Oceanic thermohaline intrusions: theory

This is a review of theories governing growth and evolution of thermohaline intrusive motions. We discuss theories based on eddy coefficients and salt finger flux ratios and also on molecular Fickian diffusion, drawing relationships and parallels where possible. We discuss linear theories of various physical configurations, effects of rotation and shear, and nonlinear theories. A key requirement for such theories to become quantitatively correct is the development and field testing of relationships between double-diffusive fluxes and average vertical gradients of temperature and salinity. While we have some ideas about the functional dependencies and rough observational constraints on the magnitudes of such flux/gradient relationships, many questions will not be answered until usable ‘flux laws’ exist. Furthermore, numerical experiments on double-diffusive intrusions are currently feasible, but will have more quantitative meaning when fluxes are parameterised with such laws. We conclude that more work needs to be done in at least two areas. Firstly, tests of linear theory against observations should continue, particularly to discover the extent to which linear theories actually explain the genesis of intrusions. Secondly, theoretical studies are needed on the nonlinear effects that control the evolution and finite amplitude state of intrusions, since these determine the lateral fluxes of salt, heat, and momentum.     

Intrusive layering of the Antarctic slope front

Cascading of cold Antarctic shelf water (ASW) initiates compensatory isopycnic upwelling of the warm Circumpolar Deep Water (CDW). The baroclinic/thermoclinic Antarctic slope front (ASF) is formed, and a mesoscale intrusive structure develops on the shelf edge and slope. Mesoscale processes when the ASF peaks are periodically accompanied by local baroclinic instability, which forms a smaller-scale intrusive structure. Therefore, the ASF is naturally subdivided into two layers according to the intrusion scales (vertical δН and horizontal L) and the horizontal parameters of the front (thermoclinity (T_L)_ρ and baroclinity γ_ρ). Analysis of ASF intrusive layering due to the baroclinic factor supports the following conclusion: the higher the (T_L)_ρ of the ASF, the greater the intrusion intensity |δθ| (temperature anomaly amplitude), while an increase in γ_ρ of the ASF leads to a decrease in intrusion scales δН and L. Frontal intrusions can be distinguished by a development degree. Regardless of the degree of development, all warm intrusions are characterized by vertical density stratification, while cold intrusions are characterized by density quasihomogeneity. According to field data, the ASF instability process is subdivided into four stages. When theASF is baroclinically unstable, the local baroclinic deformation radius Rd_L of the front is close in magnitude to the horizontal scale L of the intrusions that form, and their characteristic vertical scale δH is close to the typical vertical scale of front instability.     

Possible Density Change of the Origin of North Pacific Intermediate Water Due to Double Diffusion in the Mixed Water Region

In this study we test Talley's hypothesis that Oyashio winter mixed-layer water (26.5–26.6σ _θ) increases its density to produce the North Pacific Intermediate Water (NPIW) salinity minimum (26.7– 26.8σ_θ) in the Mixed Water Region, assuming a combination of cabbeling and double diffusion. The possible density change of Oyashio winter mixed-layer water is discussed using an instantaneous ratio of the change of temperature and salinity along any particular intrusion (R _l ). We estimate the range of R _l ^DD required to convert Oyashio winter mixed-layer water to the NPIW salinity minimum due to double diffusion, and then assume double-diffusive intrusions as this conversion mechanism. A double-diffusive intrusion model is used to estimate R _l ^DD in a situation where salt fingering dominates vertical mixing, as well as to determine whether Oyashio winter mixed-layer water can become the NPIW salinity minimum. Possible density changes are estimated from the model R _l ^DD by assuming the amount of density change due to cabbeling. From these results, we conclude that Oyashio winter mixed-layer water contributes to a freshening of the lighter layer of the NPIW salinity minimum (around 26.70σ_θ) in the MWR.     

Numerical modelling and analysis of temperature controlled density currents in Tomales Bay, California

The coastal region adjacent to Tomales Bay, California is dominated by wind-driven upwelling during spring and summer and the cold, upwelled water is moved towards Tomales Bay, entering the estuary with the flood tide. If the tidal excursion is ≥6 km and the cold water subducts beneath the warmer, less dense estuarine water, a temperature controlled density current may form and intrude towards the head of the estuary as a thermally stratified bottom layer. The numerical modelling was aimed at determining the capability of the Delft3D-FLOW model to reproduce the cold ocean water intrusion events, the response (development and progression) of these intrusions to differing physical scenarios and the comparative importance of the parameters to the intrusions. The numerical model successfully reproduced the density intrusions and showed that the persistence and break down of the density intrusions were affected by a number of physical parameters, to varying degrees. The sensitivity analysis showed that density intrusion formation is controlled by tidal conditions and ocean water temperature. The strength and persistence of the developed density intrusions are influenced by wind, insolation and estuary depth. Fresh water inflow at the head of the estuary had no impact on the density intrusions. Three-dimensional numerical modelling is thus a valuable tool in understanding the estuary and its functioning.     

Application of interleaving models for the description of intrusive layering at the fronts of deep polar water in the Eurasian Basin (Arctic)

Interleaving models of pure thermohaline and baroclinic frontal zones are applied to describe intrusions at the fronts found in the upper part of the Deep Polar Water (DPW) when the stratification was absolutely stable. It is assumed that differential mixing is the main mechanism of the intrusion formation. Important parameters of the interleaving such as the growth rate, vertical scale, and slope of the most unstable modes relative to the horizontal plane are calculated. It was found that the interleaving model for a pure thermohaline front satisfactory describes the important intrusion parameters observed at the frontal zone. In the case of a baroclinic front, satisfactory agreement over all the interleaving parameters is observed between the model calculations and observations provided that the vertical momentum diffusivity significantly exceeds the corresponding coefficient of mass diffusivity. Under specific (reasonable) constraints of the vertical momentum diffusivity, the most unstable mode has a vertical scale approximately two-three times smaller than the vertical scale of the observed intrusions. A thorough discussion of the results is presented.     

Numerical experiments on double-diffusive intrusions in the ocean and their relation to laboratory experiments

Numerical experiments on double-diffusive intrusions are reviewed briefly. Though the number of studies is very limited at present, they have undoubtedly an advantage that a heat–salt system can be studied without undesired heat loss from the boundaries.Several possibilities for future numerical experiments are summarized.     

Hydrographic observations

During the summer of 1981 a large scale sampling effort took place in the shelf waters of the southeastern United States. The goal of this effort was to quantify the effect of the intrusion of deep Gulf Stream water into these shallow, euphotic waters. By making repeated hydrographic measurements over the entire shelf area, the actual volume of the intrusions was determined. Two main intrusion events were observed: one in June and early July and a second in late July and early August. The intruding water entered the shelf in the region south of St Augustine and was transported northward by the mean northward shelf circulation. The subsurface cold water mass was isolated from the Gulf Stream by a ridge of warmer water along the shelf break.The intrusions resulted in increased stability in shelf waters with vertical temperature gradients as high as 10°C m⁻¹. The potential energy in the stratified shelf waters typically ranged from 1000 to 2000 J m⁻² that would require 2 to 4 mW m⁻² to mix. However, since only 0.1 to 1.0mW m⁻² was available from wind and tidal mixing, the water column stayed stratified in most cases.The amount of nitrate transported onto the shelf was determined by two methods: direct observation by synoptic cruises and transport measurements using current meter arrays. Both methods gave similar results with about 18,000 tons nitrogen in the large June/July intrusion. On a seasonal basis, 40,000 tons of nitrogen could be advected into shelf waters which could result in 200,000 to 400,000 tons carbon production.     

A model for Meddy formation

A particular feature of “Meddies” is that the water within them has stable gradients of salinity and temperature. In this paper a model for a dense turbulent plume falling in a stationary, linearly-stratified environment is described. The density of the plume is assumed to be a linear function of two components, while the ambient density gradient is due to a gradient in only one of these components (labelled component one). The ratio of the contributions to the source buoyancy flux of the two components within the plume is identified as the important parameter for this type of flow. After deriving the steady equations for the plume, a simplified model for the filling process which creates the Meddy is described, which shows how a layer of fluid may be formed with stable gradients in both components in the lower part of the intrusion. The intrusion is shown to be less stratified than the surrounding fluid, with relatively weak gradients in component one (identified with temperature in the Meddy) that vary from unstable at the top to stable at the bottom of the intrusion and a fairly constant (stable) gradient in the second component (salinity for a Meddy). If the stable gradients in a Meddy are due solely to the filling process then, during formation, the top of the Meddy must become cooler than the surrounding water at the same level. The observed stable temperature gradient in Meddies is likely to be due to mixing processes after their formation, whereas the stable salanity gradient is mainly due to the filling process during formation.     

阿拉伯海高盐水入侵孟加拉湾的季节形态及动力机制

本研究利用Argo温盐、Aquarius遥感盐度等资料,研究了阿拉伯海高盐水入侵孟加拉湾的主要路径及季节变化机制.分析显示阿拉伯海高盐水入侵孟加拉湾存在3种类型,即夏季型、冬季型和春季型.夏季型入侵发生在湾口西部,入侵时间为7—10月,净体积输送达1.53 Sv.冬季型(12月至次年1月)和春季型(3—5月)阿拉伯海高...     

Surface layer mixing during the SAGE ocean fertilization experiment

Vessel-based observations of the oceanic surface layer during the 14-day 2004 SAGE ocean fertilization experiment were conducted using ADCP, CTD and temperature microstructure in a frame of reference moving with a patch of injected SF₆ tracer. During the experiment the mixed layer depth z_mld ranged between 50 and 80 m, with several re-stratifying events that brought z_mld up to less than 40 m. These re-stratifying events were not directly attributable to local surface-down development of stratification and were more likely associated with horizontal variation in density structure. Comparison between the CTD and a one-dimensional model confirmed that the SAGE experiment was governed by 3-d processes. A new method for estimating z_mld was developed that incorporates a component that is proportional to density gradient. This highlighted the need for well-conditioned near-surface data which are not always available from vessel-based survey CTD profiles. A centred-displacement scale, L_c, equivalent to the Thorpe lengthscale, reached a maximum of 20 m, with the eddy-centroid located at around 40 m depth. Temperature gradient microstructure-derived estimates of the vertical turbulent eddy diffusivity of scalar (temperature) material yielded bin-averaged values around 10⁻³ m² s⁻¹ in the pycnocline rising to over 10⁻² m² s⁻¹ higher in the surface layer. This suggests transport rates of nitrate and silicate at the base of the surface layer generate mixed layer increases of the order of 38 and 13 mmol/m²/day, respectively, during SAGE. However, the variability in measured vertical transport processes highlights the importance of transient events like wind mixing and horizontal intrusions.     

Temporal Irregularities in the Macrobenthic Community and Deep-Water Advection in Wismar Bay (Western Baltic Sea)

Wismar Bay is a shallow coastal embayment in the Western Baltic Sea which is polluted by various industries. Macrobenthos data collected between 1986–91 are examined for qualitative and quantitative changes attributable to oxygen depletion and the subsequent time needed for recovery. Regular oceanographic surveys since 1976 indicate one episode of oxygen deficiency, caused by deep-water intrusion into the study area. However, principal component analyses show that the benthic community alternated between periods of relative stability and sudden change at both of the deeper sites examined. Deep-water intrusions from outside the bay are documented twice followed by sudden changes in the benthic community, but similar events may also have occurred in other years. The benthos showed little resilience when impacted, and the changes in the benthic community during July–August are proposed to monitor the future influence of the deep-water intrusions.     

On the dynamics and effects of double-diffusively driven intrusions

Some of the characteristics of intrusive finestructure observed in oceanic fronts suggest that salt fingering is active in the intrusions. An extension of Stern's 1967 study of the stability of a thermohaline front to intrusive finestructure driven by salt fingers is presented to investigate this hypothesis. Intrusions are found to grow due to the salt finger induced density fluxes even in the presence of small scale momentum dissipation. The presence of this dissipation defines a fastest growing mode for the disturbance which has physical characteristics not unlike those observed in oceanic fronts. The model results do not agree well with the laboratory studies of intrusions. For many fronts, the model requires initial perturbations in the front which can support salt fingers. Linear internal waves are investigated to determine if they can provide the initial perturbation. It is shown that, away from the equator, the interaction between internal waves and intrusions is weak because of a mismatch of time scales. Finally, growing intrusions are shown to flux heat, salt and density across fronts. The senses of these fluxes are to run down the lateral gradients of many oceanic fronts.     

Double-celled circulation in coastal upwelling

Simple numerical experiments on two-dimensional coastal upwelling are made with emphasis on the role of non-geostrophic solenoidal field of density in the formation of double-celled circulation and multi-celled density front. Geometry of shelf and slope is not taken into account. Existence of poleward undercurrent presumably caused by the longshore variation of the large scale pressure field is also suppressed for the sake of simplicity.The results are, (1) double-celled circulation revealed in the present experiment is closely related with the internal frictional layer, where the horizontal density gradient balances with the vertical gradient of the longshore velocity and the vertical diffusion of the vorticity. (2) density front formed by the emergence of the pycnocline to the sea surface is successively advected offshoreward by the Ekman transport. (3) the pycnocline intersecting the sea surface forms the density front which is nearly vertical on account of the small scale convection. The surface currents converge at the front and construct an anti-clockwise circulation (viewed from the lee side). (4) small coefficient of eddy viscosity and strong wind stress lead the Ekman transport unstable and form a multi-celled structure in the frontal region.     

A numerical experiment on the anomalous southward intrusion of the Oyashio east of Japan

In recent years, anomalous southward intrusions of the Oyashio have been observed frequently from winter to late spring. A barotropic model is used to see the occurrence of the Oyashio intrusion, with special reference to a short time lag between the change in the wind stress in midwinter and the occurrence of the Oyashio intrusion generally in spring of the same year. It is shown that the barotropic response of the ocean to the change in wind stress is fast, and its representative time scale is about 50 days at most. The southward shift of the Oyashio and the subarctic circulation are simulated quantitatively, when the imposed wind stress is changed from the mean wind stress prior to no Oyashio intrusion to that prior to the Oyashio intrusion. It is suggested that the southward intrusion of the Oyashio is a phenomenon connected with the global change in atmospheric circulation.     

Effects of tidally induced eddies on sporadic Kuroshio-water intrusion (kyucho)

The sudden intrusion of Kuroshio warm water into the Bungo Channel (kyucho) occurs mainly at neap tides during summer, suggesting that tidal mixing is one of the essential factors regulating kyucho. In order to clarify the physical mechanisms responsible for the regulation of kyucho, we carry out non-hydrostatic three-dimensional numerical experiments allowing Kuroshio warm water to intrude into a strong tidal mixing region. It is shown that the Kuroshio warm water can (or cannot) pass through the tidal mixing regions off the east coast of the Bungo Channel during neap (or spring) tides. The analysis of the dynamic balance off the east coast of the Bungo Channel shows that tidal residual currents generated by tidal flow interaction with complicated land configurations off the east coast of the Bungo Channel can also play an important role in regulating kyucho. In order to assess separately the effects of tidal mixing and tidal residual currents on kyucho, we incorporate the parameterized vertical mixing and tidal stresses into the numerical model instead of tidal currents. It is demonstrated that tidal mixing cannot by itself block the northward intrusion of Kuroshio warm water, and that an additional effect induced by tidal residual eddies equivalent to horizontal mixing is needed to regulate kyucho. This strongly suggests that the basin–ocean water exchange processes in areas with complicated land configurations can only be reproduced by taking into account the effects of tidal residual eddies on a 1-km scale in addition to tidal mixing effects evaluated by microstructure measurements.     

Variation in vertical stress in the Baram Basin, Brunei: tectonic and geomechanical implications

The vertical or lithostatic stress is an important factor in tectonic and geomechanical studies and is commonly used in the prediction of pore pressures and fracture gradients. However, the vertical stress is not always calculated in situ and the approximation of 1.0 psi/ft (22.63 MPa/km) is often used for the vertical stress gradient. Vertical stress has been determined in 24 fields in the Baram Basin, Brunei, using density log and checkshot velocity survey data. The Baram Basin shows a variation in vertical stress gradient between 18.3 and 24.3 MPa/km at 1500 m depth below the surface. This variation has a significant effect on in situ stress related issues in field development such as wellbore stability and fracture stimulation. The variation is caused by a bulk rock density change of 2.48–2.07 g/cm³ from the hinterland of the delta to its front. Differential uplift and erosion of the delta hinterland and undercompaction associated with overpressure are the interpreted causes of the density and hence vertical stress variation.     

Thermal fronts and cross-frontal heat flux in the southern Huanghai Sea and the East China Sea

Synoptic features in/around thermal fronts and cross-frontal heat fluxes in the southern Huanghai./Yellow Sea and East China Sea （HES） were examined using the data collected from four airborne expendable bathythermograph surveys with horizontal approxmately 35 km and vertical 1 m（from the surface to 400 m deep） spacings. Since the fronts are strongly affected by HES current system, the synoptic thermal features in/around them represent the interaction of currents with surrounding water masses. These features can not be obtained from climatological data. The identified thermal features are listed as follows ： （ 1 ） multiple boundaries of cold water, asymmetric thermocline intrusion, locally-split front by homogeneous water of approxmately 18 ℃, and mergence of the front by the Taiwan Warm Current in/around summertime southern Cheju - Changjiang/Yangtze front and Tsushima front; （2） springtime frontal eddy-like feature around Tsushima front; （3） year-round cyclonic meandering and summertime temperature-inversion at the bottom of the surface mixed layer in Cheju - Tsushima front; and （4） multistructure of Kuroshio front. In the Kuroshio front the mean variance of vertical temperature gradient is an order of degree smaller than that in other HES fronts. The southern Cheju- Changjiang front and Cheju -Tsushima front are connected with each other in the summer with comparable cross-frontal temperature gradient. However, cross-frontal heat flux and lateral eddy diffusivity are stronger in the southern Cheju - Changjiang front. The cross-frontal heat exchange is the largest in the mixing zone between the modified Huanghai Sea bottom cold water and the Tsushima Warm Current, which is attributable to enhanced thermocline intrusions.     

Prediction of salinity intrusion in the sheltered estuary of Terengganu River in Malaysia using 1-D empirical intrusion model

Generally one dimensional(1-D) empirical salinity intrusion model is limited to natural alluvial estuary. However,this study attempts to investigate its ability to model a sheltered alluvial estuary of the Terengganu River in Malaysia. The constructed breakwater at the mouth of the river shelters the estuary from direct influence of the open sea. The salinity density along the estuary was collected during the wet and dry seasons for scenarios before and after the constructed breakwater. Moreover, the freshwater discharges, tidal elevations and bathymetry data were also measured as model inputs. A good fit was demonstrated between simulated and observed variables,namely salinity distribution and intrusion length for both scenarios. Thus, the results show that 1-D empirical salinity model can be utilized for sheltered estuarine condition at the Terengganu Estuary, but with an appropriate determination of an initial point. Furthermore, it was observed that the salinity intrusion in the study area is largely dependent on the freshwater discharge rather than tidal elevation fluctuations. The scale of the salinity intrusion length in the study area is proportional to the river discharge of the –1/2 power. It was appeared that the two lines of the 1-D empirical salinity model and discharge power based equation fitted well to each other, with the average predicted minimum freshwater discharge of 150 m3/s is going to be required to maintain acceptable salinity levels during high water slack(HWS) near the water intake station, which is located at 10.63 km from river mouth.     

Implementation of baroclinic terms in a three-dimensional hydrodynamic model and its application to Anzali Port, Iran

Baroclinic terms have been implemented in a three-dimensional fully hydrodynamic model developed by Badiei et al. [2008. A three-dimensional non-hydrostatic boundary fitted model for free surface flows. International Journal for Numerical Methods in Fluids, 56(6), 607-627] modifying its momentum equations to account for density gradients and utilizing the scalar (salinity, temperature, etc.) conservation equation (SCE) and a state equation for the calculation of density. In the solution of advection-diffusion terms of the governing Navier-Stokes equations (NSE) and SCE, a symmetric splitting method was applied to ensure the long-term stability of simulations. Correction terms proposed by Ruddic et al. (1995) were applied to SCE to ensure the conservation of the scalar quantity. In the presence of baroclinic terms, the zero gradient pressure in the vertical direction in the vicinity of surface and bottom boundaries assumed by Badiei et al. [2008. A three-dimensional non-hydrostatic boundary fitted model for free surface flows. International Journal for Numerical Methods in Fluids, 56(6), 607-627] created spurious currents. This problem was solved by assuming a hydrostatic pressure variation at those boundaries. The ability of extended model was validated by comparing its results with an experimental test case. The simulation of hydrodynamic and salt intrusion at Anzali Port located at the southern coasts of Caspian Sea in Iran was carried out by the model with both barotropic and baroclinic modes. The simulated results with baroclinic mode show a better agreement with measured data as compared to the results of barotropic mode that clearly demonstrate the significance of baroclinic terms in the simulation of cyclic intrusion of salt wedge into the Port Basin.     

Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling

Two physical parameters are introduced into the basic ocean equations to generalize numerical ocean models for various vertical coordinate systems and their hybrid features. The two parameters are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara [Kasahara, A., 1974. Various vertical coordinate systems used for numerical weather prediction. Mon. Weather Rev. 102, 509–522], the Jacobian pressure gradient formulation of Song [Song, Y.T., 1998. A general pressure gradient formation for ocean models. Part I: Scheme design and diagnostic analysis. Mon. Weather Rev. 126 (12), 3213–3230], and a newly introduced parametric function that permits both Boussinesq (volume-conserving) and non-Boussinesq (mass-conserving) conditions. Based on this new formulation, a generalized modeling approach is proposed. Several representative oceanographic problems with different scales and characteristics––coastal canyon, seamount topography, non-Boussinesq Pacific Ocean with nested eastern Tropics, and a global ocean model––have been used to demonstrate the model’s capabilities for multiscale applications. The inclusion of non-Boussinesq physics in the topography-following ocean model does not incur computational expense, but more faithfully represents satellite-observed ocean-bottom-pressure data. Such a generalized modeling approach is expected to benefit oceanographers in solving multiscale ocean-related problems by using various coordinate systems on the same numerical platform.