Spatially varying tidal mixing and the glacial-to-deglacial meridional overturning circulation: energetics, stratification, and MOC stability

During the Last Glacial Maximum (LGM), lower sea level shifted tidal energy dissipation from the exposed shelf seas into the deep ocean, roughly tripling the mechanical energy available for abyssal vertical mixing. Green et al. (2009) showed in a coupled model that this enhanced mixing energy interacts with surface buoyancy forcing, but their experiments scaled a spatially uniform background diffusivity, and they left open how realistically localized tidal mixing and deglacial freshwater events govern the overturning; subsequent literature has since added the partitioning among tidal, wind, and eddy energy sources and model-fidelity concerns. Fifteen years of follow-up work replaced the uniform scaling with spatially varying near-field tidal mixing parameterizations, yet the central quantitative question remains open: can vigorous glacial tidal mixing overcome the strong glacial ocean stratification indicated by proxies, and does the deglacial decline of tidal energy make meltwater-induced overturning collapses persistent rather than transient? The problem is to determine how changing mechanical energy input — represented realistically in space rather than as a uniform diffusivity scaling — sets the depth, strength, and stability of the glacial and deglacial meridional overturning circulation.

Background

The ocean's meridional overturning circulation (MOC) — the global system of near-surface poleward flow and deep return flow, whose Atlantic branch (the Atlantic Meridional Overturning Circulation, AMOC) dominates the basin-scale heat transport — requires mechanical energy to sustain its abyssal limb. That energy is supplied mainly by turbulent diapycnal mixing (mixing across density surfaces), of which the conversion of surface (barotropic) tides into internal waves at rough seafloor topography is a leading source: roughly 1 TW ($1\ \mathrm{TW}=10^{12}\ \mathrm{W}$) of tidal energy currently powers the open-ocean internal wave field, about half of what is needed to maintain the deep stratification. The diapycnal diffusivity $k_z$ implied by a dissipation rate $\epsilon$ follows the Osborn relation $k_z = \Gamma\epsilon/N^2$, where $\Gamma\approx0.2$ is the mixing efficiency and $N^2$ is the buoyancy frequency (a measure of vertical density stratification); tidal energy dissipated close to its generation site (near-field) and energy radiating away as internal waves before dissipating (far-field) contribute differently to the geography of mixing.

During the Last Glacial Maximum (LGM, about 26,500–19,000 years before present), global sea level was 120–130 m lower, exposing the continental shelves where most tidal energy is dissipated today. Barotropic tide models run on LGM bathymetry consistently find that deep-ocean tidal dissipation was roughly 2.5–3 times larger than at present. Green, Green, Bigg, Rippeth, Scourse and Uehara (2009, Geophysical Research Letters 36, L13609, doi:10.1029/2009GL039309, https://doi.org/10.1029/2009GL039309) combined such a tide model with the intermediate-complexity coupled model Frugal: they scaled a horizontally uniform background vertical diffusivity $k_{z,bg}$ by a factor $\alpha$ (finding an almost linear relation between AMOC strength and $\alpha$ over $\alpha=0$–10), diagnosed the implicit dissipation of the model's mixing scheme through the Osborn relation, and imposed freshwater pulses of 0.1 and 0.3 Sv ($1\ \mathrm{Sv}=10^{6}\ \mathrm{m^3\,s^{-1}}$) over 500 years in the Barents Sea. Their glacial steady state had a weaker AMOC (14.1 Sv versus 18.9 Sv for the present day) because a fresher North Atlantic overcame the increased mixing energy, and the AMOC recovered within roughly 300 years after each freshwater pulse, failing to shut down permanently as long as the diffusivity was elevated; only a simultaneous reduction of mixing energy appeared able to produce a persistent collapse.

Several questions were left open by this design and articulated by the authors and by subsequent literature: the mixing factor $\alpha$ and $k_{z,bg}$ were spatially uniform, whereas the overturning depends on where mixing energy is deposited (near rough topography, and near the interface between North Atlantic Deep Water and Antarctic Bottom Water); the experiments did not determine how much of the glacial diffusivity change should be attributed to tides rather than wind- and eddy-driven energy inputs; the intermediate-complexity model's numerical and isopycnal (along-density-surface) diffusion contaminated the physically motivated vertical mixing; and the interplay of strong freshwater pulses with the deglacial decline of open-ocean mechanical energy (roughly a halving as sea level rose) in producing persistent versus transient overturning shutdowns remained unquantified. These questions matter beyond paleoceanography because proxies such as sedimentary $\delta^{13}\mathrm{C}$ (a carbon-isotope ratio distinguishing well-ventilated North Atlantic Deep Water from poorly ventilated deep water masses) and radiocarbon ventilation ages indicate a shoaled and possibly weaker glacial AMOC, an apparent tension with the enhanced tidal mixing, and because the strength and depth of the glacial overturning feed directly into explanations of the low glacial atmospheric $\mathrm{CO_2}$ via deep-ocean carbon storage.

Problem Statement

The problem, as left open by Green et al. (2009), is to determine how changes in tidally driven diapycnal mixing — represented realistically in space and energetically consistent with the changing tidal energy supply, rather than as a spatially uniform scaling of background diffusivity — govern the glacial-to-deglacial meridional overturning circulation, jointly with surface buoyancy and freshwater forcing. An answer should be evaluated against paleo-proxy constraints (sedimentary $\delta^{13}\mathrm{C}$, radiocarbon ventilation ages, and related tracers) and should address: (1) under what conditions the roughly 2.5–3-fold enhanced LGM tidal dissipation can overcome the strong glacial ocean stratification, reconciling the model-divergent outcomes — strengthened and deepened overturning in intermediate-complexity models versus stratification-dominated shoaling in ocean general circulation models — into a quantitatively supported account of LGM overturning depth, strength, and water-mass structure that may be regime-dependent rather than a single number; (2) how the mechanical energy available for mixing was partitioned among tidal, wind-driven, and eddy-driven sources through the LGM and the subsequent deglaciation, so that the diffusivity change attributable specifically to tides is quantified rather than assumed; and (3) whether freshwater pulses from ice-sheet collapse coincident with the deglacial decline of open-ocean tidal-mixing energy (a reduction of order one-half or more) produce persistent overturning shutdowns or only transient collapses, and on what recovery timescales. These threads share one objective — a physically consistent, proxy-constrained account of tidal-mixing control of the glacial and deglacial overturning. All three items must be addressed: items (1) and (3) are the primary deliverables, but an answer that omits (2) is incomplete. Post-2009 refinements — the near-field/far-field decomposition of tidal mixing with climate-dependent partitioning and stratification-dependent vertical decay scales (Schmittner and Egbert 2014; Wilmes et al. 2021), and the incorporation of tidal-energy dissipation into fully coupled Earth system models (Chen et al. 2024) — may inform an answer, but no particular model class or parameterization family is required.

References

1. Green, J. A. Mattias; Green, Clare L.; Bigg, Grant R.; Rippeth, Tom P.; Scourse, James D.; Uehara, Katsuto (2009). Tidal mixing and the Meridional Overturning Circulation from the Last Glacial Maximum. Geophysical Research Letters 36(15). doi:10.1029/2009GL039309, https://doi.org/10.1029/2009GL039309 (primary source)
2. Green, J. A. M.; Bigg, G. R. (2011). Impacts on the global ocean circulation from vertical mixing and a collapsing ice sheet. Journal of Marine Research 69(2), 221–244. doi:10.1357/002224011798765321, https://doi.org/10.1357/002224011798765321
3. Wilmes, S.-B.; Green, J. A. M. (2014). The evolution of tides and tidal dissipation over the past 21,000 years. Journal of Geophysical Research: Oceans 119(7), 4083–4100. doi:10.1002/2013JC009605, https://doi.org/10.1002/2013JC009605
4. Schmittner, A.; Egbert, G. D. (2014). An improved parameterization of tidal mixing for ocean models. Geoscientific Model Development 7(1), 211–224. doi:10.5194/gmd-7-211-2014, https://doi.org/10.5194/gmd-7-211-2014
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