Diapycnal mixing by meso-scale eddies

The mean available potential energy released by baroclinic instability into the meso-scale eddy field has to be dissipated in some way and Tandon and Garrett [Tandon, A., Garrett, C., 1996. On a recent parameterization of mesoscale eddies. J. Phys. Oceanogr. 26 (3), 406–416] suggested that this dissipation could ultimately involve irreversible mixing of buoyancy by molecular processes at the small-scale end of the turbulence cascade. We revisit this idea and argue that the presence of dissipation within the thermocline automatically requires that a component of the eddy flux associated with meso-scale eddies must be associated with irreversible mixing of buoyancy within the thermocline. We offer a parameterisation of the implied diapycnal diffusivity based on (i) the dissipation rate for eddy kinetic energy given by the meso-scale eddy closure of Eden and Greatbatch [Eden, C., Greatbatch, R.J., 2008. Towards a meso-scale eddy closure. Ocean Modell. 20, 223–239.] and (ii) a fixed mixing efficiency. The implied eddy-induced diapycnal diffusivity (κ) is implemented in a coarse resolution model of the North Atlantic. In contrast to the vertical diffusivity given by a standard vertical mixing scheme, large lateral inhomogeneities can be found for κ in the interior of the ocean. In general, κ is large, i.e. up to o(10) cm²/s, near the western boundaries and almost vanishing in the interior of the ocean.     

Southern Ocean transformation in a coupled model with and without eddy mass fluxes

A coupled air–sea general circulation model is used to simulate the global circulation. Different parameterizations of lateral mixing in the ocean by eddies, horizontal, isopycnal, and isopycnal plus eddy advective flux, are compared from the perspective of water mass transformation in the Southern Ocean. The different mixing physics imply different buoyancy equilibria in the surface mixed layer, different transformations, and therefore a variety of meridional overturning streamfunctions. The coupled‐model approach avoids strong artificial water mass transformation associated with relaxation to prescribed mixed layer conditions. Instead, transformation results from the more physical non‐local, nonlinear interdependence of sea‐surface temperature, air–sea fluxes, and circulation in the model's atmosphere and ocean. The development of a stronger mid‐depth circulation cell and associated upwelling when eddy fluxes are present, is examined. The strength of overturning is diagnosed in density coordinates using the transformation framework.     

Reconciling thermodynamic and dynamic methods of computation of water-mass transformation rates

The computation of the water-mass transformation rate in a particular density range from thermodynamic and dynamic methods are compared and reconciled by diagnosis of the Atlantic sector of a global integration of an ocean model driven by analyzed air–sea fluxes. In the absence of diffusive processes, the rate of subduction of fluid between two density surfaces across a fixed control surface, and integrated across the ocean from one solid boundary to another, must be equal to the rate of formation of fluid at the sea surface induced by surface fluxes in that density range. But due to the action of mixing on the body of fluid between the control surface and the sea-surface, transformation may differ from the integrated subduction. We find that vertical diffusive fluxes at the base of the winter mixed layer and in the seasonal thermocline can substantially modify transformation due to air–sea interaction and bring about an accommodation between it and the subduction rate. In high latitudes, an additional accommodation is achieved by lateral diffusive fluxes directed across the almost vertical isopycnals, typical of the deep, end-of-winter mixed layers of the sub-polar gyre. Finally we speculate on the likely nature and intensity of the mixing processes at work in the boundary layer of the ocean and their role in subduction and transformation.     

The WOCE-era 3-D Pacific Ocean circulation and heat budget

To address questions concerning the intensity and spatial structure of the three-dimensional circulation within the Pacific Ocean and the associated advective and diffusive property flux divergences, data from approximately 3000 high-quality hydrographic stations collected on 40 zonal and meridional cruises have been merged into a physically consistent model. The majority of the stations were occupied as part of the World Ocean Circulation Experiment (WOCE), which took place in the 1990s. These data are supplemented by a few pre-WOCE surveys of similar quality, and time-averaged direct-velocity and historical hydrographic measurements about the equator.An inverse box model formalism is employed to estimate the absolute along-isopycnal velocity field, the magnitude and spatial distribution of the associated diapycnal flow and the corresponding diapycnal advective and diffusive property flux divergences. The resulting large-scale WOCE Pacific circulation can be described as two shallow overturning cells at mid- to low latitudes, one in each hemisphere, and a single deep cell which brings abyssal waters from the Southern Ocean into the Pacific where they upwell across isopycnals and are returned south as deep waters. Upwelling is seen to occur throughout most of the basin with generally larger dianeutral transport and greater mixing occurring at depth. The derived pattern of ocean heat transport divergence is compared to published results based on air–sea flux estimates. The synthesis suggests a strongly east/west oriented pattern of air–sea heat flux with heat loss to the atmosphere throughout most of the western basins, and a gain of heat throughout the tropics extending poleward through the eastern basins. The calculated meridional heat transport agrees well with previous hydrographic estimates. Consistent with many of the climatologies at a variety of latitudes as well, our meridional heat transport estimates tend toward lower values in both hemispheres.     

Numerical study of the meridional overturning circulation with “mixing hotspots” in the Pacific Ocean

Using an idealized ocean general circulation model, we examine the effect of “mixing hotspots” (localized regions of intense diapycnal mixing) predicted based on internal wave-wave interaction theory (Hibiya et al., 2006) on the meridional overturning circulation of the Pacific Ocean. Although the assumed diapycnal diffusivity in the mixing hotspots is a little larger than the predicted value, the upwelling in the mixing hotspots is not sufficient to balance the deep-water production; out of 17 Sv of the downwelled water along the southern boundary, only 9.2 Sv is found to upwell in the mixing hotspots. The imbalance as much as 7.8 Sv is compensated by entrainment into the surface mixed layer in the vicinity of the downwelling region. As a result, the northward transport of the deep water crossing the equator is limited to 5.5 Sv, much less than estimated from previous current meter moorings and hydrographic surveys. One plausible explanation for this is that the magnitude of the meridional overturning circulation of the Pacific Ocean has been overestimated by these observations. We raise doubts about the validity of the previous ocean general circulation models where diapycnal diffusivity is assigned ad hoc to attain the current magnitude suggested from current meter moorings and hydrographic surveys.     

地形和风速影响下的海气相互作用大涡模拟研究

当水流经过海洋地形时,水流的不稳定性会引起垂向混合并伴随大量湍流过程。针对传统海气耦合模式缺少在湍流尺度上讨论海洋地形与风速对海气相互作用影响的问题,使用并行大涡模拟海气耦合模式(the parallelized large eddy simulation model, PALM)在5 m/s的背景风场下,引入理想立方体地形,对比有无地形的影响;设置地形边长为L,高为3L (其中大气部分高L), L与水深H之比为L/H=1/2;然后保持地形条件不变。设置5、10和15 m/s三种风速,讨论风速对小尺度海气相互作用的影响。研究表明:地形在大气部分减弱顺风向速度,增强侧风向速度,影响0～5L的高度区域,而对垂向作用较小;无地形条件下湍流垂向涡黏系数K_m在-0.3L时,水深达到最大值0.024 m²/s,有地形条件下K_m在-0.8L时,达到最大值为0.16 m²/s,地形的存在使得上层海洋混合加强, K_m最大值增加1个数量级。随风速增大海洋和大气中的净热通量、淡水通量和浮力通量都相应...     

Natural air–sea flux of CO2 in simulations of the NASA-GISS climate model: Sensitivity to the physical ocean model formulation

Results from twin control simulations of the preindustrial CO₂ gas exchange (natural flux of CO₂) between the ocean and the atmosphere are presented here using the NASA-GISS climate model, in which the same atmospheric component (modelE2) is coupled to two different ocean models, the Russell ocean model and HYCOM. Both incarnations of the GISS climate model are also coupled to the same ocean biogeochemistry module (NOBM) which estimates prognostic distributions for biotic and abiotic fields that influence the air–sea flux of CO₂. Model intercomparison is carried out at equilibrium conditions and model differences are contrasted with biases from present day climatologies. Although the models agree on the spatial patterns of the air–sea flux of CO₂, they disagree on the strength of the North Atlantic and Southern Ocean sinks mainly because of kinematic (winds) and chemistry (pCO₂) differences rather than thermodynamic (SST) ones. Biology/chemistry dissimilarities in the models stem from the different parameterizations of advective and diffusive processes, such as overturning, mixing and horizontal tracer advection and to a lesser degree from parameterizations of biogeochemical processes such as gravitational settling and sinking. The global meridional overturning circulation illustrates much of the different behavior of the biological pump in the two models, together with differences in mixed layer depth which are responsible for different SST, DIC and nutrient distributions in the two models and consequently different atmospheric feedbacks (in the wind, net heat and freshwater fluxes into the ocean).     

The diffusive component of particulate organic carbon export in the North Atlantic estimated from SeaWiFS ocean color

The diffusive component of the particulate organic carbon (POC) export from the ocean's surface layer has been estimated using a combination of the mixed layer model and SeaWiFS ocean color data. The calculations were carried out for several example sites located in the North Atlantic over a 10-year time period (1998–2007). Satellite estimates of surface POC derived from ocean color were applied as an input to the model driven by local surface heat and momentum fluxes. For each year of the examined period, the diffusive POC flux was estimated at a 200 m depth. The highest flux is generally observed in the spring and fall seasons, when surface waters are weakly stratified. In addition, the model results demonstrate significant interannual and geographical variability of the flux. The highest diffusive POC flux occurs in the northern North Atlantic and the lowest in the subtropical region. The interannual variability of the diffusive POC flux is associated with mixed layer dynamics and underscores the importance of atmospheric forcing for POC export from the surface layer to the ocean's interior.     

Effects in a climate model of slope tapering in neutral physics schemes

In many global ocean climate models, mesoscale eddies are parameterized as along isopycnal diffusion and eddy-induced advection (or equivalently skew-diffusion). The eddy-induced advection flattens isopycnals and acts as a sink of available potential energy, whereas the isopycnal diffusion mixes tracers along neutral directions. While much effort has gone into estimating diffusivities associated with this closure, less attention has been paid to the details of how this closure (which tries to flatten isopycnals) interacts with the mixed layer (in which vertical mixing tries to drive the isopycnals vertical). In order to maintain numerical stability, models often stipulate a maximum slope S_max which in combination with the thickness diffusivity A_gm defines a maximum eddy-induced advective transport A_gm1S_max. In this paper, we examine the impact of changing S_max within the GFDL global coupled climate model. We show that this parameter produces significant changes in wintertime mixed layer depth, with implications for wintertime temperatures in key regions, the distribution of precipitation, and the vertical structure of heat uptake. Smaller changes are seen in details of ventilation and currents, and even smaller changes as regards the overall hydrography. The results suggest that not only the value of the coefficient, but the details of the tapering scheme, need to be considered when comparing isopycnal mixing schemes in models.     

Tidal Mixing in the Kuril Straits and Its Impact on Ventilation in the North Pacific Ocean

A numerical study using a 3-D nonhydrostatic model has been applied to baroclinic processes generated by the K ₁ tidal flow in and around the Kuril Straits. The result shows that large-amplitude unsteady lee waves are generated and cause intense diapycnal mixing all along the Kuril Island Chain to levels of a maximum diapycnal diffusivity exceeding 10³ cm²s⁻¹. Significant water transformation by the vigorous mixing in shallow regions produces the distinct density and potential vorticity (PV) fronts along the Island Chain. The pinched-off eddies that arise and move away from the fronts have the ability to transport a large amount of mixed water (∼14 Sv) to the offshore regions, roughly half being directed to the North Pacific. These features are consistent with recent satellite imagery and in-situ observations, suggesting that diapycnal mixing within the vicinity of the Kuril Islands has a greater impact than was previously supposed on the Okhotsk Sea and the North Pacific. To examine this influence of tidal processes at the Kurils on circulations in the neighboring two basins, another numerical experiment was conducted using an ocean general circulation model with inclusion of tidal mixing along the islands, which gives a better representation of the Okhotsk Sea Mode Water than in the case without the tidal mixing. This is mainly attributed to the added effect of a significant upward salt flux into the surface layer due to tidal mixing in the Kuril Straits, which is subsequently transported to the interior region of the Okhotsk Sea. With a saline flux into the surface layer, cooling in winter in the northern part of the Okhotsk Sea can produce heavier water and thus enhance subduction, which is capable of reproducing a realistic Okhotsk Sea Mode Water. The associated low PV flux from the Kuril Straits to the open North Pacific excites the 2nd baroclinic-mode Kelvin and Rossby waves in addition to the 1st mode. Interestingly, the meridional overturning in the North Pacific is strengthened as a result of the dynamical adjustment caused by these waves, leading to a more realistic reproduction of the North Pacific Intermediate Water (NPIW) than in the case without tidal mixing. Accordingly, the joint effect of tidally-induced transport and transformation dominating in the Kuril Straits and subsequent eddy-transport is considered to play an important role in the ventilation of both the Okhotsk Sea and the North Pacific Ocean. This revised version was published online in July 2006 with corrections to the Cover Date.     

Circulation and mixing at the New England shelfbreak front: Results of purposeful tracer experiments

We present the results of six dye tracer experiments that measured the mixing and circulation at the shelfbreak front on the New England Shelf. The last three were conducted during the New England Shelfbreak Productivity Experiment (NESPEX) with concurrent isopycnal float deployments. The results are consistent with the Chapman and Lentz [Chapman, D.C., and Lentz, S.J. (1994). Trapping of a coastal density front by the bottom boundary layer. Journal of Physical Oceanography, 24, 1465–1479.] model prediction of the separation and upwelling along the shelfbreak front of bottom boundary layer (BBL) water forced by an Ekman buoyancy flux, but show considerable variability. Cross-shelf velocities at the detachment point are 2–3 × 10⁻² m/s. But seaward, over the slope region, dye tagged water was sheared from the main patch into small filaments that upwelled along the front with cross-shelf speeds up to 0.1 m/s. Cross-shelf diffusion was of order 10 m²/s in the mixed bottom layer and 1 m²/s in the interior along the front. Within the stratified front, the mean vertical diffusivity was K_z  4 × 10⁻⁶ m²/s. The dispersion of shelfwater in the slope region is effected by turbulent flow with advective speeds exceeding the small scale diffusive mixing. The mean flux of the detached BBL water is sufficient to account for the net loss of shelf water during its transit from Cape Cod to Cape Hatteras.     

Modified parameterization for near-inertial waves

The near-inertial waves (NIWs) are important for energy cascade in the ocean. They are usually significantly reinforced by strong winds, such as typhoon. Due to relatively coarse resolutions in contemporary climate models, NIWs and associated ocean mixing need to be parameterized. In this study, a parameterization for NIWs proposed by Jochum in 2013 (J13 scheme), which has been widely used, is compared with the observations in the South China Sea, and the observations are treated as model outputs. Under normal conditions, the J13 scheme performs well. However, there are noticeable discrepancies between the J13 scheme and observations during typhoon. During Typhoon Kalmaegi in 2014, the inferred value of the boundary layer is deeper in the J13 scheme due to the weak near-inertial velocity shear in the vertical. After typhoon, the spreading of NIWs beneath the upper boundary layer is much faster than the theoretical prediction of inertial gravity waves, and this fast process is not rendered well by the J13 scheme. In addition, below the boundary layer, NIWs and associated diapycnal mixing last longer than the direct impacts of typhoon on the sea surface. Since the energy dissipation and diapycnal mixing below the boundary layer are bounded to the surface winds in the J13 scheme, the prolonged influences of typhoon via NIWs in the ocean interior are missing in this scheme. Based on current examination, modifications to the J13 scheme are proposed, and the modified version can reduce the discrepancies in the temporal and vertical structures of diapycnal mixing.     

Sensitivity of CFCs and Anthropogenic CO2 Uptake in a North Pacific GCM to Mixing Parameterization and Surface Forcing

Distributions and characteristics of water mass and chlorofluorocarbons (CFCs) in the North Pacific are investigated by using a General Circulation Model (GCM). The anthropogenic CO₂ uptake by the ocean is estimated with velocity fields derived from the GCM experiments. The sensitivity of the uptake to different diffusion parameterizations and different surface forcing used in the GCM is investigated by conducting the three GCM experiments; the diffusive processes are parameterized by horizontal and vertical eddy diffusion which is used in many previous models (RUN1), parameterized by isopycnal diffusion (RUN2), and isopycnal diffusion and perpetual winter forcing for surface temperature and salinity (RUN3). Realistic features for water masses and CFCs can be simulated by the isopycnal diffusion models. The horizontal and vertical diffusion model fails to simulate the salinity minimum and realistic penetration of CFCs into the ocean. The depth of the salinity minimum layer is better simulated under the winter forcing. The results suggest that both isopycnal parameterization and winter forcing are crucial for the model water masses and CFCs simulations. The oceanic uptake of anthropogenic CO₂ in RUN3 is about 19.8 GtC in 1990, which is larger by about 10% than that in RUN1 with horizontal and vertical diffusive parameterization. RUN3 well simulates the realistic water mass structure of the intermediate layer considered as a candidate of oceanic sink for anthropogenic CO₂. The results suggest that the previous models with horizontal and vertical diffusive parameterization may give the oceanic uptake of anthropogenic CO₂ underestimated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimates of mixing on the South China Sea shelf

1 Introduction The outer shelf of the South China Sea is a di- verse environment characterized by sharp changes in bottom topography (Wang et al., 2002). Internal wave and diapycnal mixing may be a vital mechanism con- trolling the distribution of physical water properties, nutrient fluxes, and concentrations of particulate mat- ter. Therefore, the research on diapycnal mixing on the outer shelf in the South China Sea is of great impor- tance to explore the level and variability of the abov…     

Dynamical structure of vertically two-dimensional estuary in steady state

The dynamical structure of a two-dimensional (depth and axial directions) estuary is studied analytically. A set of governing equations describing the time-averaged velocity and salinity in the estuary is used, where all of the external parameters (depth, width, freshwater discharge and horizontal and vertical coefficients of eddy viscosity and eddy diffusivity) are assumed to be constant along the estuary.Two dynamical relations are taken into consideration in the theory. One of them is the dependence of the longitudinal scaleL _d on the balance of longitudinal salt transport, and the other is the relation between the vertical stratification of salinity and the the Prandtl numberP _r=A_v/K_v, whereA _v andK _v denote the coeffcients of the vertical eddy viscosity and diffusivity, respectively. The two relations result in an extension of the parameter range in which the linear balance of momentum holds.A linear state of motion (LM-state) is defined as the state where the momentum balance is linear. The LM-state comprises the so-called vertically homogeneous and the so-called partially mixed state. Perturbation analysis is introduced and dynamical theory is developed in the LM-state. Since the LM-state covers a fairly wide regime with respect to the balance of salt transport, the state is subdivided into three stages: the diffusive, intermediate and advective stages. In the diffusive stage the upstream salt transport is mainly attributed to the horizontal diffusion, whereas in the advective stage it is attributed to advection caused by gravitational circulation. The salinity balance is also linear in the diffusive and intermediate stages, whereas the balance is nonlinear in the advective stage. The advective stage of the LM-state is regarded as a stage bordering the salt wedge state.The longitudinal distribution of depth-mean salinity is found to take an exponential form in the diffusive stage, a nearly linear form in the advective stage and an intermediate form between them in the intermediate stage.     

2001年秋季风对坦帕湾盐度平衡的影响

利用三维高分辨率有限体积的近海海域模型FVCOM来分析2001年秋季期间风作用对坦帕湾区域盐度平衡的影响。为了区分风的影响,分别设计了两个实验：一个由潮汐和河流作为驱动,另一个由潮汐、河流以及风场共同驱动。结论如下：首先,风作用会使盐度产生变化,能够明显地使坦帕湾内的盐度增加,并导致水平和垂直方向上盐度梯度的减少;随后,本文分析了坦帕湾区域内的盐度平衡,主要的盐度平衡来自于全部（水平和垂直方向上）平流的盐度流量分歧以及除去海峡底部的垂直方向上盐度流量分歧;最后,对由风引起的盐度变化进一步进行分析,结果表明风作用不能改变盐度平衡地位的相对重要性,由风引起的盐度平衡改变高度依靠于特殊的地形,除此之外,全部平流盐度流量分歧和垂直散布盐度通量分歧能够抵消,并且两者都远大于水平散步盐度流量分歧。     

The seasonal cycle of submesoscale flows

The seasonal cycle of submesoscale flows in the upper ocean is investigated in an idealised model domain analogous to mid-latitude open ocean regions. Submesoscale processes become much stronger as the resolution is increased, though with limited evidence for convergence of the solutions. Frontogenetical processes increase horizontal buoyancy gradients when the mixed layer is shallow in summer, while overturning instabilities weaken the horizontal buoyancy gradients as the mixed layer deepens in winter. The horizontal wavenumber spectral slopes of surface temperature and velocity are steep in summer and then shallow in winter. This is consistent with stronger mixed layer instabilities developing as the mixed layer deepens and energising the submesoscale. The degree of geostrophic balance falls as the resolution is made finer, with evidence for stronger non-linear and high-frequency processes becoming more important as the mixed layer deepens. Ekman buoyancy fluxes can be much stronger than surface cooling and are locally dominant in setting the stratification and the potential vorticity at fronts, particularly in the early winter. Up to 30% of the mixed layer volume in winter has negative potential vorticity and symmetric instability is predicted inside mesoscale eddies as well as in the frontal regions outside of the vortices.     

Parameterization of the depth of the upper quasi-homogeneous layer based on measurements in the North Atlantic (Section along 53° N)

The dependence of the variation in the depth of the upper mixed layer (MLD) on the governing parameters (the momentum flux, the buoyancy fluxes at the ocean surface, and the density gradient in the pycnocline) is considered. It is shown that, in the spring storm season, wind mixing dominates over convective mixing. In this case, the MLD is linearly correlated with the Ekman scale calculated from the friction velocity observed approximately 12 h before the measurement of the MLD.     

The effect of topography-enhanced diapycnal mixing on ocean and atmospheric circulation and marine biogeochemistry

The impact of topographically catalysed diapycnal mixing on ocean and atmospheric circulation as well as marine biogeochemistry is studied using an earth system model of intermediate complexity. The results of a model run in which diapycnal mixing depends on seafloor roughness are compared to a control run that uses a simple depth-dependent parametrization for vertical background diffusivity. A third model run is conducted that uses the horizontal mean of the topographically catalysed mixing as vertical profile in order to distinguish between the overall effect of larger diffusivities and the spatial heterogeneity of the novel mixing parametrization.The new mixing scheme results in a strengthening of the deep overturning cell and enhances equatorial upwelling. Surface temperatures in the Southern Ocean increase by about 1 K (in the overall effect) whereas cooling of a similar magnitude in low latitudes is generated by the spatial heterogeneity of the mixing. The corresponding changes in the atmospheric circulation involve a weakening of the southern hemispheric Westerlies and a strengthening of the Walker circulation. Biogeochemical changes are dominated by an improved ventilation of the deep ocean from the south. Water mass ages decline significantly in the deep Indian Ocean and the deep North Pacific whereas oxygen increases in the two ocean basins. The representation of the global volume of water with an oxygen concentration lower than 90 μmol/kg in the model is improved using the topography catalysed mixing. Furthermore, primary production is stimulated in equatorial regions through increased upwelling of nutrients and reduced in the oligotrophic gyres.