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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. 

Abstract Small-scale mixing drives the diabatic upwelling that closes the abyssal ocean overturning circulation. Indirect microstructure measurements of in-situ turbulence suggest that mixing is bottom-enhanced over rough topography, implying downwelling in the interior and stronger upwelling in a sloping bottom boundary layer. Tracer Release Experiments (TREs), in which inert tracers are purposefully released and their dispersion is surveyed over time, have been used to independently infer turbulent diffusivities—but typically provide estimates in excess of microstructure ones. In an attempt to reconcile these differences, Ruan and Ferrari (2021) derived exact tracer-weighted buoyancy moment diagnostics, which we here apply to quasi-realistic simulations. A tracer’s diapycnal displacement rate is exactly twice the tracer-averaged buoyancy velocity, itself a convolution of an asymmetric upwelling/downwelling dipole. The tracer’s diapycnal spreading rate, however, involves both the expected positive contribution from the tracer-averaged in-situ diffusion as well as an additional non-linear diapycnal distortion term, which is caused by correlations between buoyancy and the buoyancy velocity, and can be of either sign. Distortion is generally positive (stretching) due to bottom-enhanced mixing in the stratified interior but negative (contraction) near the bottom. Our simulations suggest that these two effects coincidentally cancel for the Brazil Basin Tracer Release Experiment, resulting in negligible net distortion. By contrast, near-bottom tracers experience leading-order distortion that varies in time. Errors in tracer moments due to realistically sparse sampling are generally small (< 20%), especially compared to the O (1) structural errors due to the omission of distortion effects in inverse models. These results suggest that TREs, although indispensable, should not be treated as “unambiguous” constraints on diapycnal mixing. 

We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasigeostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The ‘vortex gas’ scaling predictions put forward in the context of the two-layer QG model carry over to this fully three-dimensional system: the functional dependence of the meridional flux on the control parameters is the same, the two adjustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional heat flux is depth-independent. The vertical heat flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical heat flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical heat fluxes, and of the emergent stratification, without additional fitting parameters. 

Abstract ABSTRACT: The abyssal overturning circulation is thought to be primarily driven by small-scale turbulent mixing. Diagnosed watermass transformations are dominated by rough topography “hotspots”, where the bottom-enhancement of mixing causes the diffusive buoyancy flux to diverge, driving widespread downwelling in the interior—only to be overwhelmed by an even stronger up-welling in a thin Bottom Boundary Layer (BBL). These watermass transformations are significantly underestimated by one-dimensional (1D) sloping boundary layer solutions, suggesting the importance of three-dimensional physics. Here, we use a hierarchy of models to generalize this 1D boundary layer approach to three-dimensional eddying flows over realistically rough topography. When applied to the Mid-Atlantic Ridge in the Brazil Basin, the idealized simulation results are roughly consistent with available observations. Integral buoyancy budgets isolate the physical processes that contribute to realistically strong BBL upwelling. The downwards diffusion of buoyancy is primarily balanced by upwelling along the sloping canyon sidewalls and the surrounding abyssal hills. These flows are strengthened by the restratifying effects of submesoscale baroclinic eddies and by the blocking of along-ridge thermal wind within the canyon. Major topographic sills block along-thalweg flows from restratifying the canyon trough, resulting in the continual erosion of the trough’s stratification. We propose simple modifications to the 1D boundary layer model which approximate each of these three-dimensional effects. These results provide local dynamical insights into mixing-driven abyssal overturning, but a complete theory will also require the non-local coupling to the basin-scale circulation. 

Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network. Network DA exploits diverse sources of health data together with the proximity data from mobile devices that exposure notification apps rely upon. It provides users with continuously assessed individual risks of exposure and infection, which can form the basis for targeting individual contact interventions. Simulations of the early COVID-19 epidemic in New York City are used to establish proof-of-concept. In the simulations, network DA identifies up to a factor 2 more infections than contact tracing when both harness the same contact data and diagnostic test data. This remains true even when only a relatively small fraction of the population uses network DA. When a sufficiently large fraction of the population (≳ 75%) uses network DA and complies with individual contact interventions, targeting contact interventions with network DA reduces deaths by up to a factor 4 relative to TTI. Network DA can be implemented by expanding the computational backend of existing exposure notification apps, thus greatly enhancing their capabilities. Implemented at scale, it has the potential to precisely and effectively control future epidemics while minimizing economic disruption. 

Abstract Turbulent mixing across density surfaces transforms abyssal ocean waters into lighter waters and is vital to close the deepest branches of the global overturning circulation. Over the last 20 years, mixing rates inferred from in situ microstructure profilers and tracer release experiments (TREs) have provided valuable insights in the connection between small-scale mixing and large-scale ocean circulation. Problematically, estimates based on TREs consistently exceed those from collocated in situ microstructure measurements. These differences have been attributed to a low bias in the microstructure estimates that can miss strong, but rare, mixing events. Here we demonstrate that TRE estimates can suffer from a high bias, because of the approximations generally made to interpret the data. We first derive formulas to estimate mixing from the temporal growth of the second moment of a tracer patch by extending Taylor’s celebrated formula to account for both density stratification and variations in mixing rates. The formulas are validated with tracers released in numerical simulations of turbulent flows and then used to discuss biases in the interpretation of TREs based estimates and how to possibly overcome them. 

Abstract Between 5% and 25% of the total momentum transferred between the atmosphere and ocean is transmitted via the growth of long surface gravity waves called “swell.” In this paper, we use large-eddy simulations to show that swell-transmitted momentum excites near-inertial waves and drives turbulent mixing that deepens a rotating, stratified, turbulent ocean surface boundary layer. We find that swell-transmitted currents are less effective at producing turbulence and mixing the boundary layer than currents driven by an effective surface stress. Overall, however, the differences between swell-driven and surface-stress-driven boundary layers are relatively minor. In consequence, our results corroborate assumptions made in Earth system models that neglect the vertical structure of swell-transmitted momentum fluxes and instead parameterize all air–sea momentum transfer processes with an effective surface stress. 

Abstract Stirring in the subsurface Southern Ocean is examined using RAFOS float trajectories, collected during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), along with particle trajectories from a regional eddy permitting model. A central question is the extent to which the stirring is local, by eddies comparable in size to the pair separation, or nonlocal, by eddies at larger scales. To test this, we examine metrics based on averaging in time and in space. The model particles exhibit nonlocal dispersion, as expected for a limited resolution numerical model that does not resolve flows at scales smaller than ~10 days or ~20–30 km. The different metrics are less consistent for the RAFOS floats; relative dispersion, kurtosis, and relative diffusivity suggest nonlocal dispersion as they are consistent with the model within error, while finite-size Lyapunov exponents (FSLE) suggests local dispersion. This occurs for two reasons: (i) limited sampling of the inertial length scales and a relatively small number of pairs hinder statistical robustness in time-based metrics, and (ii) some space-based metrics (FSLE, second-order structure functions), which do not average over wave motions and are reflective of the kinetic energy distribution, are probably unsuitable to infer dispersion characteristics if the flow field includes energetic wave motions that do not disperse particles. The relative diffusivity, which is also a space-based metric, allows averaging over waves to infer the dispersion characteristics. Hence, given the error characteristics of the metrics and data used here, the stirring in the DIMES region is likely to be nonlocal at scales of 5–100 km. 

The meridional temperature profile of the upper layers of planetary atmospheres is set through a balance between differential radiative heating by a nearby star, or by intrinsic heat fluxes emanating from the deep interior, and the redistribution of that heat across latitudes by turbulent flows. These flows spontaneously arise through baroclinic instability of the meridional temperature gradients maintained by the forcing. When planetary curvature is neglected, this turbulence takes the form of coherent vortices that mix the meridional temperature profiles. However, the curvature of the planet favors the emergence of Rossby waves and zonal jets that restrict the meridional wandering of the fluid columns, thereby reducing the mixing efficiency across latitudes. A similar situation arises in the ocean, where the baroclinic instability of zonal currents leads to enhanced meridional heat transport by a turbulent flow consisting of vortices and zonal jets. A recent scaling theory for the turbulent heat transport by vortices is extended to include the impact of planetary curvature, in the framework of the two‐layer quasi‐geostrophic beta‐plane model. This leads to a quantitative parameterization providing the meridional temperature profile in terms of the externally imposed heat flux in an idealized model of planetary atmospheres and oceans. In addition, it provides a quantitative prediction for the emergent criticality, that is, the degree of instability in a canonical model of planetary atmosphere or ocean.