Isopycnal Diffusion Research Articles

Isopycnal Eddy Diffusivities and Critical Layers in the Kuroshio Extension from an Eddying Ocean Model

Abstract High spatial resolution isopycnal diffusivities are estimated in the Kuroshio Extension (KE) region (28°–40°N, 120°–190°E) from a global ° Parallel Ocean Program (POP) simulation. The numerical float tracks are binned using a clustering approach. The number of tracks in each bin is thus roughly the same leading to diffusivity estimates that converge better than those in bins defined by a regular geographic grid. Cross-stream diffusivities are elevated in the southern recirculation gyre region, near topographic obstacles and downstream in the KE jet, where the flow has weakened. Along-stream diffusivities, which are much larger than cross-stream diffusivities, correlate well with the magnitudes of eddy velocity. The KE jet suppresses cross-stream mixing only in some longitude ranges. This study estimates the critical layer depth both from linear local baroclinic instability analysis and from eddy phase speeds in the POP model using the Radon transform. The latter is a better predictor of large mixing length in the cross-stream direction. Critical layer theory is most applicable in the intense jet regions away from topography.

Formation and transport of intermediate water masses in a model of the Pacific Ocean

A basin-wide ocean general circulation model of the Pacific Ocean was used to investigate how the interior restoration in the Okhotsk Sea and the isopycnal diffusion affect the circulation and intermediate water masses. Four numerical experiments were conducted, including a run with the same isopycnal and thickness diffusivity of 1.0×103 m2/s, a run employing the interior restoration of temperature and salinity in the Okhotsk Sea with a time scale of 3 months, a run that is the same as the first run except for the enhanced isopycnal mixing, and a final run with the combination of the restoration in the Okhotsk Sea and large isopycnal diffusivity. Simulated results show that the intermediate water masses reproduced in the first run are relatively weak. An increase in isopycnal diffusivity can improve the simulation of both Antarctic and North Pacific intermediate waters, mainly increasing the transport in the interior ocean, but inhibiting the outflow from the Okhotsk Sea. The interior restoration generates the reverse current from the observation in the Okhotsk Sea, whereas the simulation of the temperature and salinity is improved in the high latitude region of the Northern Hemisphere because of the reasonable source of the North Pacific Intermediate Water. A comparison of vertical profiles of temperature and salinity along 50°N between the simulation and observations demonstrates that the vertical mixing in the source region of intermediate water masses is very important.

Energetics of lateral eddy diffusion/advection: Part II. Numerical diffusion/diffusivity and gravitational potential energy change due to isopycnal diffusion

Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and advection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial horizontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models; therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with horizontal advection in the commonly used Eulerian coordinates may become one of the most challenging obstacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion (mixing) has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps: stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.

Eulerian and Lagrangian Isopycnal Eddy Diffusivities in the Southern Ocean of an Eddying Model

Abstract Lagrangian isopycnal diffusivities quantify the along-isopycnal mixing of any tracer with mean gradients along isopycnal surfaces. They are studied in the Southern Ocean of the 1/10° Parallel Ocean Program (POP) model using more than 50 000 float trajectories. Concurrent Eulerian isopycnal diffusivities are estimated directly from the eddy fluxes and mean tracer gradients. Consistency, spatial variation, and relation to mean jets are evaluated. The diffusivities are calculated in bins large enough to reduce contributions from the rotational components that do not lead to net tracer mixing. Because the mean jets are nonzonal and nonparallel, meridional dispersion includes standing eddies and is significantly different from cross-stream dispersion. With the subtraction of the local Eulerian mean, the full Lagrangian diffusivity tensor can be estimated. Along-stream diffusivities are about 6 times larger than cross-stream diffusivities. Along-streamline averages of Eulerian and Lagrangian isopycnal diffusivities are similar in that they are larger north of the Antarctic Circumpolar Current (ACC) and smaller in the ACC in the upper 500 m. Eulerian diffusivities are often twice as large as the Lagrangian diffusivities below 500 m. There is large longitudinal variability in the diffusivities and in their relation to the mean flow. In bins with one prominent jet, diffusivities are reduced at the surface in the jet and increased to the north and south of the jet. There is a local maximum at depths of 500–1000 m. In other bins where mean jets merge and diverge because of topography, there is no consistent relation of the diffusivities with the mean flow. Eulerian fluxes are upgradient in about 15% of the bins.

Float-Derived Isopycnal Diffusivities in the DIMES Experiment

AbstractAs part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), 210 subsurface floats were deployed west of the Drake Passage on two targeted density surfaces. Absolute (single particle) diffusivities are calculated for the floats. The focus is on the meridional component, which is less affected by the mean shear. The diffusivities are estimated in several ways, including a novel method based on the probability density function of the meridional displacements. This allows the determination of the range of possible lateral diffusivities, as well as the period over which the spreading can be said to be diffusive. The method is applied to the float data and to synthetic trajectories generated with the Massachusetts Institute of Technology General Circulation Model (MITgcm). Because of ballasting problems, many of the floats did not remain on their targeted density surface. However, the float temperature records suggest that most occupied a small range of densities, so the floats were grouped together for the analysis. The latter focuses on a subset of 109 of the floats, launched near 105°W. The different methods yield a consistent estimate for the diffusivity of 800 ± 200 m2 s−1. The same calculations were made with model particles deployed on 20 different density surfaces and the result for the particles deployed on the neutral density surface γ = 27.7 surface was the same within the errors. The model was then used to map the variation of the diffusivity in the vertical, near the core of the Antarctic Circumpolar Current (ACC). The results suggest mixing is intensified at middepths, between 1500 and 2000 m, consistent with several previous studies.

A global map of meso-scale eddy diffusivities based on linear stability analysis

Using a hydrographic climatology, global maps of meso-scale eddy kinetic energy (EKE), diffusivities for mixing along isopycnals (isopycnal diffusivity) and for the advective effect of meso-scale eddies (skew diffusivity) are created using properties of the fastest growing unstable baroclinic waves and a simple ad hoc scaling of the amplitudes from linear stability theory. Amplitudes of EKE compare well with near-surface observational estimates based on satellite data and results of an eddy-permitting model, but show a low bias in regions where eddies are not generated locally but propagate into, which will likely transfer both to the diffusivities. In agreement with previous studies we find largest diffusivities in the deep Antarctic Circumpolar Current, and in the shallow western boundary and low latitude westward currents. In agreement with analytical consideration, we find that isopycnal diffusivities are increased at the depth of the steering level where unstable waves and mean flow propagate at the same speed, while skew diffusivities exhibit less vertical dependency, and that isopycnal diffusivities are roughly three times larger than skew diffusivities at the steering level. It is shown that the vertical structure of the diffusivities can be explained to a large extent by the effect of the planetary vorticity gradient which leads to a decrease of skew diffusivities at the surface (bottom) and to a downward (upward) shift of the steering level, and thus the maximum of isopycnal diffusivities, for eastward (westward) flow.

Diagnostics of isopycnal mixing in a circumpolar channel

Mesoscale eddies mix tracers along isopycnals and horizontally at the sea surface. This paper compares different methods of diagnosing eddy mixing rates in an idealized, eddy-resolving model of a channel flow meant to resemble the Antarctic Circumpolar Current. The first set of methods, the “perfect” diagnostics, are techniques suitable only to numerical models, in which detailed synoptic data is available. The perfect diagnostic include flux-gradient diffusivities of buoyancy, QGPV, and Ertel PV; Nakamura effective diffusivity; and the four-element diffusivity tensor calculated from an ensemble of passive tracers. These diagnostics reveal a consistent picture of isopycnal mixing by eddies, with a pronounced maximum near 1000m depth. The isopycnal diffusivity differs from the buoyancy diffusivity, a.k.a. the Gent–McWilliams transfer coefficient, which is weaker and peaks near the surface and bottom. The second set of methods are observationally “practical” diagnostics. They involve monitoring the spreading of tracers or Lagrangian particles in ways that are plausible in the field. We show how, with sufficient ensemble size, the practical diagnostics agree with the perfect diagnostics in an average sense. Some implications for eddy parameterization are discussed.

Effects of increased isopycnal diffusivity mimicking the unresolved equatorial intermediate current system in an earth system climate model

Earth system climate models generally underestimate dissolved oxygen concentrations in the deep eastern equatorial Pacific. This problem is associated with the “nutrient trapping” problem, described by Najjar et al. [1992], and is, at least partially, caused by a deficient representation of the Equatorial Intermediate Current System (EICS). Here we emulate the unresolved EICS in the UVic earth system climate model by locally increasing the zonal isopycnal diffusivity. An anisotropic diffusivity of ∼50,000 m2 s−1 yields an improved global representation of temperature, salinity and oxygen. In addition, it (1) resolves most of the local “nutrient trapping” and associated oxygen deficit in the eastern equatorial Pacific and (2) reduces spurious zonal temperature gradients on isopycnals without affecting other physical metrics such as meridional overturning or air‐sea heat fluxes. Finally, climate projections of low‐oxygenated waters and associated denitrification change sign and apparently become more plausible.

Adaptive time stepping algorithm for Lagrangian transport models: Theory and idealised test cases

Random walk simulations have an excellent potential in marine and oceanic modelling. This is essentially due to their relative simplicity and their ability to represent advective transport without being plagued by the deficiencies of the Eulerian methods. The physical and mathematical foundations of random walk modelling of turbulent diffusion have become solid over the years. Random walk models rest on the theory of stochastic differential equations. Unfortunately, the latter and the related numerical aspects have not attracted much attention in the oceanic modelling community. The main goal of this paper is to help bridge the gap by developing an efficient adaptive time stepping algorithm for random walk models. Its performance is examined on two idealised test cases of turbulent dispersion; (i) pycnocline crossing and (ii) non-flat isopycnal diffusion, which are inspired by shallow-sea dynamics and large-scale ocean transport processes, respectively. The numerical results of the adaptive time stepping algorithm are compared with the fixed-time increment Milstein scheme, showing that the adaptive time stepping algorithm for Lagrangian random walk models is more efficient than its fixed step-size counterpart without any loss in accuracy.

Eighteen Degree Water formation within the Gulf Stream during CLIMODE

Analysis of wintertime CLIMODE data for 2007 indicates that a substantial portion of new Eighteen Degree Water (EDW) is likely ventilated within the eastward flowing Gulf Stream (GS) between 67°W and 52°W longitudes, possibly exceeding that formed elsewhere in the northern Sargasso Sea. Use of some global air–sea interaction data sets applied to the study region for Feb/Mar of 2007 indicate that this winter may have been anomalously energetic in air–sea exchange compared to the mean of the prior 19yr. The largest heat and freshwater fluxes found directly over the meandering warm core of the Gulf Stream are capable of removing most of the subtropical heat anomaly of the GS, but cross-frontal fluxes of salinity are required to account for the observed regional salinity structure. An isopycnal diffusivity of ∼100m2s−1 is inferred from the salinity balance. This mixing would also account for the observation that EDW formed in the GS is slightly fresher than that formed in northern Sargasso Sea. The lateral flux of heat across the GS north wall also acts to cool the resulting EDW water, but the heat balance for EDW production is largely determined from GS advection and air–sea fluxes, in contrast to salinity. Based on oxygen saturation data, we estimate that 1.8–3.0Sv-yr of new EDW is formed in the GS for the winter of 2007. EDW originating from the GS is generated in a separate location from where it is accumulated in the northern Sargasso Sea. This manner of EDW formation will produce unique characteristics of EDW found in the northern Sargasso Sea: ones that differ in T/S properties from that formed south of the GS under the more traditional 1D, cooling-driven convection process.

Eddy parameterization challenge suite I: Eady spindown

The first set of results in a suite of eddy-resolving Boussinesq, hydrostatic simulations is presented. Each set member consists of an initially linear stratification and shear as in the Eady problem, but this profile occupies only a limited region of a channel and is allowed to spin-down via baroclinic instability. The diagnostic focus is on the spatial structure and scaling of the eddy transport tensor, which is the array of coefficients in a linear flux–gradient relationship. The advective (antisymmetric) and diffusive (symmetric) components of the tensor are diagnosed using passive tracers, and the resulting diagnosed tensor reproduces the horizontal transport of the active tracer (buoyancy) to within ±7% and the vertical transport to within ±12%. The derived scalings are shown to be close in form to the standard Gent–McWilliams (antisymmetric) and Redi diffusivity (symmetric) tensors with a magnitude that varies in space (concentrated in the horizontal and vertical near the center of the frontal shear) and time as the eddies energize. The Gent–McWilliams eddy coefficient is equal to the Redi isopycnal diffusivity to within ±6%, even as these coefficients vary with depth. The scaling for the magnitude of simulation parameters is determined empirically to within ±28%. To achieve this accuracy, the eddy velocities are diagnosed directly and used in the tensor scalings, rather than assuming a correlation between eddy velocity and the mean flow velocity where ±97% is the best accuracy achievable. Plans for the next set of models in the challenge suite are described.

The influence of eddy parameterizations on the transport of the Antarctic Circumpolar Current in coupled climate models

The transport of the Antarctic Circumpolar Current (ACC) varies strongly across the coupled GCMs (general circulation models) used for the IPCC AR4. This note shows that a large fraction of this across-model variance can be explained by relating it to the parameterization of eddy-induced transports. In the majority of models this parameterization is based on the study by Gent and McWilliams (1990). The main parameter is the quasi-Stokes diffusivity κ (often referred to less accurately as ”thickness diffusion”). The ACC transport and the meridional density gradient both correlate strongly with κ across those models where κ is a prescribed constant. In contrast, there is no correlation with the isopycnal diffusivity κiso across the models. The sensitivity of the ACC transport to κ is larger than to the zonal wind stress maximum. Experiments with the fast GCM FAMOUS show that changing κ directly affects the ACC transport by changing the density structure throughout the water column. Our results suggest that this limits the role of the wind stress magnitude in setting the ACC transport in FAMOUS. The sensitivities of the ACC and the meridional density gradient are very similar across the AR4 GCMs (for those models where κ is a prescribed constant) and among the FAMOUS experiments. The strong sensitivity of the ACC transport to κ needs careful assessment in climate models.

Shear dispersion in the thermocline and the saline intrusion

Over the mid-Atlantic shelf of the North America, there is a pronounced shoreward intrusion of the saltier slope water along the seasonal thermocline, whose genesis remains unexplained. Taking note of the observed broad-band baroclinic motion, we postulate that it may propel the saline intrusion via the shear dispersion. Through an analytical model, we first examine the shear-induced isopycnal diffusivity (“shear diffusivity” for short) associated with the monochromatic forcing, which underscores its varied even anti-diffusive short-term behavior and the ineffectiveness of the internal tides in driving the shear dispersion. We then derive the spectral representation of the long-term “canonical” shear diffusivity, which is found to be the baroclinic power band-passed by a diffusivity window in the log-frequency space. Since the baroclinic power spectrum typically plateaus in the low-frequency band spanned by the diffusivity window, canonical shear diffusivity is simply 1/8 of this low-frequency plateau — independent of the uncertain diapycnal diffusivity. Applied to the mid-Atlantic shelf, this canonical shear diffusivity is about 20m2s−1, which is sufficient to account for the observed tracer dispersion or saline intrusion in the thermocline.

Stability of the Atlantic meridional overturning circulation and stratification in a zonally averaged ocean model: Effects of freshwater flux, Southern Ocean winds, and diapycnal diffusion

The Atlantic Meridional Overturning Circulation (AMOC) is a crucial component of the global climate system. In this study, using a zonally averaged ocean model, we reexamine the sensitivity of this circulation, and ocean density structure in general, to several types of external forcing. The basin of the model extends from northern high latitudes to Antarctica and includes an implicit representation of a circumpolar channel in the South, and ocean circulation is driven by surface buoyancy fluxes and wind forcing. In contrast to earlier two-dimensional studies of the AMOC, our approach involves a careful treatment of the residual mean circulation (comprising the Eulerian-mean and eddy-induced flows), which is especially important for the Southern Ocean dynamics. Using boundary conditions consistent with present-day observations the model reproduces realistic ocean stratification and meridional overturning. The structure, intensity, and stability of the overturning are then extensively studied using three control parameters: the strength of westerly wind stress over the Southern Ocean, the magnitude of freshwater fluxes imposed on the northern Atlantic, and ocean diapycnal diffusivity. In a realistic parameter range, we estimate the AMOC sensitivity to changes in the Southern Ocean winds on the order of 1 Sv per 20% increase in the wind stress. The overturning also increases with diapycnal diffusivity, but the dependence is weaker than in the absence of the winds. The model can undergo a shutdown of the overturning (subject to a hysteresis) when either the freshwater forcing gradually increases or the wind stress decreases. The hysteresis loop disappears for large values of isopycnal diffusivity. Changes in the AMOC intensity are accompanied by changes in the volume transport of the Antarctic Circumpolar Current. Specifically, the AMOC collapse leads to a strengthening of this transport. Ultimately, our calculations produce stability maps for the steady states of the meridional overturning circulation and provide a general framework that potentially can be used to compare different models, or to understand past abrupt climate changes related to reorganization of the AMOC.

Assessing Lagrangian schemes for simulating diffusion on non-flat isopycnal surfaces

In large-scale ocean flows diffusion mostly occurs along the density surfaces and its representation resorts to the Redi isopycnal diffusivity tensor containing off-diagonal terms. This study focuses on the Lagrangian/particle framework for simulating such diffusive processes. A two-dimensional idealised test case for purely isopycnal diffusion on non-flat isopycnal surfaces is considered. Implementation of the higher order strong Euler, Milstein and order 1.5 Taylor schemes on our idealised test case shows that the higher order strong schemes produce the better pathwise approximations. The effective spurious diapycnal diffusivity is measured for each Lagrangian scheme under consideration. The propensity of the particles to move away from the isopycnal surface on which they were released is also measured. This shows that for non-flat isopycnals the order of convergence of the Euler scheme is not sufficient to achieve the desired accuracy. However, the Milstein scheme seems to be a good choice to achieve in an efficient way a fairly accurate result.

Barotropic instability in the West Spitsbergen Current

Barotropic instability in the shoreward branch of the West Spitsbergen Current is investigated on the basis of data from an array of current meter moorings along 78.83°N, across the upper continental slope and shelf break west of Svalbard. The slowly varying background current profile is modeled as an along‐slope, asymmetric jet anchored to the shelf break. Numerical linear stability analyses are performed on the idealized current profile and topography, revealing the characteristic period, wavelength, and growth rate of unstable vorticity waves. Detailed analysis of the ambient current profile in 2007–2008 shows that unstable conditions are present during ∼40% of the 10 month measurement record, depending on the localization, width, and amplitude of the current jet. The resulting vorticity waves are localized at the shelf break and are able to exchange water masses across the oceanic Arctic front. Typical wavelengths and periods are 20–40 km and 40–70 h, respectively. Wavelet, coherence, and complex demodulation analyses of the current meter data confirm that transient signals of similar periodicity as predicted by the stability analysis exist in the data record, prominently during the winter and spring months. Estimates of the heat loss contribution from isopycnal diffusion reach 1.4 TW during the time intervals when unstable vorticity waves are active at the shelf break, implying that the dynamics of the West Spitsbergen Current play a significant role in the cooling process of the Atlantic water on the way to the Arctic Ocean. This cooling corresponds to an along‐shelf cooling rate of −0.08°C per 100 km.

Isopycnal diffusivities in the Antarctic Circumpolar Current inferred from Lagrangian floats in an eddying model

Lagrangian subsurface isopycnal eddy diffusivities are calculated from numerical floats released in several regions of the Antarctic Circumpolar Current (ACC) of the 0.1° Parallel Ocean Program. Lagrangian diffusivities are horizontally highly variable with no consistent latitudinal dependence. Elevated values are found in some areas in the core of the ACC, near topographic features, and close to the Brazil‐Malvinas Confluence Zone and Agulhas Retroflection. Cross‐stream eddy diffusivities are depth invariant in the model ACC. An increase of Lagrangian eddy length scales with depth is masked by the strong decrease with depth of eddy velocities. The cross‐stream diffusivities average 750 ± 250 m2s−1around the Polar Frontal Zone. The results imply that parameterizations that (only) use eddy kinetic energy to parameterize the diffusivities are incomplete. We suggest that dominant correlations of Lagrangian eddy diffusivities with eddy kinetic energy found in previous studies may have been due to the use of too short time lags in the integration of the velocity autocovariance used to infer the diffusivities. We find evidence that strong mean flow inhibits cross‐stream mixing within the ACC, but there are also areas where cross‐stream diffusivities are large in spite of strong mean flows, for example, in regions close to topographic obstacles such as the Kerguelen Plateau.

Seasonal evolution of upper‐ocean horizontal structure and the remnant mixed layer

We discuss the seasonal evolution of upper‐ocean thermohaline structure at small horizontal scales. The upper 350 m of a 1000 km long section in the subtropical North Pacific was observed in winter, spring, and summer with 3–14 km horizontal resolution. Four vertical regions had distinct density and salinity structure: the mixed layer, remnant mixed layer, high‐stratification layer, and permanent thermocline. The remnant mixed layer consists of water from the winter mixed layer left over after restratification. The remnant mixed layer was most similar to the mixed layer in winter and spring, and most similar to the high‐stratification layer below in summer. The high‐stratification layer had elevated stratification that varied seasonally. The permanent thermocline varied little seasonally and was horizontally and vertically uniform in comparison. In all seasons, density ratios showed that mixed‐layer θ‐S differences tended to compensate in density with the strongest tendency toward compensation in winter. Density ratios were temperature dominated in the remnant mixed layer consistent with salt‐fingering. Salinity anomalies were largest at the surface and decayed with depth in all seasons. Spectra of isopycnal depth and θ‐S anomalies along isopycnals are compared between the three seasons and four vertical layers. Isopycnal depth variance at 30–46 km wavelengths decreased from winter to spring to summer by a factor of 2–10 in stratified regions. By treating salinity anomalies as a tracer, the effective isopycnal diffusivity in the remnant mixed layer was estimated to be 1.4 m2 s−1 over 30–46 km wavelengths.

Eddy-Driven Buoyancy Gradients on Eastern Boundaries and Their Role in the Thermocline

Abstract It is demonstrated that eddy fluxes of buoyancy at the eastern and western boundaries maintain alongshore buoyancy gradients along the coast. Eddy fluxes arise near the eastern and western boundaries because on both coasts buoyancy gradients normal to the boundary are strong. The eddy fluxes are accompanied by mean vertical flows that take place in narrow boundary layers next to the coast where the geostrophic constraint is broken. These ageostrophic cells have a velocity component normal to the coast that balances the geostrophic mean velocity. It is shown that the dynamics in these thin ageostrophic boundary layers can be replaced by effective boundary conditions for the interior flow, relating the eddy flux of buoyancy at the seaward edge of the boundary layers to the buoyancy gradient along the coast. These effective boundary conditions are applied to a model of the thermocline linearized around a mean stratification and a state of rest. The linear model parameterizes the eddy fluxes of buoyancy as isopycnal diffusion. The linear model produces horizontal gradients of buoyancy along the eastern coast on a vertical scale that depends on both the vertical diffusivity and the eddy diffusivity. The buoyancy field of the linear model agrees very well with the mean state of an eddy-resolving computation. Because the east–west difference in buoyancy is related to the zonally integrated meridional velocity, the linear model successfully predicts the meridional overturning circulation.

Transport of momentum and scalar in turbulent flows with anisotropic dispersive waves

Most geophysical flows encompass turbulence and internal and/or Rossby waves. We demonstrate that these two different classes of waves cause remarkably similar anomalies in the turbulent transport. While all scales in both types of flows contribute to the momentum diffusion, the vertical (diapycnal) scalar diffusion in stratified flows and lateral diffusion in β‐plane turbulence can be carried out only by turbulent eddies whose size is smaller than the thresholds of turbulence anisotropization. Beyond these thresholds, both flows become dominated by waves that provide no contribution to the scalar diffusion. Stably stratified flows exhibit enhanced isopycnal diffusion of both momentum and scalar. These results shed new light on the Osborn mixing model, diapycnal and isopycnal viscosity and diffusivity, absence of the critical gradient Richardson number, and large scale meridional transport.