Energetics of lateral eddy diffusion/advection：Part Ⅲ. Energetics of horizontal and isopycnal diffusion/advection

Gravitational Potential Energy （GPE） change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps： stirring and sub scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.     

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 ad vection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial hori zontal 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 hori zontal advection in the commonly used Eulerian coordinates may become one of the most challenging ob stacles 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.     

Energetics of lateral eddy diffusion/advection：Part Ⅰ. Thermodynamics and energetics of vertical eddy diffusion

Two important nonlinear properties of seawater thermodynamics linked to changes of water density, cabbeling and elasticity(compressibility), are discussed. Eddy diffusion and advection lead to changes in density; as a result, gravitational potential energy of the system is changed. Therefore, cabbeling and elasticity play key roles in the energetics of lateral eddy diffusion and advection. Vertical eddy diffusion is one of the key elements in the mechanical energy balance of the global oceans. Vertical eddy diffusion can be conceptually separated into two steps: stirring and subscale diffusion. Vertical eddy stirring pushes cold/dense water upward and warm/light water downward; thus, gravitational potential energy is increased. During the second steps, water masses from different places mix through subscale diffusion, and water density is increased due to cabbeling. Using WOA01 climatology and assuming the vertical eddy diffusivity is equal to a constant value of 2×103 Pa2/s, the total amount of gravitational potential energy increase due to vertical stirring in the world oceans is estimated at 263 GW. Cabbeling associated with vertical subscale diffusion is a sink of gravitational potential energy, and the total value of energy lost is estimated at 73 GW. Therefore, the net source of gravitational potential energy due to vertical eddy diffusion for the world oceans is estimated at 189 GW.     

Appendix.Why GPE source due to sigma diffusion is so large

The GPE source and sink due to stirring and cabbeling along sigma surfaces is much larger than that associated with hori zontal diffusion or isopycnal diffusion. This must be linked to the special way of handling lateral diffusion in the sigma mod els. We argue that the largeness of source and sink associated with sigma diffusion is due to the fact that in sigma models, warm water parcels from shallow levels is assumed to be mixed with cold water parcel from deeper levels. Mixing water par cels with such a large difference in properties can leads to big change in density and thus strong source and sink of GPE. As an example, we demonstrate the large GPE source asso ciated with sigma-surface stirring related to steep topography. For simplicity, we will use a simple one-dimensional periodic topography with valleys and seamounts lining up one next to another, as shown in Fig. A1. The pressure grid over the valley stations is taken as the standard pressure grid for the commonly used climatological datasets, such as WOA01 and WOA09, i.e. the center of the bottom grid in the valley is at 5500 （104 Pa）, with the corresponding sea floor at 5 750 （104 PaL Thus, the cen- ters of grid box in the vertical direction at the valley station are at O, 10, 20, 30, 50, 75, 100, 125, 150, 200, 250, 300, 400, 500, 600, 700, 800, 900, 1000, 1 100, 1200, 1300, 1400, 1500, 1750, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500 （104 Pa）.     

Simulation of three-dimensional cohesive sediment transport in Hangzhou Bay, China

Sediment transport in the Hangzhou Bay is extremely complicated due to its bathymetry and hydrodynamic conditions. The ECOMSED model is employed to simulate three-dimensional (3-D) cohesive sediment transport in Hangzhou Bay. Dynamical factors such as Coriolis force, tides, salinity, river discharges, and waves are considered in the model. The wave parameters, including the significant wave height, period, and direction, are calculated with the SWAN model. The Grant-Madsen model is introduced for the bed shear stress due to the combined effect of waves and currents. The formulation of bed shear stress used to calculate the sink/source terms is modified based on previous research that sufficiently validated the formulation with measurement data. The integrated model of the above-mentioned models is applied to simulate sediment transport in Hangzhou Bay. The results of the simulation agree well with field observations concerning the distribution of suspended sediment, indicating that the sediments are remarkably suspended in Hangzhou Bay under the action of waves and currents.     

PHYSICAL AND MATHEMATICAL MODELS OF POLLUTION DISPERSION IN THE YANGTZE ESTUARY

The method of combining physical model with mathematical model is described to study the concentration profile of pollutant dispersion in the Yangtze Estuary. Two contents are included, the experiment of jet in the tidal physical model and two-dimensional calculations of advection and diffusion using momentum and mass conservation equations of unsteady flow. The feature of dispersion in the tidal flow, which is different from that in the steady flow such as rivers, is explained. The capabilities of dillution and dispersion mainly depend on the volume of runoff and tidal range. Finally, the results of the measurement and calculation are presented, and it can be seen that they are in good agreement.     

Tracing surface seawater mixing and nutrient transport by 222Rn on the northern coast of Beibu Gulf,China

The transport and diffusion of substances in seawater are limited by the mixing motion of water bodies, while the main forms of mixing in offshore water bodies are advection and eddy diffusion. The eddy diffusion process of water indicates the possible transport direction of dissolved substances. However, the complex environment in the coastal zone makes it difficult to quantitatively assess the water diffusion process. ²²²Rn is a useful tool to trace the diffusion process of water bo...     

Simulation of the Fate of Faecal Bacteria in Estuarine and Coastal Waters Based on A Fractionated Sediment Transport Model

A two-dimensional depth-integrated numerical model is refined in this paper to simulate the hydrodynamics, graded sediment transport process and the fate of faecal bacteria in estuarine and coastal waters. The sediment mixture is divided into several fractions according to the grain size. A bed evolution model is adopted to simulate the processes of the bed elevation change and sediment grain size sorting. The faecal bacteria transport equation includes enhanced source and sink terms to represent bacterial kinetic transformation and disappearance or reappearance due to sediment deposition or re-suspension. A novel partition ratio and dynamic decay rates of faecal bacteria are adopted in the numerical model. The model has been applied to the turbid water environment in the Bristol Channel and Severn estuary, UK. The predictions by the present model are compared with field data and those by non-fractionated model.     

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.     

A preliminary analysis of physical mechanism of transformation process from a landed typhoon into an extratropical cyclone

A diagnostic study is performed in the paper on the process of typhoon Norris (1980) transforming into an ex-tratropical cyclone after its landing over Southeast China. The main findings are as follows:The changes of kinetic energy are mainly attributed to the generation due to non-divergent wind. During the early stage of the typhoon landing, there exits only a small quantity of kinetic energy exchanging with the environment. And after it is transformed into an extratropical cyclone, a large amount of kinetic energy is exported from the system toward the environment.The horizontal and vertical flux-divergence terms of eddy available potenlial energy are the prominent sinks in the budgets of eddy kinetic energy. The generations of eddy kinetic energy due to both the barotropic and baroclinic processes are source terms. The former is remarkable during the initial stage. But after the depression is transformed into an extratropical cyclone, the roles of the generation by the barotropic and baroclinic proc     

北冰洋水体对格陵兰海混合增密对流的可能影响分析

格陵兰海内发生的等密度混合后产生的增密对流是重要的对流现象之一。北冰洋正在发生快速变化,其内水团变性以及环流系统的改变都将使格陵兰海等密度混合对流发生明显变化,继而对全球气候变化产生影响。以往关于等密度混合对流的研究很少,大都集中在对流发生海域。由于等密度混合的主体是大西洋回流水与北冰洋流出水体,本文目的是探讨北极内部不同海域的水体会对混合增密对流造成的可能影响。文中定义了有效对流速度,强调水平温度梯度和垂向层化强度是影响有效对流速度的决定性因素;水平温度差越大,垂向层化越弱,产生的对流越强。发生在东格陵兰极锋处的有效对流都是大西洋的水体,一部分是在格陵兰海回流的大西洋回流水;一部分是在北冰洋潜沉并回流的北极大西洋水,该水体在北冰洋循环的时间越长,温度差越大,产生的有效对流越强。而横越北冰洋的太平洋水因密度过低而不能参与等密度混合对流,加拿大海盆主盐跃层之上的水体也都不能参与对流。北冰洋几个海盆深层水的温度差异明显,有可能与格陵兰海深层水形成有效对流;但是,由于深层水流速低、湍流混合弱、水平温度梯度小,是否可以产生有效对流尚不清楚。     

琼州海峡的一个三维泥沙扩散模式

通过建立一个三维陆架海数值模式来预报近海潮流和泥沙浓度的对流扩散,并应用于琼州海峡跨海工程的前期数值预测。预测结果表明,海区潮流的涨落、岸线形状、海底地形及源强位置与泥沙在近海的输运扩散关系密切,模拟情形基本合理,表明该模式适合应用于河口、近岸等涉海海洋工程海域的流场及泥沙扩散的三维数值预测,为相关的水动力环境要素和水质影响评价提供一定的参考价值。     

A BFG model for calculation of tidal current and diffusion of pollutants in nearshore areas

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再谈海冰边缘区域中尺度涡旋形成机制——非线性平流

利用三维海洋模式与二维海冰模式耦合,研究海冰边缘区域中尺度涡旋形成最重要的机制之一——非线性平流机制。二维海洋模型模拟结果表明,非线性平流机制在水深比较浅的时候更加重要。不同于把海洋考虑成一个正压流体的二维模型,三维海洋模型中海冰通过海-冰相互作用直接影响海洋表层。我们发现在三维海洋模型实验中,中尺度涡旋和海洋表面抬升都对水深变化敏感。海流速度的垂直结构表面,当海水变浅,各层海流都变得更快。相同风应力作用相同时间之后,表面抬升与海水深度成反比关系。同时我们还发现由于垂直运动,在三维海洋模型实验结果中,海面抬升非常小,只有二维海洋模型实验结果的1%。垂直运动是三维海洋模型和二维海洋模型实验结果不同的根本原因。     

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.     

The effects of horizontal advection on the spring bloom of phytoplankton in the central Southern Huanghai Sea

An algal bloom is defined as a relatively rapid increase in the biomass of phytoplankton in an aquatic system. During 30 March to 24 April 2007, a cruise was conducted in the central Southern Huanghai Sea to investigate the spring bloom processes. The spatial and temporal variations of phytoplankton are discussed based on the in-situ observations and simultaneous remote sensing data. The explosive algal blooming varied quickly in temporal and spatial scales, due to the highly patchy distribution. Data obtained at the 2 anchor stations (BM1 and BM2) were analyzed in the present study. Horizontal advection is speculated to be responsible for the abrupt decrease in the concentration of chlorophyll-a at stations BM1 and BM2. At station BM2, the intermediate high chlorophyll-a concentration, coinciding with the low temperature, was found to be advected from the inshore colder water mass located to the east of the site.