Abstract The middepth ocean temperature profile was found by Munk in 1966 to agree with an exponential profile and shown to be consistent with a vertical advective–diffusive balance. However, tracer release experiments show that vertical diffusivity in the middepth ocean is an order of magnitude too small to explain the observed 1-km exponential scale. Alternative mechanisms suggested that nearly all middepth water upwells adiabatically in the Southern Ocean (SO). In this picture, SO eddies and wind set SO isopycnal slopes and therefore determine a nonvanishing middepth interior stratification even in the adiabatic limit. The effect of SO eddies on SO isopycnal slopes can be understood via either a marginal criticality condition or a near-vanishing SO residual deep overturning condition in the adiabatic limit. We examine the interplay between SO dynamics and interior mixing in setting the exponential profiles of σ 2 and ∂ z σ 2 . We use eddy-permitting numerical simulations, in which we artificially change the diapycnal mixing only away from the SO. We find that SO isopycnal slopes change in response to changes in the interior diapycnal mixing even when the wind forcing is constant, consistent with previous studies (that did not address these near-exponential profiles). However, in the limit of small interior mixing, the interior ∂ z σ 2 profile is not exponential, suggesting that SO processes alone, in an adiabatic limit, do not lead to the observed near-exponential structures of such profiles. The results suggest that while SO wind and eddies contribute to the nonvanishing middepth interior stratification, the exponential shape of the ∂ z σ 2 profiles must also involve interior diapycnal mixing.
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Vertical Structure of the Beaufort Gyre Halocline and the Crucial Role of the Depth-Dependent Eddy Diffusivity
Abstract Theories of the Beaufort Gyre (BG) dynamics commonly represent the halocline as a single layer with a thickness depending on the Eulerian-mean and eddy-induced overturning. However, observations suggest that the isopycnal slope increases with depth, and a theory to explain this profile remains outstanding. Here we develop a multilayer model of the BG, including the Eulerian-mean velocity, mesoscale eddy activity, diapycnal mixing, and lateral boundary fluxes, and use it to investigate the dynamics within the Pacific Winter Water (PWW) layer. Using theoretical considerations, observational data, and idealized simulations, we demonstrate that the eddy overturning is critical in explaining the observed vertical structure. In the absence of the eddy overturning, the Ekman pumping and the relatively weak vertical mixing would displace isopycnals in a nearly parallel fashion, contrary to observations. This study finds that the observed increase of the isopycnal slope with depth in the climatological state of the gyre is consistent with a Gent–McWilliams eddy diffusivity coefficient that decreases by at least 10%–40% over the PWW layer. We further show that the depth-dependent eddy diffusivity profile can explain the relative magnitude of the correlated isopycnal depth and layer thickness fluctuations on interannual time scales. Our inference that the eddy overturning generates the isopycnal layer thickness gradients is consistent with the parameterization of eddies via a Gent–McWilliams scheme but not potential vorticity diffusion. This study implies that using a depth-independent eddy diffusivity, as is commonly done in low-resolution ocean models, may contribute to misrepresentation of the interior BG dynamics.
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- Award ID(s):
- 1829969
- NSF-PAR ID:
- 10298804
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 51
- Issue:
- 3
- ISSN:
- 0022-3670
- Page Range / eLocation ID:
- 845 to 860
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Mixing along isopycnals plays an important role in the transport and uptake of oceanic tracers. Isopycnal mixing is commonly quantified by a tracer diffusivity. Previous studies have estimated the tracer diffusivity using the rate of dispersion of surface drifters, subsurface floats, or numerical particles advected by satellite‐derived velocity fields. This study shows that the diffusivity can be more efficiently estimated from the dispersion of coherent mesoscale eddies. Coherent eddies are identified and tracked as the persistent sea surface height extrema in both a two‐layer quasigeostrophic (QG) model and an idealized primitive equation (PE) model. The Lagrangian diffusivity is estimated using the tracks of these coherent eddies and compared to the diagnosed Eulerian diffusivity. It is found that the meridional coherent eddy diffusivity approaches a stable value within about 20–40 days in both models. In the QG model, the coherent eddy diffusivity is a good approximation to the upper‐layer tracer diffusivity in a broad range of flow regimes, except for small values of bottom friction or planetary vorticity gradient, where the motions of same‐sign eddies are correlated over long distances. In the PE model, the tracer diffusivity has a complicated vertical structure and the coherent eddy diffusivity is correlated with the tracer diffusivity at the e‐folding depth of the energy‐containing eddies where the intrinsic speed of the coherent eddies matches the rms eddy velocity. These results suggest that the oceanic tracer diffusivity at depth can be estimated from the movements of coherent mesoscale eddies, which are routinely tracked from satellite observations.
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Abstract Isopycnal mixing of tracers is important for ocean dynamics and biogeochemistry. Previous studies have primarily focused on the horizontal structure of mixing, but what controls its vertical structure is still unclear. This study investigates the vertical structure of the isopycnal tracer diffusivity diagnosed by a multiple‐tracer inversion method in an idealized basin circulation model. The first two eigenvalues of the symmetric part of the 3D diffusivity tensor are approximately tangent to isopycnal surfaces. The isopycnal mixing is anisotropic, with principal directions of the large and small diffusivities generally oriented along and across the mean flow direction. The cross‐stream diffusivity can be reconstructed from the along‐stream diffusivity after accounting for suppression of mixing by the mean flow. In the circumpolar channel and the upper ocean in the gyres, the vertical structure of the along‐stream diffusivity follows that of the rms eddy velocity times a depth‐independent local energy‐containing scale estimated from the sea surface height. The diffusivity in the deep ocean in the gyres instead follows the profile of the eddy kinetic energy times a depth‐independent mixing time scale. The transition between the two mixing regimes is attributed to the dominance of nonlinear interactions and linear waves in the upper and deep ocean, respectively, distinguished by a nonlinearity parameter. A formula is proposed that accounts for both regimes and captures the vertical variation of diffusivities better than extant theories. These results inform efforts to parameterize the vertical structure of isopycnal mixing in coarse‐resolution ocean models.
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Abstract There are two distinct parameterizations for the restratification effect of mesoscale eddies: the Greatbatch and Lamb (1990, GL90,
https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485_1990_020_1634_opvmom_2_0_co_2.xml?tab_body=abstract-display ) parameterization, which mixes horizontal momentum in the vertical, and the Gent and McWilliams (1990, GM90,https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485_1990_020_0150_imiocm_2_0_co_2.xml ) parameterization, which flattens isopycnals adiabatically. Even though these two parameterizations are effectively equivalent under the assumption of quasi‐geostrophy, GL90 has been used much less than GM90, and exclusively inz ‐coordinate models. In this paper, we compare the GL90 and GM90 parameterizations in an idealized isopycnal coordinate model, both from a theoretical and practical perspective. From a theoretical perspective, GL90 is more attractive than GM90 for isopycnal coordinate models because GL90 provides an interpretation that is fully consistent with thickness‐weighted isopycnal averaging, while GM90 cannot be entirely reconciled with any fully isopycnal averaging framework. From a practical perspective, the GL90 and GM90 parameterizations lead to extremely similar energy levels, flow and vertical structure, even though their energetic pathways are very different. The striking resemblance between the GL90 and GM90 simulations persists from non‐eddying through eddy‐permitting resolution. We conclude that GL90 is a promising alternative to GM90 for isopycnal coordinate models, where it is more consistent with theory, computationally more efficient, easier to implement, and numerically more stable. Assessing the applicability of GL90 in realistic global ocean simulations with hybrid coordinate schemes should be a priority for future work. -
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1175/JPO-D-20-0077.1
