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1.
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
2.
斜压海洋动力学的一种三维数值模式 Ⅰ.动力学方程数值格式 总被引：1，自引：0，他引：1
依据自由海面海洋动力学原始方程建立了一种三维有限差分数值模式,可用于潮波、风暴潮和海流的数值模拟和预报。运动方程和连续方程的数值格式采用内、外模态分离的技术。外模态采用交替方向隐格式,用于计算海面高度和垂直平均流速,时间步长不受Ｃｏｕｒａｎｔ－Ｆｒｉｄｅｒｉｃｈｓ－Ｌｅｗｙ条件限制;内模态采用半隐格式,用于计算海流的垂直２颁布,其时间步长可大于外模态时间步长。模式的计算程度比一般显式模式可快１０倍 相似文献
3.
Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution 总被引：5，自引：0，他引：5
In this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. This error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. In the case of ROMS, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. We show that the common idea that spurious mixing decreases with resolution is generally false. In a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. At finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. The solution to this problem requires a specifically designed advection scheme. We propose and validate the RSUP3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the Peclet constraint. The rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. Realistic model experiments in a southwest Pacific configuration show that RSUP3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. There are residual errors from the rotated diffusion operator, but they remain acceptable. The use of a constant diffusivity rather than the Peclet hyperdiffusivity tends to increase these residual errors which become unacceptable with Laplacian diffusion. Finally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. A temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper. 相似文献
4.
An Eta-Coordinate Version of the Princeton Ocean Model 总被引：1，自引：0，他引：1
The Princeton Ocean Model (POM) is widely used in both the research and real-time marine forecast communities. However, there
is a single heavily criticized feature and shortcoming of POM, i.e., the pressure gradient (PG) error associated with sloping
topography. To overcome this problem, in this paper we present an eta-coordinate POM (ECPOM). The eta-coordinate system was
originally adopted in atmospheric numerical models and has proved to be effective in removing the large errors associated
with the horizontal pressure gradient force and advection and diffusion terms along a steeply sloping topography. A familiar
idealized seamount problem is used to test the PG error in the ECPOM in order to isolate errors from other sources, as is
done in the literature. The model is set up so that, ideally, the ocean should be at rest forever; any development of circulation
is regarded as numerically artificial. Results show that in ECPOM, errors are dramatically reduced by two orders of magnitude
over a wide range of parameters. As a trade-off, the bottom boundary of the ECPOM is a stepwise instead of a continuous one,
as in the sigma-coordinate POM (SCPOM). Modification of the SCPOM to the ECPOM is straightforward and minimal. Compared to
the z-coordinate model, the ECPOM is numerically simpler since the eta-coordinate has a surface-following character.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
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
6.
在海底地形陡变、垂向密度分层明显的水域,三维σ坐标模式中会出现一种"伪"水平斜压梯度力,并会引起"伪"密度流,以至于影响模拟的精度。垂向上引入双σ坐标变换,建立河口海岸水域三维斜压水流数值模型。数值试验结果表明,在海底地形陡变水域,双σ坐标模式可以减小水平斜压梯度力处理引起的误差。 相似文献
7.
A simple numerical model, based on the Reynolds stress equations and k–ε turbulence closure scheme, is developed for the coastal wave and current bottom boundary layer. The current friction velocity is introduced to account for the effect of currents on waves. The implicit Crank–Nicolson finite difference method discretizes the governing equations. Vertical changing step grids with the constant ratio for two adjacent spatial steps are used together with the equal time steps in the modeling. Vertical profiles of mean current velocity and wave velocity amplitude are obtained. These modeled results are compared with the laboratory experimental data of Van Doorn [1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. It has been shown that modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands) mean velocity profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands) wave velocity amplitude profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled wave velocity amplitudes are in good agreement with the laboratory experimental data of Van Doorn [1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. 相似文献
8.
A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity.The Euler predictor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones,respectively,thus leading both the time and spatial derivatives to the second-order accuracy.The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift.Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach,respectively,and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor.From comparison of numerical results with theoretical or experimental ones,it is found that they are in reasonable agreement. 相似文献
9.
D. V. Alekseev V. A. Ivanov E. V. Ivancha V. V. Fomin L. V. Cherkesov 《Physical Oceanography》2007,17(1):1-16
The processes of roiling of the bottom sediments, diffusion transport of the suspension, and its repeated sedimentation on
the northwest shelf of the Black Sea caused by a moving cyclone are studied by using a numerical sigma-coordinate model. It
is supposed that bottom sediments are formed by particles of the same type. We determine the regions of the most intense rise
of the suspension, directions of its transport by the flows of water, and the vertical profiles of concentration of suspended
bottom sediments in different regions. In particular, it is shown that the distribution of suspended substances at a distance
of 1 m from the bottom reflects the location of the active and inactive centers of erosion.
__________
Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 3–20, January–February, 2007. 相似文献
10.
A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model. 相似文献
11.
A coastal ocean -coordinate model of Monterey Bay (MOB) with realistic bottom topography and coastlines is developed using the Princeton Ocean Model (POM) and grid generation technique (GGT) to study the horizontal pressure gradient errors associated with the MOB steep topography. The submarine canyon in MOB features some of the steepest topography encountered anywhere in the world oceans. The MOB grids are designed using the EAGEAL View and GENIE++ grid generation systems. A grid package developed by Ly and Luong (1993) is used in this study to couple grids to the model. The MOB model is tested with both orthogonal and curvilinear nearly-orthogonal (CNO) grids. The CNO grid has horizontal resolution which varies from 300 m to 2 km, while the resolution of the orthogonal grid is uniform with x = 1.25 km and y = 1.38 km. These grids cover a domain of 180 × 160 km with the same number of grid points of 131 × 131. Vertical resolutions of 25, 35 and 45 vertical sigma levels are tested. The error in the MOB are evaluated in terms of mean kinetic energy and velocity against various grids, vertical, horizontal resolution and distributions, and bottom topography smoothing. Simulations with various grids show that GGT can be used as another tool in reducing -coordinate errors in coastal ocean modeling besides increasing resolution and smoothing bottom topography. Topographical smoothing not only reduces topographic slope, but changes realistic topography. A CNO grid with a high grid density packed along steep slopes and Monterey Submarine Canyon reduces the errors by 40% compared to a rectangular grid with the same number of grid points. The CNO grid is more efficient than the rectangular grid, since it has most of its grids over water. The simulations show that the presented MOB -coordinate model can be used with a confidence regarding horizontal pressure gradient error. 相似文献
12.
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
13.
Ａｑｕａｓｉ－ｔｈｒｅｅ－ｄｉｍｅｎｓｉｏｎａｌｎｕｍｅｒｉｃａｌｐｒｅｄｉｃｔｉｏｎｍｏｄｅｌｏｆｓａｌｉｎｉｔｙｓｔｒｕｃｔｕｒｅｉｎＢｏｈａｉＳｅａａｎｄＨｕａｎｇｈａｉＳｅａ￥ＳｕｎＷｅｉｙａｎｇａｎｄＷａｎｇＺｏｎｇｓｈａｎ（Ｒｅｃｅｉｖｅ... 相似文献
14.
A three-dimensional finite-difference hydrodynamic model has been developed using σ-coordinate for the vertical dimension. An explicit scheme for temporal integration and a staggered grid for spatial discretization have been adopted. The model has been tested against analytical or literature cases for wind and tide induced circulation. Results are in good agreement both with analytical solutions under idealised conditions and with results from the model of Shankar et al. (1996). 相似文献
15.
本文以蓝蟹为例,研究海洋环境对甲壳动物幼体迁移规律和机制的影响。利用不规则三角形网格和有限体积模型(finite-volume coastal ocean model, FVCOM)耦合kinesis模型的方法,分析研究了墨西哥湾物理环境对蓝蟹(Callinectessapidus)幼体的分布和扩散途径的影响。蓝蟹在每年的四、五月份海水落潮期间产卵,通过跟踪算法从产卵区域沿着墨西哥湾海域进行模拟,获得了80天内蓝蟹幼体的粒子移动轨迹,记录并分析了幼体经过海域的盐度值。研究结果证明了该方法可有效模拟蓝蟹幼体在特定海域的迁移规律和扩散机制,进一步研究可为了解海洋物理环境对蓝蟹和其他渔业资源的影响提供借鉴。 相似文献
16.
Numerical Simulation of Residual Circulation due to Bottom Roughness Variability Under Tidal Flows in A Semi-Enclosed Bay 总被引：7，自引：0，他引：7
1 .IntroductionWater pollution has a large influence on water environment and our life ;for example ,it some-times induces oxygen depression,blue tide andredtide in a bay.For water purificationin a semi-en-closed sea ,some new methods to activate the tidal exchange between an inner bay and an outer seaarea by control of a tidal residual current have been proposed (Awayaet al .,1995) . Huthnance(1973) ,Zimmerman (1978 ,1981) , Loder (1980) ,and Robinson (1983) considered cases wherethe fricti… 相似文献
17.
Bang-Fuh Chen 《Ocean Engineering》1999,26(1):47
A finite-differnece method was used to calculate the nonlinear hydrodynamic pressures acting on the coastal embankment faces by seismic-wave actions. The nonlinearity of free surface flow, convective acceleration, viscosity and surface tension of fluid are included in the analysis. The kinematic and dynamic free surface boundary conditions are employed for calculating the horizontal fluid velocity, pressure at the free surface and the surface profile of the fluid. The time-dependent water surface is transformed to the horizontal plane, and the flow field is mapped onto a rectangular, making it convenient to model the complex sea bottom geometry and the wavy water surface by the finite-difference method. Fully nonlinear and weakly nonlinear dynamic free surface conditions are used and compared. The effects of surface tension of fluid are also discussed. The nonslip boundary condition is applied on the most part of the interface between fluid and solid face, except the region near the intersection between free surface and wall face. The numerical results are presented for various water depths and ground motion intensities, and their associate viscous effects on coastal embankment hydrodynamics are discussed. 相似文献
18.
HUANG Rui Xin 《海洋学报(英文版)》2014,33(3):40-57
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. 相似文献
19.
A. L. Brekhovskikh 《Oceanology》2011,51(2):199-212
A numerical model of the sea’s thermohydrodynamics with a finite-difference approximation of the equations of the nonhydrostatic
dynamics on a grid with a triangular form of the horizontal section of its element is formulated. The slope of the lower side
of the grid’s bottom cell is determined by the given linear profile of the bottom relief. Within the shallow-water approach,
the dispersion relations of the B and C grids and the developed discrete model are compared; the results of tests for different approximations of the bottom relief
for a rectangular basin are given and analyzed. The developed model of the thermohaline dynamics is used for studying the
influence of the nonhydrostatic effects on the circulation of the Baltic Sea and a part of Vistula Bay. The comparison of
the simulation results obtained according to the version with the full equation of the vertical momentum and to that using
the hydrostatic approach shows the influence of the effects of the nonhydrostatic dynamics on the structure of the simulated
fields even with small horizontal resolution (the step of the grid is 3.5 km). This is manifested in the strengthening of
the field of the vorticity and the increasing of the sea level gradients and the velocities of the horizontal currents, whose
growth reaches 1.5 cm/s. 相似文献
20.
Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field 总被引：2，自引：0，他引：2
SONG Zhiyao XUE Hongchao YAN Yixin MAO Lihua XU Fumin
Doctor Senior Engineer College of Harbor Waterway Coastal Engineering Hohai University 《中国海洋工程》1999,(3)
Based on the 2D horizontal plane numerical model,a quasi-3D numerical model is establishedfor coastal regions of shallow water.The characteristics of this model are that the velocity profiles can be ob-tained at the same time when the equations of the value of difference between the horizontal current velocityand its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent withthe results of the 2D model.The circulating flow in the rectangular area induced by wind is simulated and ap-plied to the tidal flow field of the radial sandbanks in the South Yellow Sea.The computational results fromthis quasi-3D model are in good agreement with analytical results and observed data.The solution of the finitedifference equations has been found to be stable,and the model is simple,effective and practical. 相似文献