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 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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null (Ed.)Abstract ‘Horizontal convection’ (HC) is the generic name for the flow resulting from a buoyancy variation imposed along a horizontal boundary of a fluid. We study the effects of rotation on three-dimensional HC numerically in two stages: first, when baroclinic instability is suppressed and, second, when it ensues and baroclinic eddies are formed. We concentrate on changes to the thickness of the near-surface boundary layer, the stratification at depth, the overturning circulation and the flow energetics during each of these stages. Our results show that, for moderate flux Rayleigh numbers ( $O(1{0}^{11} )$ ), rapid rotation greatly alters the steady-state solution of HC. When the flow is constrained to be uniform in the transverse direction, rapidly rotating solutions do not support a boundary layer, exhibit weaker overturning circulation and greater stratification at all depths. In this case, diffusion is the dominant mechanism for lateral buoyancy flux and the consequent buildup of available potential energy leads to baroclinically unstable solutions. When these rapidly rotating flows are perturbed, baroclinic instability develops and baroclinic eddies dominate both the lateral and vertical buoyancy fluxes. The resulting statistically steady solution supports a boundary layer, larger values of deep stratification and multiple overturning cells compared with non-rotating HC. A transformed Eulerian-mean approach shows that the residual circulation is dominated by the quasi-geostrophic eddy streamfunction and that the eddy buoyancy flux has a non-negligible interior diabatic component. The kinetic and available potential energies are greater than in the non-rotating case and the mixing efficiency drops from ${\sim }0. 7$ to ${\sim }0. 17$ . The eddies play an important role in the formation of the thermal boundary layer and, together with the negatively buoyant plume, help establish deep stratification. These baroclinically active solutions have characteristics of geostrophic turbulence.more » « less
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Bathymetric sills are important features in the ocean-filled cavities beneath a few fast-retreating ice shelves in West Antarctica and northern Greenland. The sills can be high enough to obstruct the cavity circulation and thereby modulate glacial melt rates. This study focuses on the idealized problem of diabatically driven, sill-constrained overturning circulation in a cavity. The circulation beneath fast-melting ice shelves can generally be characterized by an inflow of relatively warm dense water (with temperatures of a few degrees Celsius above the local freezing point) at depth and cold, less-dense, outflowing water, which exhibits an approximately two-layer structure in observations. We use a two-layer isopycnal hydrostatic model to study the cross-sill exchange of these waters in ice shelf cavities wide enough to be rotationally dominated. A quasigeostrophic constraint is determined for the transport imposed by the stratification. Relative to this constraint, the key parameters controlling the transport and its variability are the sill height relative to the bottom layer thickness and the strength of the friction relative to the potential vorticity (PV) gradient imposed by the sill. By varying these two key parameters, we simulate a diversity of flow phenomena. For a given meridional pressure gradient, the cross-sill transport is controlled by sill height beyond a critical threshold in the eddy-permitting, low-friction regime, while it is insensitive to friction in both the low-friction and high-friction regimes. We present theoretical ideas to explain the flow characteristics: a Stommel boundary layer for the friction-dominated regime; mean–eddy PV balances and energy conversion in the low-friction, low-sill regime; and hydraulic control in the low-friction, high-sill regime, with various estimates for transport in each of these regimes.
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Abstract The Indo-Pacific Ocean appears exponentially stratified between 1- and 3-km depth with a decay scale on the order of 1 km. In his celebrated paper “Abyssal recipes,” W. Munk proposed a theoretical explanation of these observations by suggesting a pointwise buoyancy balance between the upwelling of cold water and the downward diffusion of heat. Assuming a constant upwelling velocity w and turbulent diffusivity κ , the model yields an exponential stratification whose decay scale is consistent with observations if κ ∼ 10 −4 m 2 s −1 . Over time, much effort has been made to reconcile Munk’s ideas with evidence of vertical variability in κ , but comparably little emphasis has been placed on the even stronger evidence that w decays toward the surface. In particular, the basin-averaged w nearly vanishes at 1-km depth in the Indo-Pacific. In light of this evidence, we consider a variable-coefficient, basin-averaged analog of Munk’s budget, which we verify against a hierarchy of numerical models ranging from an idealized basin-and-channel configuration to a coarse global ocean simulation. Study of the budget reveals that the decay of basin-averaged w requires a concurrent decay in basin-averaged κ to produce an exponential-like stratification. As such, the frequently cited value of 10 −4 m 2 s −1 is representative only of the bottom of the middepths, whereas κ must be much smaller above. The decay of mixing in the vertical is as important to the stratification as its magnitude . Significance Statement Using a combination of theory and numerical simulations, it is argued that the observed magnitude and shape of the global ocean stratification and overturning circulation appear to demand that turbulent mixing increases quasi-exponentially toward the ocean bottom. Climate models must therefore prescribe such a vertical profile of turbulent mixing in order to properly represent the heat and carbon uptake accomplished by the global overturning circulation on centennial and longer time scales.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1175/JPO-D-20-0077.1
