Energetics of lateral eddy diffusion/advection：Part Ⅳ. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy （GPE） source and sink due to stirring and cabbeling associated with sigma dif fusion/ advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the exces sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.     

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）.     

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...     

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     

Radium-traced nutrient outwelling from the Subei Shoal to the Yellow Sea: Fluxes and environmental implication

The Subei Shoal is the largest sandy ridge in the southern Yellow Sea and is important source for nutrient loading to the sea. Here, the nutrient fluxes in the Subei Shoal associated with eddy diffusion and submarine groundwater discharge（SGD） were assessed to understand their impacts on the nutrient budget in the Yellow Sea. Based on the analysis of 223 Ra and 224 Ra in the field observation, the offshore eddy diffusivity mixing coefficient and SGD were estimated to be 2.3×10⁸ cm     

A new efficient finite volume modeling of small amplitude free surface flows with unstructured grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k-ε equations in this model. The eddy viscosity is calculated from the k-ε turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field,and then applied to simulate the tidal flow in the Bohai Sea.     

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.     

Development of A Fully Nonlinear Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in eonjunetion with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method, the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWF are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.     

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。     

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。     

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.     

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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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.     

浅海水域水平扩散系数的推算研究

本文根据拉格朗日流与欧拉流自相关系数的相似关系,用渤中8号平台1987年1月和8月的实测资料,分别推算了水平扩散系数。推算结果表明:研究长时间水平扩散时,把潮流看作湍流,所求的扩散系数实际上是潮流扩散系数,其值在10~6cm~2/s范围内;研究短时间水平扩散时,把潮流看作平流,用富里叶变换的长周期合成值从实测值中扣除,所求的扩散系数消除了长周期潮流部分,可认为是湍流扩散,其值在10~4cm~2/s范围内。