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1.
HUANG Rui Xin 《海洋学报(英文版)》2014,33(3):58-81
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. 相似文献
2.
An unrealistically high-salinity maximum is found to develop in a high-resolution model of the north and equatorial Atlantic below the shallow halocline in the Gulf of Guinea. The spurious water mass with salinities too high by as much as 1 psu is formed when the vertical advection is treated by the standard central-differencing advection scheme. The problem is considerably reduced either by increasing the vertical resolution of the numerical grid, or by switching to a higher-order upwind-weighted scheme for vertical advection. This note stresses the need for a careful consideration of vertical discretization even in typical high-resolution ocean general circulation models (OGCMs). Particular attention is needed for studying heat and salt budgets or transports of biogeochemical tracers. 相似文献
3.
HUANG Rui Xin 《海洋学报(英文版)》2014,33(3):19-39
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. 相似文献
4.
Ensuring confidence in radionuclide-based sediment chronologies and bioturbation rates 总被引：1，自引：0，他引：1
Sedimentary records of naturally occurring and fallout-derived radionuclides are widely used as tools for estimating both the ages of recent sediments and rates of sedimentation and bioturbation. Developing these records to the point of data interpretation requires careful sample collection, processing, analysis and data modeling. In this work, we document a number of potential pitfalls that can impact sediment core records and their interpretation. This paper is not intended as an exhaustive treatment of these potential problems. Rather, the emphasis is on potential problems that are not well documented in the literature, as follows: (1) the mere sampling of sediment cores at a resolution that is too coarse can result in an apparent diffusive mixing of the sedimentary record at rates comparable to diffusive bioturbation rates observed in many locations; (2) 210Pb profiles in slowly accumulating sediments can easily be misinterpreted to be driven by sedimentation, when in fact bioturbation is the dominant control. Multiple isotopes of different half lives and/or origin may help to distinguish between these two possible interpretations; (3) apparent mixing can occur due simply to numerical artifacts inherent in the finite difference approximations of the advection diffusion equation used to model sedimentation and bioturbation. Model users need to be aware of this potential problem. Solutions to each of these potential pitfalls are offered to ensure the best possible sediment age estimates and/or sedimentation and bioturbation rates can be obtained. 相似文献
5.
Sensitivity studies with a new generalized coordinate ocean model are performed in order to compare the behavior of bottom boundary layers (BBLs) when terrain-following (sigma or combined sigma and z-level) or z-level vertical grids are used, but most other numerical aspects remain unchanged. The model uses a second-order turbulence closure scheme that provides surface and BBL mixing and results in a quite realistic climatology and deep water masses after 100 year simulations with a coarse resolution (1° × 1°) basin-scale terrain-following grid. However, with the same turbulence scheme but using a z-level grid, the model was unable to produce dense water masses in the deep ocean. The latter is a known problem for coarse resolution z-level models, unless they include highly empirical BBL schemes.A set of dense water overflow experiments with high-resolution grids (10 and 2.5 km) are used to investigate the influence of model parameters such as horizontal diffusivity, vertical mixing, horizontal resolution, and vertical resolution on the simulation of bottom layers for the different coordinate systems. Increasing horizontal diffusivity causes a thinner BBL and a bottom plume that extends further downslope in a sigma grid, but causes a thicker BBL and limited downslope plume extension in a z-level grid. A major difference in the behavior of the BBL in the two grids is due to the larger vertical mixing generated by the turbulence scheme over the step-like topography in the z-level grid, compared to a smaller vertical mixing and a more stably stratified BBL in the sigma grid. Therefore, the dense plume is able to maintain its water mass better and penetrates farther downslope in the sigma grid than in the z-level grid. Increasing horizontal and vertical resolution in the z-level grid converges the results toward those obtained by a much coarser resolution sigma coordinate grid, but some differences remain due to the basic differences in the mixing process in the BBL. 相似文献
6.
We point out one problem of the grid advection schemes when used in wave models in coastal areas. The deficiency of the schemes is investigated by means of the ‘third' generation WAM wave model, in which the wave energy is advected by a first order upwind scheme. Two similar, alternative modifications of this scheme are analyzed, the second of which is shown to solve most of the problems encountered with advection along the co-ordinate axes. 相似文献
7.
W. E. Rogers J. M. Kaihatu H. A. H. Petit N. Booij L. H. Holthuijsen 《Ocean Engineering》2002,29(11):1357-1390
The numerical schemes for the geographic propagation of random, short-crested, wind-generated waves in third-generation wave models are either unconditionally stable or only conditionally stable. Having an unconditionally stable scheme gives greater freedom in choosing the time step (for given space steps). The third-generation wave model SWAN (“Simulated WAves Nearshore”, Booij et al., 1999) has been implemented with this type of scheme. This model uses a first order, upwind, implicit numerical scheme for geographic propagation. The scheme can be employed for both stationary (typically small scale) and nonstationary (i.e. time-stepping) computations. Though robust, this first order scheme is very diffusive. This degrades the accuracy of the model in a number of situations, including most model applications at larger scales. The authors reduce the diffusiveness of the model by replacing the existing numerical scheme with two alternative higher order schemes, a scheme that is intended for stationary, small-scale computations, and a scheme that is most appropriate for nonstationary computations. Examples representative of both large-scale and small-scale applications are presented. The alternative schemes are shown to be much less diffusive than the original scheme while retaining the implicit character of the particular SWAN set-up. The additional computational burden of the stationary alternative scheme is negligible, and the expense of the nonstationary alternative scheme is comparable to those used by other third generation wave models. To further accommodate large-scale applications of SWAN, the model is reformulated in terms of spherical coordinates rather than the original Cartesian coordinates. Thus the modified model can calculate wave energy propagation accurately and efficiently at any scale varying from laboratory dimensions (spatial scale O(10 m) with resolution O(0.1 m)), to near-shore coastal dimension (spatial scale O(10 km) with resolution O(100 m)) to oceanic dimensions (spatial scale O(10 000 km) with resolution O(100 km). 相似文献
8.
Ulf Gräwe 《Ocean Modelling》2011,36(1-2):80-89
Stochastic differential equations (SDEs) offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications, which are dominated by stochastic processes, such as diffusion. As for deterministic ordinary differential equations (ODEs), various numerical scheme exist for solving SDEs. In this paper various particle-tracking schemes are presented and tested for accuracy and efficiency (time vs. accuracy). To test the schemes, the particle tracking algorithms are implemented into a community wide used 1D water column model. Modelling individual particles allows a straightforward physical interpretation of the involved processes. Further, this approach is strictly mass conserving and does not suffer from the numerical diffusion that plagues grid-based methods. Moreover, the Lagrangian framework allows to assign properties to the individual particles, that can vary spatially and temporally. The movement of the particles is described by a stochastic differential equation, which is consistent with the advection–diffusion equation. Here, the concentration profile is represented by a set of independent moving particles, which are advected according to the velocity field, while the diffusive displacements of the particles are sampled from a random distribution, which is related to the eddy diffusivity field.The paper will show that especially the 2nd order schemes are accurate and highly efficient. At the same level of accuracy, the 2nd order scheme can be significantly faster than the 1st order counterpart. This gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost. 相似文献
9.
1 IntroductionThe shallow water equations (SWE) are frequent-ly used as a mathematical model for water flows incoastal areas, lakes, estuaries, etc. Thus, they are animportant tool to simulate a variety of problems relat-ed to coastal engineering, environment, ecology, etc.(Bermúdez et al., 1998). On the basis of solving theone-dimensional (1D) SWE, Hu et al. (2000) have de-veloped a model capable of simulating storm wavespropagating in the coastal surf zone and overtopping asea wall. Ano… 相似文献
10.
A complication of finite-volume triangular C-grid methods is the numerical emergence of horizontal divergence errors that lead to grid-scale oscillations in vertical velocity. Nonlinear feedback via advection of momentum can lead to numerical instability in velocity modes via positive feedback with spurious vertical velocities induced by horizontal divergence truncation error. Existing strategies to mitigate divergence errors such as direct divergence averaging and increased diffusion do not completely mitigate horizontal vertical velocity oscillations. We present a novel elliptic filtering approach to mitigate this spurious error and more accurately represent vertical velocities via improved calculation of horizontal divergences. These results are applied to laminar curved channel flows, demonstrating the applicability of the method to reproduce secondary flow features. 相似文献
11.
用数值模式对河口海岸地区的物质输运进行计算时，平流项的数值格式必须要能对物质浓度锋面进行正确处理，以避免产生过多的数值耗散或频散。本文中设计了一种在网格内设置一些质点并对质点进行跟踪的格式计算平流项。结果表明，质点跟踪格式在一维情形下无频散和几乎没有耗散，在二维情形下无频散和在水深变化剧烈的地方基本避免了垂向数值耗散。与其他数值格式的耗散性和频散性相比，本文中设计的数值格式明显地提高了物质输运方程中平流项的计算精度，在河口海洋物质输运的计算中具有较大的应用价值。 相似文献
12.
为完全拟合河口近海复杂岸线和工程结构以及有效局部加密,设计并建立了一个无结构三角形网格二维河口海岸水动力数值模式。空间离散主要基于有限体积法以保证守恒性,时间积分采用预估修正法以提高精度。水位在三角形网格中心通过连续方程求解;水平x方向和y方向的流速U和V均在网格边中点上通过动量方程求解。流速平流项的求解中采用了TVD格式。TVD流速平流通量为一个一阶迎风格式通量和一个二阶格式通量的组合,一阶格式通量和二阶格式通量根据流速的局部分布情况得出配比,最终组合得到TVD通量。TVD格式具有低耗散和无频散的优点,提高了模式的稳定性。应用实测资料验证建立的模式,结果显示水位、流速和流向的计算值与实测值均符合良好。 相似文献
13.
《Ocean Modelling》2008,20(2):115-133
Using an ice–ocean coupled model on an eddy-admitting, global, 0.4° mesh, we find that simulations of tracer properties and kinetic energy differ much more at high latitudes than at mid-to-low latitudes under different choices for the lateral tracer mixing parameterization, particularly between Gent and McWilliams (GM) mixing, which is Laplacian in form, and biharmonic tracer diffusion. Besides the more physical, rotated diffusivity used in GM, the differences in these two formulations can be traced to two effects, (1) scale selectivity, in which Laplacian forms damp wave energy more quickly than biharmonic mixing formulations, and (2) grid dependence of the diffusion coefficient, which is particularly important at high latitudes where the grid scale decreases dramatically on the sphere. This study explores some effects of these parameterization choices at high latitudes, including the anisotropic GM formulation. Regardless of the mixing parameterization chosen, future global simulations should take into account variations in grid cell area, in order to prevent diffusion from dominating advection in the evolution of high latitude tracers and circulation. 相似文献
14.
A three-dimensional finite difference transport model appropriate for the coastal environment is developed for the solution of the three-dimensional convection-diffusion equation. A higher order upwind scheme is used for the convective terms of the convection-diffusion equation, to minimise the numerical diffusion. The validity of the numerical model is verified through five test problems, whose exact solutions are known. 相似文献
15.
When a steep bottom slope exists, it is well known that conventional methods for calculating horizontal diffusion in sigma-coordinate coastal ocean models causes spurious transport (e.g. salinity, temperature, and sediments) and currents. In this study, a second-order accurate finite-difference algorithm and program have been developed to reduce the spurious numerical diffusion errors. In the proposed algorithm, the finite differencing is performed in the x-z coordinate system to approximate the horizontal gradient. Each variable in the finite differential formation is calculated in the sigma-coordinate grid cells using a second-order Lagrangian interpolation polynomial. In conjunction with a stepwise bottom boundary condition, numerical experiments show that the proposed finite-difference scheme considerably reduces numerical errors compared to conventional approaches when dealing with horizontal diffusion over steep topography, which often occurs in coastal oceans and navigation channels. 相似文献
16.
《Ocean Modelling》2011,40(3-4):351-361
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. 相似文献
17.
When a steep bottom slope exists, it is well known that conventional methods for calculating horizontal diffusion in sigma-coordinate coastal ocean models causes spurious transport (e.g. salinity, temperature, and sediments) and currents. In this study, a second-order accurate finite-difference algorithm and program have been developed to reduce the spurious numerical diffusion errors. In the proposed algorithm, the finite differencing is performed in the x–z coordinate system to approximate the horizontal gradient. Each variable in the finite differential formation is calculated in the sigma-coordinate grid cells using a second-order Lagrangian interpolation polynomial. In conjunction with a stepwise bottom boundary condition, numerical experiments show that the proposed finite-difference scheme considerably reduces numerical errors compared to conventional approaches when dealing with horizontal diffusion over steep topography, which often occurs in coastal oceans and navigation channels. 相似文献
18.
在三维海洋模式POM基础上建立水质模型,采用中心差分格式、迎风格式以及Smolarkiewicz迎风格式离散物质输运方程.以三维理想水槽中连续源排放的浓度场预测为例,分析3种离散格式求解所得的浓度场.结果表明,3种格式的数值解与解析解的偏差均小于20%.中心差分格式会引起解的震荡,导致物质的反向输移,出现浓度负值.迎风格式能够保证浓度的正值,但该格式带来的数值耗散导致数值解与解析解偏离较大.Smolarkiewicz迎风格式在普通迎风格式基础上引入抗扩散流速,经多次叠代,能有效降低计算中的数值耗散,提高了计算精度. 相似文献
19.
A global eddy-permitting ocean-ice coupled model with a horizontal resolution of 0.25 by 0.25 is established on the basis of Modular Ocean Model version 4 (MOM4) and Sea Ice Simulator (SIS). Simulation results are compared with those of an intermediate resolution ocean-ice coupled model with a horizontal resolution of about 1 by 1 . The results show that the simulated ocean temperature, ocean current and sea ice concentration from the eddy-permitting model are better than those from the intermediate resolution model. However, both the two models have the common problem of ocean general circulation models (OGCMs) that the majority of the simulated summer sea surface temperature (SST) is too warm while the majority of the simulated subsurface summer temperature is too cold. Further numerical experiments show that this problem can be alleviated by incorporating the non-breaking surface wave-induced vertical mixing into the vertical mixing scheme for both eddy-permitting and intermediate resolution models. 相似文献
20.
《Oceanologica Acta》2003,26(4):299-309
Effects of discretization scheme on the numerical modeling of 3D Rhône River plume dynamics are investigated. A higher order scheme of total variation diminishing (TVD) type is used to discretize advection terms of both momentum and scalar equations. It is shown that this scheme widely damps the numerical diffusion and improves the representation of the dynamical and density fronts bounding the flow. It enables to accurately investigate the effects of the turbulent diffusion, which was previously masked by the numerical one. Numerical results are also compared to in situ data for two situations related to different wind conditions. For the case without wind stress, associated to supercritical values of the Richardson number, optimized turbulent parameterization allows to recover the plume spreading and thickness, although local diffusion mechanisms are not precisely described. On the other hand, for the seaward wind case, associated to subcritical values of the Richardson number, numerical results and in situ data well agree on both the surface flow and the vertical density structure. 相似文献