Towards a mesoscale eddy closure

A turbulence closure for the effect of mesoscale eddies in non-eddy-resolving ocean models is proposed. The closure consists of a prognostic equation for the eddy kinetic energy (EKE) that is integrated as an additional model equation, and a diagnostic relation for an eddy length scale (L), which is given by the minimum of Rhines scale and Rossby radius. Combining EKE and L using a standard mixing length assumption gives a diffusivity (K), corresponding to the thickness diffusivity in the [Gent, P.R., McWilliams, J.C. 1990. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 20, 150–155] parameterisation. Assuming downgradient mixing of potential vorticity with identical diffusivity shows how K is related to horizontal and vertical mixing processes in the horizontal momentum equation, and also enables us to parameterise the source of EKE related to eddy momentum fluxes.The mesoscale eddy closure is evaluated using synthetic data from two different eddy-resolving models covering the North Atlantic Ocean and the Southern Ocean, respectively. The diagnosis shows that the mixing length assumption together with the definition of eddy length scales is valid within certain limitations. Furthermore, implementation of the closure in non-eddy-resolving models of the North Atlantic and the Southern Ocean shows consistently that the closure has skill at reproducing the results of the eddy-resolving model versions in terms of EKE and K.     

Effects of different closures for thickness diffusivity

The effects of spatial variations of the thickness diffusivity (K) appropriate to the parameterisation of [Gent, P.R. and McWilliams, J.C., 1990. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155.] are assessed in a coarse resolution global ocean general circulation model. Simulations using three closures yielding different lateral and/or vertical variations in K are compared with a simulation using a constant value. Although the effects of changing K are in general small and all simulations remain biased compared to observations, we find systematic local sensitivities of the simulated circulation on K. In particular, increasing K near the surface in the tropical ocean lifts the depth of the equatorial thermocline, the strength of the Antarctic Circumpolar Current decreases while the subpolar and subtropical gyre transports in the North Atlantic increase by increasing K locally. We also find that the lateral and vertical structure of K given by a recently proposed closure reduces the negative temperature biases in the western North Atlantic by adjusting the pathways of the Gulf Stream and the North Atlantic Current to a more realistic position.     

Vertical diffusion and oxygen consumption during stagnation periods in the deep North Aegean

Ventilation of the deep basins of the North Aegean Sea takes place during relatively scarce events of massive dense water formation in that region. In the time intervals between such events, the bottom waters of each sub-basin are excluded from interaction with other water masses through advection or isopycnal mixing and the only process that changes their properties is diapycnal mixing with overlying waters. In this work we utilize a simple one-dimensional model in order to estimate the vertical eddy diffusion coefficient K_ρ based on the observed rate of change of density and stratification. Vertical diffusivity is estimated for each of three sub-basins of the North Aegean, one of convex shape of the seabed and the other two of concave topography. It is noteworthy that the convex sub-basin exhibited much higher vertical diffusivity than the two concave sub-basins, a fact consistent with theoretical predictions that internal-wave-induced mixing is higher over the former shape of seabed. Furthermore, the estimates of K_ρ are exploited in computing the vertical transport of dissolved oxygen through diffusion and the rate of oxygen consumption by decaying organic matter. The different levels of the estimated diffusion and oxygen consumption rates testify to the dynamical and biogeochemical characteristics of each basin.     

Estimates of the lateral eddy diffusivity in the Indian Ocean as derived from drifter data

The Global Drifter Program data set is applied to develop 2° × 2° bin estimates of the lateral eddy diffusivity K in the Indian Ocean (IO) by means of a modification of the Davis approach. The calculations were performed relative to the seasonal change in the mean currents, which is especially important in the case of monsoon-driven circulation in the IO. Estimates of K were found to be below 1 × 10⁴ m²/s almost every-where in the IO. The spatial variations of K were analyzed in relation to the instabilities of the ocean circulation.     

A 2—D section of 228Ra and 226Ra in the Northeast Pacific

Seawater samples collected in the northeast Pacific from 112° 50′W to 126° 36′W along a latitudinal band (21–25° N) have been analysed for ²²⁸RA and ²²⁶Ra. Both nuclides exhibit their characteristic distributions. In the surface water, the exponential-like decrease of ²²⁸ Ra away from Baja California can be interpreted by horizontal water mixing with eddy diffusion coefficients (K_x) of 1 × 10⁶ cm² s⁻¹ and 5 × 10⁷ cm² S⁻¹ for scale lengths of 200 km and 1000 km, respectively. In the bottom waters, the decrease of ²²⁸Ra away from bottom sediments can be modeled by vertical eddy diffusivities (K_z) of 15–30 cm² s⁻¹ except at one station (24° 16.9′ N, 115° 8.9′ W) where a value of 120 cm² s⁻¹ is obtained. The ²²⁸Ra-derived diffusivities were used to compute the mass balance of ²²⁶Ra using a two-box model. The model results show a mean mixing coefficient of 3.8 cm² s⁻¹ for the thermocline and a mean upwelling velocity of 7.7 m y⁻¹ in the study area, both are about two or three times higher than those generally quoted for the Pacific.     

Mixing and biological production at eddy margins in the eastern Gulf of Alaska

We performed a multi-day shipboard experiment in June 2001 to test whether combining water from within an anticyclonic mesoscale eddy in the eastern Gulf of Alaska with water from outside could result in enhanced phytoplankton growth and to determine how mixing might influence planktonic assemblages. Initially, the eddy had lower standing stocks of algal pigments (chlorophyll a [chl a] and accessory pigments), nutrients, phytoplankton, and particulate organic carbon/nitrogen compared to waters outside of the eddy. The eddy possessed a greater diversity and abundance of coastal diatoms while the outside waters had a greater proportion of oceanic species, including the endemic pennate diatom, Nitzschia cylindroformis. After one week of incubation, rates of primary production were significantly higher in the mixed water compared to both the eddy and outside treatments. Pigment concentrations (except chl c₃, alloxanthin, and zeaxanthin) and the proportion of large diatoms (mainly Pseudo-nitzschia spp.) and heterotrophic dinoflagellates were greater in the mixed water than would be expected from the simple combination of inside and outside waters. Nutrient limitation (most likely by trace metals) appeared to be less severe in the mixed water. Chl a was enhanced in the mixed water, particularly when compared to the eddy water. The mixing of eddy and outside water masses stimulated primary production by ∼20%, but more importantly, the mixing resulted in a distinct planktonic assemblage. The biomass enrichment was short-lived, indicating that the maintenance of elevated chl a would require further mixing events in a physical setting that also permits an accumulation of biomass. We note that submesoscale processes, including the intensification of ageostrophic circulation that elicits strong vertical mixing in the presence of strain, might explain observed patterns of high phytoplankton standing stocks at the inner edges of Haida eddies in the field.     

2012年夏季海南岛东岸上升流区的混合观测

The turbulent mixing in the upwelling region east of Hainan Island in the South China Sea is analyzed based on in situ microstructure observations made in July 2012. During the observation, strong upwelling appears in the coastal waters, which are 3℃ cooler than the offshore waters and have a salinity 1.0 greater than that of the offshore waters. The magnitude of the dissipation rate of turbulent kinetic energy ε in the upwelling region is O(10–9 W/kg), which is comparable to the general oceanic dissipation. The inferred eddy diffusivity K_ρ is O(10–6 m~2/s), which is one order of magnitude lower than that in the open ocean. The values are elevated to K_ρ≈O(10–4 m~2/s) near the boundaries. Weak mixing in the upwelling region is consistent with weak instability as a result of moderate shears versus strong stratifications by the joint influence of surface heating and upwelling of cold water.The validity of two fine-scale structure mixing parameterization models are tested by comparison with the observed dissipation rates. The results indicate that the model developed by Mac Kinnon and Gregg in 2003 provides relatively better estimates with magnitudes close to the observations. Mixing parameterization models need to be further improved in the coastal upwelling region.     

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.     

赤道深层射流对深层浮力源响应解之特征的分析

基于赤道深层射流动力模型，研究赤道深层射流对深层浮力源的响应特征，指出线性、连续层化海洋中浮力源驱动下的单一垂直模态建立深层环流的过程等介于线性浅水系统中深水源驱动的深层环流的建立过程。分析赤道深层射流对深层浮力源响应解的某些特征，结果表明，在给定确定波数量值的诸参数下，浮力源在纬向上范围的大小对赤道深层的射流     

On the eddy mixing and energetics of turbulence in a stable atmospheric boundary layer

Some changes in the eddy mixing in the atmospheric boundary layer (ABL) are investigated with the use of the mesoscale RANS turbulence model. It is found that the behavior of parameters of the eddy turbulence mixing is in compliance with the recently obtained data of laboratory and atmospheric measurements. In particular, the flow Richardson number (Ri _f ) during the transient flow to a strongly stable state can behave nonmonotonically, growing with the increasing gradient Richardson number (Ri _g ) to the state of saturation at a certain gradient Richardson number (Ri _g ? 1), which separates two different turbulent regimes: the regimes of strong mixing and weak mixing. An analysis of the energetics based on the balance equations of kinetic and potential turbulence energies shows, in particular, that the weak mixing (Ri _g > 1) is quite capable of transferring momentum. This phenomenon can be explained not only by the fact that the flow is sustained by propagating internal waves, which effectively transfer momentum under strong stratification conditions, but also by the fact that turbulence permanently arises in the free atmosphere and in the deep ocean at Ri _g ? 1.     

Zonal versus meridional velocity variance in satellite observations and realistic and idealized ocean circulation models

Global, high-quality, satellite-based observation of oceanic currents over the past 13 years has revealed ubiquitous quasi-horizontal eddies in the mesoscale (tens to hundreds of kilometers), confirming the view of a highly turbulent ocean suggested by observational programs in the 1970s. Idealized quasigeostrophic turbulence models suggest mesoscale turbulent flow can vary between isotropic, and highly anisotropic zonal jets. Here we compare the zonal and meridional velocity variance from satellite altimetry. We find that, for an unexplained reason and despite the chaotic nature of turbulence, the surface flow is organized into mesoscale patches where either zonal or meridional velocity variance dominates. The patches persist over 13 years, much longer than the turbulent timescale of a few months. Implications include potentially highly anisotropic redistribution of tracers by the mesoscale flow. Zonally averaged velocity variances reveal a slight preference for meridional over zonal velocity variance. Realistic primitive equation models succeed in reproducing both the patchy structure in local preference for either zonal or meridional velocity variance, and the zonally averaged preference for meridional variance. Idealized models of fully developed, quasigeostrophic turbulence fail in both regards.     

Tidal Currents in the Tsushima Straits Estimated from ADCP Data by Ferryboat

Tidal currents in the Tsushima Straits have been analyzed using measurements obtained since February 1997 by an acoustic Doppler current profiler (ADCP) mounted on the ferryboat Camellia. Tidal current constituents (M ₂, S ₂, K ₁, O ₁) are dominant among the ten tidal current constituents (Q ₁, O ₁, P ₁, K ₁, N ₂, M ₂, S ₂, K ₂, MSf, Mf), and generally 1.4–2.1 times stronger at the western channel of the straits than those at the eastern channel. The ratio between amplitude of M ₂, S ₂, K ₁ and O ₁ averaged along the ferryboat track is 1:0.45:0.59:0.51. The major axis directions of tidal current ellipses are generally SW to NE, exceptionally in the vicinity of the Tsushima Islands. Approaching the Tsushima Islands from the Korean Peninsula side, the major axis gradually rotates clockwise. At the western channel, the M ₂ and K ₁ constituents change the rotation direction of current vectors from clockwise to counterclockwise at about 90–130 m depth. The contributions of the tidal currents to the mean kinetic energy and the mean eddy kinetic energy along the ferryboat track are, on average, 0.56 and 0.71, respectively. This suggests that tidal current activities are generally more dominant than the mean current activities and much more dominant than eddy activities. The only region where the eddy activities are comparable to the tidal current activities is located on the east side of the Tsushima Islands. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulation of Formation and Spreading of Salinity Minimum Associated with NPIW Using a High-Resolution Model

A series of numerical experiments were conducted with a high-resolution (eddy-permitting) North Pacific model to simulate the formation and spreading of the salinity minimum associated with the North Pacific Intermediate Water (NPIW). It was found that two factors are required to simulate a realistic configuration of the salinity minimum: a realistic wind stress field and small-scale disturbances. The NCEP reanalyzed wind stress data lead to better results than the Hellerman and Rosenstein wind stress data, due to the closer location of the simulated Oyashio and Kuroshio at the western boundary. Small-scale disturbances formed by relaxing computational diffusivity included in the advection scheme promote the large-scale isopycnal mixing between the Oyashio and Kuroshio waters, simulating a realistic configuration of the salinity minimum. A detailed analysis of the Oyashio water transport was carried out on the final three-year data of the experiment with reduced computational diffusivity. Simulated transport of the Kuroshio Extension in the intermediate layer is generally smaller than the observed value, while those of the Oyashio and the flow at the subarctic front are comparable to the observed levels. In the Oyashio-Kuroshio interfrontal zone the zonally integrated southward transport of the Oyashio water (140–155°E) is borne by the eddy activity, though the time-mean flow reveals the existence of a coastal Oyashio intrusion. In the eastern part (155°E–180°) the zonally integrated transport of the Oyashio water indicates a southward peak at the southern edge of the Kuroshio Extension, which corresponds to the branching of the recirculating flow from the Kuroshio Extension. This revised version was published online in July 2006 with corrections to the Cover Date.     

带有侧摩擦和底摩擦的绕岛理论

绕岛理论来自于Sverdrup理论,被广泛用于估计和分析通过岛屿之间海峡的输运情况。以往的研究得到了带有侧摩擦或底摩擦的单岛理论或多岛理论。本文在线性情况下考虑了风驱动环流下的解析模型。在同时考虑侧摩擦和底摩擦的情况下,推导出了岛屿周围输运流函数的解析解,并给出了通过岛屿之间通道的流量输运。其结果与Wajsowicz相似,但摩擦常数表示不同的值。从解析解上看,摩擦常数与侧摩擦和底摩擦之间的关系比较复杂,为了推导出它们之间的相互作用原理,本文在正压β平面上随机选取了一些侧摩擦和底摩擦的值。结果表明,在构成摩擦常数方面,侧摩擦和底摩擦近似呈线性关系。我们研究了宽度对通道输运值的影响,结果表明摩擦在一定宽度内提高了流量,这种现象和只考虑侧摩擦时比较相似。本文也比较了在不同深度下的流量,发现当水平涡粘性系数和底部拖曳系数固定时,水深越大,输运减少率越小。为了进一步揭示侧摩擦和底摩擦耗散的联合作用,在两个岛屿的情况下,本文在不同宽度的通道中与Wajsowicz的只考虑底摩擦或侧摩擦的模型进行了比较。结果表明,当通道比较窄,尤其是在小于Munk边界层厚度时,侧摩擦的作用大于底摩擦。当通道宽度远大于Munk边界层厚度时,底摩擦的作用大于侧摩擦。将模型应用到印尼贯穿流,得到大约20%的输运减少量。     

A Generation Mechanism for Mesoscale Eddies in the Kuril Basin of the Okhotsk Sea: Baroclinic Instability Caused by Enhanced Tidal Mixing

Mesoscale eddies, particularly anticyclonic ones, are dominant features in the Kuril Basin of the Okhotsk Sea. In 1999, both surface drifter and hydrographic observations caught the same anticyclonic eddy northwest of Bussol’ Strait, which has a diameter of ∼100 km, typical surface velocity of 0.2–0.3 m s⁻¹, and less dense core extending to a depth of ∼1200 m. Based on an idea that the generation of mesoscale eddies is caused by strong tidal mixing in and around Kuril Straits, we have conducted a series of three-dimensional numerical model experiments, in which strong tidal mixing is simply parameterized by increasing coefficients of vertical eddy viscosity and diffusivity along the eastern boundary. Initially, a regular series of disturbances with a wavelength of ∼70 km starts to develop. The disturbances can be clearly explained by a linear instability theory and regarded as the baroclinic instability associated with the near-surface front formed in the region between the enhanced mixing and offshore regions. In the mature phase, the disturbances grow large enough that some eddies pinch off and advect offshore (westward), with the scale of disturbances increasing gradually. Typical eddy scale and its westward propagation speed are ∼100 km and ∼0.6 km day⁻¹, respectively, which are consistent with the observations by satellites. The westward propagation can be explained partly due to nonlinear effect of self-offshore advection and partly due to the β-effect. With the inclusion of the upper ocean restoring, the dominance of anticyclonic eddy, extending from surface to a depth of ∼1200 m, can be reproduced.     

Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution

In this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. This error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. In the case of ROMS, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. We show that the common idea that spurious mixing decreases with resolution is generally false. In a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. At finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. The solution to this problem requires a specifically designed advection scheme. We propose and validate the RSUP3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the Peclet constraint. The rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. Realistic model experiments in a southwest Pacific configuration show that RSUP3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. There are residual errors from the rotated diffusion operator, but they remain acceptable. The use of a constant diffusivity rather than the Peclet hyperdiffusivity tends to increase these residual errors which become unacceptable with Laplacian diffusion. Finally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. A temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper.     

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.     

Dissipation of baroclinic tidal energy and diapycnal mixing in the White Sea

The modeling results obtained using the original version of the three-dimensional finite-element hydrostatic model QUODDY-4 testify that the spatial distributions of dissipation of baroclinic tidal energy and the related coefficient of diapycnal mixing in the deepwater stratified subdomain of the White Sea (the Basin and Kandalaksha and Dvina bays together) are highly similar to those found for low- and midlatitude oceans. It is in the open part of the sea that their values remain equal to the minimum possible values determined by the molecular kinematic viscosity; at its lateral boundaries (not all boundaries, but only individual segments (sites of mixing)), their values increase. In the shallow homogeneous subdomain of the White Sea, the dissipation of baroclinic tidal energy is considerably larger than in the deep stratified subdomain. Accordingly, the vertical eddy viscosity in the first subdomain is a few orders of magnitude higher than the coefficient of diapycnal mixing in the second subdomain. This is caused by an increased tidal velocity due to reduced depths.     

Eddy activities of the surface layer in the western North Pacific detected by satellite altimeter and radiometer

Geosat radar altimeter data during the first year (from November 1986 to November 1987) of its Exact Repeat Mission are analyzed to estimate the eddy kinetic energy and propagation characteristics of anomalies of sea surface dynamic topography (SSDT) for the western North Pacific. SSDT anomalies are compared with anomalies of sea surface temperature (SST) derived from NOAA satellite radiometer data. The eddy kinetic energy (K _e ) is large in the Kuroshio stationary meander region and Kuroshio Extension region. In the downstream region of the Kuroshio Extension,K _e is especially large on the upstream and downstream sides of prominent bathymetric features. In the interior region of the subtropical gyre is found a zonal tongue of largeK _e at around 20–20°N. Westward propagation is dominant in the SSDT and SST anomaly field at mid-latitudes. Longitude-time lag correlation diagrams reveal the coincidence of SSDT and SST anomalies statistically, which fact suggests the baroclinic nature of the anomalies. Zonal phase speeds of SSDT anomalies are approximately equal to the theoretical speeds of baroclinic first-mode long Rossby waves, but the meridional variation of observed phase speeds does not follow the simple theoretical variation of decreasing speeds monotonously with increasing latitudes.     

北太平洋涡旋对基于细尺度参数化的海洋内部混合的影响

基于Vector Geometry方法对2016—2018年的高度计资料进行涡旋识别,并使用细尺度参数化方法和Argo数据计算了涡旋附近的海洋内部扩散率,分析了北太平洋的涡旋对海洋内部混合的影响。结果显示,研究区域在涡旋影响下的平均扩散率比无涡旋影响下的值大6%,并且气旋涡增强了600—1200m深度的混合,对600—900m深度的混合影响最大,可达18%;反气旋涡明显增强了300—900m深度的混合,但对900—1200m深度的混合没有明显影响。随着与涡旋中心距离的增大,涡旋外围混合扩散率缓慢减小,涡旋内部混合扩散率变化不明显,此结果与2014年3—10月在24°—36°N、132°—152°E区域的一个个例分析结果一致。此外,随着涡旋强度的增大,海洋内部混合明显增强。统计结果表明,在研究区域, 90%的扩散率值在10^-5.5—10^-4m²/s范围内。