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1.
A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations
A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments. 相似文献
2.
The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust. 相似文献
3.
Based on a wave bottom boundary layer model and a sediment advection-diffusion model, seven turbulence schemes are compared regarding their performances in prediction of near-bed sediment suspension beneath waves above a plane bed. These turbulence algorithms include six empirical eddy viscosity schemes and one standard two-equation k-ε model. In particular, different combinations of typical empirical formulas for the eddy viscosity profile and for the wave friction factor are examined. Numerical results are compared with four laboratory data sets, consisting of one wave boundary layer hydrodynamics experiment and three sediment suspension experiments under linear waves and the Stokes second-order waves. It is shown that predictions of near-bed sediment suspension are very sensitive to the choices of the empirical formulas in turbulence schemes. Simple empirical turbulence schemes are possible to perform equally well as the two-equation k-ε model. Among the empirical schemes, the turbulence scheme, combining the exponential formula for eddy viscosity and Swart formula for wave friction factor, is the most accurate. It maintains the simplicity and yields identically good predictions as the k-ε model does in terms of the wave-averaged sediment concentration. 相似文献
4.
不同TVD 格式对内孤立波数值模拟结果影响研究 总被引：1，自引：0，他引：1
为了研究不同TVD格式对内孤立波模拟结果的影响,利用改进后的SUNTANS三维非静压海洋模型,通过理想算例和南海东北部海域内孤立波的模拟,比较分析了求解温盐方程TVD格式的4种经典通量限制函数(superbee, minmod, van Leer和MUSCL)对计算结果的影响。综合理想算例和南海东北部海域模拟结果,在所讨论的4种通量限制函数中,利用MUSCL限制函数所得模拟结果最优,建议在南海东北部海域内孤立波模拟中采用MUSCL限制函数。 相似文献
5.
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
6.
Kern E. Kenyon 《Journal of Oceanography》1978,34(6):288-294
East-west vertical sections centered on Kinmei Seamount (35N, 172E) of potential temperature, salinity, and oxygen, based on recent standard hydrographic measurements, and vertical profiles ofin situ temperature and density (
4) east of the seamount, based on STD data, show contrasting variability in the deep water characteristics east and west of the seamount. These data are consistent with horizontal variations in water mass properties (temperature-salinity and temperature-oxygen curves) east of the seamount between 2,600–3,900 m but not west of the seamount. East of the seamount on surfaces of constant potential temperature (or density) salinity and oxygen are higher at a station 200 km from the seamount than at stations on either side. From these relations and from known deep water properties of the North Pacific, it is suggested that east of the seamount, between 2,600–3,900 m, the observations are consistent with northward flow, which is interpreted to be a western boundary current with an east-west scale of about 300 km. 相似文献
7.
《Ocean Modelling》2008,20(3):293-311
A diagnostic method for calculating physical and numerical mixing of tracers in ocean models is presented. The physical mixing is defined as the turbulent mean tracer variance decay rate. The numerical mixing due to discretisation errors of tracer advection schemes is shown to be the decay rate between the advected square of the tracer variance and the square of the advected tracer and can be easily implemented into any ocean model. The applicability of the method is demonstrated for four test cases: (i) a one-dimensional linear advection equation with periodic boundary conditions, (ii) a two-dimensional flat-bottom lock exchange test case without mixing, (iii) a two-dimensional marginal sea overflow study with mixing and entrainment and (iv) the DOME test case with a dense bottom current propagating down a broad linear slope. The method has a number of advantages over previously introduced estimates for numerical mixing. 相似文献
8.
为了了解海山富钴结壳中金属元素的来源及其形成环境,对中太平洋某海山周围两个站位(一个位于海山斜坡上部,另一个位于海山外围较远处)进行了海水水柱综合水化学分析,发现两个站位溶解氧、pH及营养盐的分布是一致的,反映了两个站位海水化学环境的相似性,而剖面上金属元素含量却存在很大差异,位于海山斜坡上部站位的金属元素含量明显高于离海山较远的站位,说明海山结壳的主要金属来源于海山当地的水岩反应甚至低温热液活动。尽管存在差异,但在两个不同站位均存在近底层金属元素含量高,这印证了通过势温分布推断的本区存在南极底层水(AABW)影响的判断,说明AABW在本研究区确实存在,并且是维持海山斜坡强氧化环境的主要因素,AABW可能同时起着输运部分成矿元素的作用,但两个站位水柱金属元素含量的差异主要揭示了海山区存在水岩反应或者低温热液等当地物质的输入。 相似文献
9.
《Ocean Modelling》1999,1(1):1-15
In regions of sloping isopycnals, isopycnal mixing acting in conjunction with biological cycling can produce patterns in the nutrient field which have negative values of tracer in light water and unrealistically large values of tracer in dense water. Under certain circumstances, these patterns can start to grow unstably. This paper discusses why such behavior occurs. Using a simple four-box model, it demonstrates that the instability appears when the isopycnal slopes exceed the grid aspect ratio (Δz/Δx). In contrast to other well known instabilities of the CFL type, this instability does not depend on the time step or time-stepping scheme. Instead it arises from a fundamental incompatibility between two requirements for isopycnal mixing schemes, namely that they should produce no net flux of passive tracer across an isopycnal and everywhere reduce tracer extrema. In order to guarantee no net flux of tracer across an isopycnal, some upgradient fluxes across certain parts of an isopycnal are required to balance downgradient fluxes across other parts of the isopycnal. However, these upgradient fluxes can cause local maxima in the nutrient field to become self-reinforcing. Although this is less of a problem in larger domains, there is still a strong tendency for isopycnal mixing to overconcentrate tracer in the dense water. The introduction of eddy-induced advection is shown to be capable of counteracting the upgradient fluxes of nutrient which cause problems, stabilizing the solution. The issue is not simply a numerical curiosity. When used in a GCM, different parameterizations of eddy mixing result in noticeably different distributions of nutrient and large differences in biological production. While much of this is attributable to differences in convection and circulation, the numerical errors described here may also play an important role in runs with isopycnal mixing alone. 相似文献
10.
A number of parameterisations for the simulation of mixing processes in the thermocline are compared and tested against the microstructure data of the PROVESS campaigns, conducted in the northern part of the North Sea during the autumn of 1998. The transport term in the turbulent kinetic energy equation is parameterised via the introduction of a third stability function Sk for turbulent energy diffusion. The formulations are compared with a simpler scheme based upon limiting conditions for turbulence variables. Improved results are obtained with a new form of Sk. The best agreement is, however, found with the simpler limiting scheme. This is explained in terms of a turbulence length scale theory for stably stratified turbulence. In agreement with previous laboratory and ocean data it is found that the ratios of the Thorpe and Kolmogorov scales to the Ozmidov length scale approach critical limiting values in the thermocline. The first of these conditions is satisfied when limiting conditions are implemented into the scheme, providing the necessary minimum value for the dissipation rate, whereas the schemes without limiting conditions fail to produce this critical ratio. The basic reason for this failure is that the Thorpe scale is overestimated, which is shown to be connected to an even larger overprediction of the dissipation rate of temperature variance. To investigate the impact of non-resolved advective processes and salinity stratification on the turbulence predictions, additional numerical experiments were conducted using a simple scheme for data assimilation. The best agreement is found again with the limiting scheme, which is able to make reasonable predictions for the dissipation rate without knowing the detailed shape of the mean stratification profile. It is shown that advective transport due to tidally and wind-driven motions has a non-negligible impact on vertical mixing. This is seen in the data and the models by periodic enhancements of turbulent mixing inside the thermocline. 相似文献
11.
针对遥感资料与实况观测融合重构三维海温场的问题，改进了最优插值中的先验统计信息估计，并研究了背景场和观测项的各自影响机制。在最优插值中，将背景场分别取为平均气候场（静态方案）和遥感合成场（动态方案）；在最优融合前，用后验诊断方法迭代优化了背景误差和观测误差协方差；融合完成后，用观测空间诊断误差和模式格点指标对比分析两种方案。主要结论:（1）动态方案相对于静态方案分析误差减小的绝对量值由二者的观测误差之差决定、减小的相对程度由二者的背景误差之比决定；（2）背景场的调整作用在中高纬占优势、在赤道海域与观测项调整作用相当，是由协方差相关尺度的准纬向分布特征决定的；（3）动态分析场的中尺度信号谱能量整体比静态分析场高1~3个量级，但在热带海域相当；（4）遥感资料通过分辨实况观测所无法分辨出来的海温中尺度特征，达到减小误差、提高有效分辨率的效果。 相似文献
12.
2014年冬季对西太平洋雅浦Y3海山区和从西太平洋暖池区到黑潮源区之间的大洋海域的浮游动物进行了调查研究，分析了海山区和大洋海域大型浮游动物群落的物种组成、丰度和分布，并比较了两个海域大型浮游动物群落的差异，结合温度、盐度和叶绿素a浓度等环境因子数据，分析了海山对大型浮游动物群落的影响。结果表明，Y3海山区和大洋海域的大型浮游动物群落物种组成存在差异，二者的群落相似度系数为68.4%，两个海域的优势种/类群也不尽相同，海山区的优势种/类群是磷虾各期幼体、尖额磷虾和蛮𧊕，而大洋海域的优势种/类群分别是磷虾后期幼体、手磷虾、蛮𧊕、尖额磷虾和莹虾。大型浮游动物群落在海山区的平均丰度和最大丰度都要高于大洋海域，但海山区的生物多样性指数、均匀度指数和生物量占比都低于大洋海域，因而Y3海山对大型浮游动物群落的海山效应不明显。通过相关性分析和主成分分析结果可以看出，海山区的首要影响环境因子是盐度，而大洋海域则是温度；海山区和大洋海域的大型浮游动物丰度分别与200m层盐度和平均温度呈负相关关系，并且在两个调查海域均未发现大型浮游动物的丰度和生物量分布与叶绿素a浓度之间存在显著的相关关系。 相似文献
13.
A data assimilation scheme used in the updated Ocean three-dimensional Variational Assimilation System (OVALS),OVALS2,is described.Based on a recursive filter (RF) to estimate the background error covariance (BEC) over a predetermined scale,this new analysis system can be implemented with anisotropic and isotropic BECs.Similarities and differences of these two BEC schemes are briefly discussed and their impacts on the model simulation are also investigated.An idealized experiment demonstrates the ability of the updated analysis system to construct different BECs.Furthermore,a set of three years experiments is implemented by assimilating expendable bathythermograph (XBT) and ARGO data into a Tropical Pacific circulation model.The TAO and WOA01 data are used to validate the assimilation results.The results show that the model simulations are substantially improved by OVALS2.The inter-comparison of isotropic and anisotropic BEC shows that the corresponding temperature and salinity produced by the anisotropic BEC are almost as good as those obtained by the isotropic one.Moreover,the result of anisotropic RF is slightly closer to WOA01 and TAO than that of isotropic RF in some special area (e.g.the cold tongue area in the Tropic Pacific). 相似文献
14.
一个两时间层分裂显格式海洋环流模式(MASNUM)及其检验 总被引：1，自引：0，他引：1
HAN Lei 《海洋学报(英文版)》2014,33(11):11-35
A two-time-level, three-dimensional numerical ocean circulation model（named MASNUM） was established with a two-level, single-step Eulerian forward-backward time-differencing scheme. A mathematical model of large-scale oceanic motions was based on the terrain-following coordinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-backward method was adopted to replace the most preferred leapfrog scheme as the time-differencing method for both barotropic and baroclinic modes. The forward-backward method is of second-order of accuracy, computationally efficient by requiring only one function evaluation per time step, and free of the computational mode inherent in the three-level schemes. This method is superior to the leapfrog scheme in that the maximum time step of stability is twice as large as that of the leapfrog scheme in staggered meshes thus the computational efficiency could be doubled. A spatial smoothing method was introduced to control the nonlinear instability in the numerical integration. An ideal numerical experiment simulating the propagation of the equatorial Rossby soliton was performed to test the amplitude and phase error of this new model. The performance of this circulation model was further verified with a regional（northwest Pacific） and a quasi-global（global ocean simulation with the Arctic Ocean excluded） simulation experiments. These two numerical experiments show fairly good agreement with the observations. The maximum time step of stability in these two experiments were also investigated and compared between this model and that model which adopts the leapfrog scheme. 相似文献
15.
MASNUM-WAM海浪模式集合Kalman滤波同化研究-I.风场扰动对海浪模拟影响 总被引：1，自引：1，他引：0
模式集合样本的代表性和观测信息的可靠性是制约数据同化效果的重要因素,而前者对海浪模式同化的影响尤为显著。由于海浪模式对初始场的敏感性较弱,来自大气的风输入源函数是海浪的重要能量输入,如何合理地对风输入进行扰动,构造海浪的集合模式运行,是实现和改进海浪模式集合Kalman滤波同化的关键问题。为了实现海浪模式集合运行,本文提出了风场的三种集合扰动方案,分别为：纯随机数、随机场和时间滞后的风场扰动方法。本研究利用2014年1月ECMWF全球风场,基于这三种风场扰动方法开展了集合海浪模式的集合运行实验,并统计分析了海浪特征要素（有效波高）和二维波数谱对风场扰动的响应。结果表明,随机场集合扰动方案所构造的风场集合效果最佳,所得海浪模拟结果的集合样本发散度适中,能够较为合理地反映背景误差的统计特征,可用于进一步的集合Kalman滤波海浪数据同化实验。 相似文献
16.
象山港水交换数值研究──Ⅰ.对流-扩散型的水交换模式 总被引：9，自引：2，他引：7
以溶解态的保守性物质作为湾内水的示踪剂,建立了对流－扩散型的海湾水交换数值模型。数值模型使用参数化的方法把重力环流和潮振荡的垂向剪切作用的水平混合效应包纳在水平二维的示踪剂对流－扩散方程中。在空间网距较小时,模型的稳定性和守恒性均可满足海湾水交换研究的需要。 相似文献
17.
A two-dimensional vertical (2DV) non-hydrostatic boundary fitted model based on a Godunov-type shock-capturing scheme is introduced and applied to the simulation of waves from deep water up to the swash zone. The effects of shoaling, breaking, surf zone dissipation and swash motions are considered. The application of a Godunov-type shock-capturing algorithm together with an implicit solver on a standard staggered grid is proposed as a new approach in the 2DV simulation of large gradient problems such as wave breaking and hydraulic jumps. The complete form of conservative Reynolds averaged Navier–Stokes (RANS) equations are solved using an implicit finite volume method with a pressure correction technique. The horizontal advection of the horizontal velocity is solved by an explicit predictor–corrector method. Fluxes are predicted by an exact Riemann solver and corrected by a downwind scheme. A simple total variation diminishing (TVD) method with a monotonic upstream-centered scheme for conservation laws (MUSCL) limiter function is employed to eliminate undesirable oscillations across discontinuities. Validation of the model is carried out by comparing the results of the simulations with several experimental test cases of wave breaking and run-up and the analytical solution to linear short waves in deep water. Promising performance of the model has been observed. 相似文献
18.
《Ocean Modelling》2002,4(3-4):249-267
During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system (ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, their numerical algorithms, code structure, and parameterization options are very different. Sensitivity studies with an idealized channel flow and a steep seamount configuration demonstrate how different algorithms in the two models may affect numerical errors, the stability of the code and the computational efficiency. For example, new pressure gradient schemes using polynomial fits and new time stepping algorithms may reduce numerical errors and allow using longer time steps than standard schemes do. However, the new schemes may require more careful choices of time steps and the use of higher order advection schemes to maintain numerical stability. 相似文献
19.
Hydrosweep mapping of crust in the Central Indian Ocean Basin reveals abundant volcanoes ocurring both as isolated seamounts and linear seamount chains parallel to flow lines. Their shapes, sizes and overall style of occurrence are indistinguishable from near-axis seamounts in the Pacific. Evidence from seamount morphology, distributions and petrography of dredged samples suggests that they were generated near the fast-spreading Southeast Indian Ridge at 50–60 Ma. If so, this style of near-axis seamount generation may be a result of fast-spreading rate rather than a peculiarity of the present Pacific spreading ridges. In fact, the results of several recent studies, taken together, suggest that the style of axis/near-axis seamount volcanism varies systematically as a function of spreading rate. 相似文献
20.
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