s00382-011-1063-8.
Yang, D., and O. A. Saenko, 2012: Ocean heat transport and its projected change in CanESM2. J. Climate, 25, 8148–8163, https://doi.org/10.1175/JCLI-D-11-00715.1.
Zika, J. D., W. P. Sijp, and M. H. England, 2013: Vertical heat transport by ocean circulation and the role of mechanical and haline forcing. J. Phys. Oceanogr., 43, 2095–2112, https://doi.org/10.1175/JPO-D-12-0179.1.
Zika, J. D., F. Laliberté, L. R. Mudryk, W. P. Sijp, and A. J. G. Nurser, 2015: Changes in ocean vertical heat transport with global warming. Geophys. Res. Lett., 42, 4940–4948, https://doi.org/10.1002/2015GL064156.
Marshall et al. (2017) build their arguments for changes in