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1.
Bin Li   《Ocean Engineering》2008,35(17-18):1842-1853
A spatial fixed σ-coordinate is used to transform the Navier–Stokes equations from the sea bed to the still water level. In the fixed σ-coordinate system only a very small number of vertical grid points are required for the numerical model. The time step for using the spatial fixed σ-coordinate is efficiently larger than that of using a time dependent σ-coordinate, as there is substantial truncation error involved in the time dependent σ-coordinate transformation. There is no need to carry out the σ-coordinate transformation at each time step, which can reduce computational times. It is important that wave breaking can be potentially modeled in the fixed σ-coordinate system, but in a time-dependent σ-coordinate system the wave breaking cannot be modeled. A projection method is used to separate advection and diffusion terms from the pressure terms in Navier–Stokes equations. The pressure variable is further separated into hydrostatic and hydrodynamic pressures so that the computer rounding errors can be largely avoided. In order to reduce computational time of solving the hydrodynamic pressure equation, at every time step the initial pressure is extrapolated in time domain using computed pressures from previous time steps, and then corrected in spatial domain using a multigrid method. For each time step, only a few of iterations (typically six iterations) are required for solving the pressure equation. The model is tested against available experimental data for regular and irregular waves and good agreement between calculation results and the measured data has been achieved.  相似文献   

2.
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   

3.
The dense water formation process under polynya or lead is examined by numerical experiments using a three-dimensional non-hydrostatic model. Many numerical experiments on isolated convection in an initially homogeneous fluid have been performed for different sets of external parameters, in order to investigate a relationship between the convection process and the external parameters. The main focus is on the situation in which the horizontal length scale of disk-shaped buoyancy forcing (radius R) is comparable with the total water depth (H). The two dynamical regimes described in previous work—the baroclinically unstable convection and the baroclinically stable convection—are confirmed in the experiments. A horizontal shift of a convective chimney is important to a density anomaly in baroclinically stable convection. For the stable range, as R is reduced R/H < 0.7, a new regime is found, called “single-plume convection”, in which multiple convective plumes do not fully develop, and the density anomaly scale has nearly no dependency on R. This change of dependency on R is consistent with that derived by scaling analysis. The non-hydrostatic component is more significant than the hydrostatic one in the single-plume convection. The information obtained is useful for parameterizing dense water formation under ice cover in a numerical model with a large grid size; i.e., the newly formed water has a density anomaly independent of the polynya size smaller than the water depth, while the anomaly increases as the size exceeds the depth.  相似文献   

4.
A 1/8° global version of the Navy Coastal Ocean Model (NCOM) is described with details of its formulation, implementation, and configuration of the vertical coordinate. NCOM is a baroclinic, hydrostatic, Boussinesq, free-surface ocean model that allows its vertical coordinate to consist of σ coordinates for the upper layers and z-levels below a user-specified depth. This flexibility allows implementation of a hybrid σ–z coordinate system that is expected to mitigate some of the weaknesses that can be associated with either pure coordinate option. For the global NCOM application, the σ–z coordinate is used to allow terrain-following σ coordinates in the upper ocean, providing better resolution and topographic fidelity in shelf regions where flow is most sensitive to its representation. Including z coordinates for deeper regions efficiently maintains high near-surface vertical resolution in the open ocean. Investigation into the impact of the selected coordinate system focuses on differences between atmospherically-forced free-running (no assimilation) global solutions using σ–z and pure z coordinates. Comparisons with independent temperature observations indicate that global NCOM using the σ–z coordinate has improved skill relative to its z coordinate implementation. Among other metrics, we show that in comparison with time series of surface temperature from National Oceanic Data Center (NODC) buoys, mostly located in coastal regions, root mean squared differences (RMSD) improved for 63% and correlation improved for 71% of the stations when σ–z coordinates were used instead of pure z. For the exclusively open-ocean Tropical Atmosphere-Ocean (TAO) buoys, differences between the simulations were small, with the σ–z showing smaller RMSD for 45% of the stations and higher correlation for 65% of the stations. Additional comparisons using temperature profile observations further confirm a tendency for improved performance using the hybrid σ–z coordinates.  相似文献   

5.
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   

6.
A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave.  相似文献   

7.
A three dimensional hydrostatic finite volume ocean model has been developed to solve the integral dynamical equations. Since the basic (integral) equations are solved for finite volumes rather than grid points, the flux conservation is easily enforced, even on arbitrary meshes. Both upwind and high-order combined compact schemes can be incorporated into the model to increase computational stability and accuracy. This model uses a highly distorted grid system near the boundary. The lateral boundaries of each finite volume are perpendicular to x and y axes and the two vertical boundaries are not purely horizontal. Four types of finite volumes are designed to follow the terrain with four (Type-A), three (Type-B), two (Type-C), and one (Type-D) vertices in the lower surface. Such a terrain-following grid discretization has superior features to z- and σ-coordinate systems. The accuracy of this model was tested.  相似文献   

8.
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   

9.
An original implementation of a non-hydrostatic, free-surface algorithm based on a pressure correction method is proposed for ocean modelling. The free surface is implemented through an explicit scheme combined with a mode-spitting method but the depth-averaged velocity and the position of the free surface are updated at each non-hydrostatic iteration. The vertical momentum equation is also integrated up to the surface enabling a natural and accurate treatment of the surface layer. The consistent specification of the numerical schemes provides balanced transfers of potential and kinetic energy. This algorithm is well-suited for implementation as a non-hydrostatic kernel on originally hydrostatic free-surface ocean models such as Symphonie (http://poc.obs-mip.fr/pages/research_topics/modelling/symphonie/symphonie.htm) for which it has originally been developed.Energy balances associated with the propagation of short surface waves and solitary waves are presented for two dedicated well-documented configurations over closed domains. The buoyancy flux, the work rate of the pressure force together with the power of the advective terms are evaluated and discussed for the generation and the propagation of these two types of waves. The dissipation rate is in particular shown to be several orders of magnitude smaller than the work rates of the hydrostatic and non-hydrostatic pressure forces confirming the necessity for the exchanges of energy to be numerically balanced. The algorithm is subsequently applied to the complex generation of non-linear solitary internal waves by surface tides over Georges Bank, in the Gulf of Maine. The generation and the propagation of the observed non-linear and non-hydrostatic features in this region are correctly reproduced.  相似文献   

10.
A simple relationship has been developed between the wall coordinate y+ and Kolmogorov's length scale using direct numerical simulation (DNS) data for a steady boundary layer. This relationship is then utilized to modify two popular versions of low Reynolds number k–ε model. The modified models are used to analyse a transitional oscillatory boundary layer. A detailed comparison has been made by virtue of velocity profile, turbulent kinetic energy, Reynolds stress and wall shear stress with the available DNS data. It is observed that the low Reynolds number models used in the present study can predict the boundary layer properties in an excellent manner.  相似文献   

11.
Realistic representation of sea ice in ocean models involves the use of a non-linear free-surface, a real freshwater flux and observance of requisite conservation laws. We show here that these properties can be achieved in practice through use of a rescaled vertical coordinate “z*” in z-coordinate models that allows one to follow undulations in the free-surface under sea ice loading. In particular, the adoption of “z*” avoids the difficult issue of vanishing levels under thick ice.Details of the implementation within MITgcm are provided. A high resolution global ocean sea ice simulation illustrates the robustness of the z* formulation and reveals a source of oceanic variability associated with sea ice dynamics and ice-loading effects. The use of the z* coordinate allows one to achieve perfect conservation of fresh water, heat and salt, as shown in extended integration of coupled ocean sea ice atmospheric model.  相似文献   

12.
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   

13.
A non-hydrostatic ocean model using an effective Poisson solver is developed. The Poisson solver is a combination of the multigrid method, the Krylov-subspace method, and the sparse approximate inverse. Its numerical cost only linearly increases with total number of computational cells, and it also has high parallel computing efficiency. The numerical cost of the non-hydrostatic model described in the present paper remains only twice of that of a hydrostatic model, even with non-smooth topography and with a huge number of computational grid cells on massively parallelized computer systems. Therefore, it has a potential to expand the applicability of non-hydrostatic ocean models. We also present the preliminary result of the high-resolution non-hydrostatic experiment on Ice Shelf Water overflow in the southern Weddell Sea, which shows good agreement with observations in terms of the pathway of dense water and velocity field.  相似文献   

14.
Sea ice drift is mainly controlled by ocean currents, local wind, and internal ice stress. Information on sea ice motion, especially in situ synchronous observation of an ice velocity, a current velocity, and a wind speed, is of great significance to identify ice drift characteristics. A sea ice substitute, the so-called "modelled ice", which is made by polypropylene material with a density similar to Bohai Sea ice, is used to complete a free drift experiment in the open sea. The trajectories of isolated modelled ice, currents and wind in the Bohai Sea during non-frozen and frozen periods are obtained. The results show that the currents play a major role while the wind plays a minor role in the free drift of isolated modelled ice when the wind is mild in the Bohai Sea. The modelled ice drift is significantly affected by the ocean current and wind based on the ice–current–wind relationship established by a multiple linear regression. The modelled ice velocity calculated by the multiple linear regression is close to that of the in situ observation, the magnitude of the error between the calculated and observed ice velocities is less than12.05%, and the velocity direction error is less than 6.21°. Thus, the ice velocity can be estimated based on the observed current velocity and wind speed when the in situ observed ice velocity is missing. And the modelled ice of same thickness with a smaller density is more sensitive to the current velocity and the wind speed changes. In addition, the modelled ice drift characteristics are shown to be close to those of the real sea ice, which indicates that the modelled ice can be used as a good substitute of real ice for in situ observation of the free ice drift in the open sea, which helps solve time availability, safety and logistics problems related to in situ observation on real ice.  相似文献   

15.
Seagrass beds occur in various morphological forms, ranging from small patches to continuous meadows. The endemic Mediterranean seagrass Posidonia oceanica forms dense and extensive stands that occur in several different morphotypes, including reticulate (seagrass interspersed with a different habitat type, such as bare sand) and continuous beds. This study, undertaken in the Maltese Islands, examined whether reticulate and continuous P. oceanica beds, located adjacent to each other and at similar depths, had different within-bed architectural characteristics. Five commonly used architectural measures (shoot density, number of leaves per shoot, mean leaf length, mean leaf width and shoot biomass) were measured from P. oceanica shoots collected from the two bed types at three different spatial scales: (1) tens of metres (‘small’ scale); (2) hundreds of metres (‘medium’ scale); and (3) kilometres (‘large’ scale). Results of 2-factor ANOVA (factor 1=bed type; factor 2=sampling locality) carried out at the three spatial scales indicated significant differences between the two bed types in shoot density (P<0.01) and leaf length (P<0.05) at the small scale, and in leaf number (P<0.05) at the large scale. Significant interactions were also apparent for shoot density (at the large scale) and for shoot biomass (at the medium scale). However, the results obtained did not indicate consistent architectural differences between the two P. oceanica bed types over the spatial scales considered. Spatial variations in within-bed architectural characteristics observed were therefore thought to be attributable mainly to the influence of local environmental factors. The findings are discussed with reference to the conservation and management of P. oceanica habitat.  相似文献   

16.
A finite-volume formulation is presented that solves the three-dimensional, nonhydrostatic Navier–Stokes equations with the Boussinesq approximation on an unstructured, staggered, z-level grid, with the goal of simulating nonhydrostatic processes in the coastal ocean with grid resolutions of tens of meters. In particular, the code has been developed to simulate the nonlinear, nonhydrostatic internal wave field in the littoral ocean. The method is based on the formulation developed by Casulli, in that the free-surface and vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly with the second-order Adams–Bashforth method, while the pressure-correction method is employed for the nonhydrostatic pressure in order to achieve overall second-order temporal accuracy. Advection of momentum is accomplished with an Eulerian discretization which conserves momentum in cells that do not contain the free surface, and scalar advection is discretized in a way that ensures consistency with continuity, thereby ensuring local and global mass conservation using a velocity field that conserves volume on a local and global basis. The nonhydrostatic pressure field is solved efficiently using a block-Jacobi preconditioner, and while stability is limited by the internal gravity wave speed and vertical advection of momentum, applications requiring relatively small time steps due to accuracy or stability constraints are run efficiently on parallel computers, since the present formulation is written entirely with the message-passing interface (MPI). The ParMETIS libraries are employed in order to achieve a load-balanced parallel partitioning that minimizes interprocessor communication, and the grid is reordered to optimize per-processor performance by limiting cache misses while accessing arrays in memory. Test cases demonstrate the ability of the code to efficiently and accurately compute the nonhydrostatic lock exchange and internal waves in idealized as well as real domains, and we evaluate the parallel efficiency of the code using up to 32 processors.  相似文献   

17.
An analysis is presented of snapshot data (eastward and northward velocity components: u and v; tracer such as potential temperature: τ) from an eddy-resolving (Rgrid: 1/12°) ocean model experiment, in order to explore a method for improving eddy-permitting model performance. Horizontal 3 × 3 R-grid averages give the eddy-permitting grid (P-grid: 1/4°) variables: 〈u〉, 〈v〉, and 〈τ〉, where 〈〉 denotes the spatial P-grid scale average. The difference between the horizontal tracer flux across the boundary face of a P-grid and that across the corresponding faces of R-grids is estimated as F2E. It is found that the correlations among the gradients of u, v, and τ give a good approximation F2C to the estimated flux F2E. The approximated flux is a function of these gradients and the grid size. A method is presented for implementing the F2C for density to an eddying ocean model as an additional advection. Practical experiments were conducted with a realistic configuration. It is shown that the zonal mean isotherms in the Kuroshio extension region are more flattened in the run using the proposed method than in another run using the conventional horizontal biharmonic operator, suggesting that the additional flux correction leads to an enhancement of sub-basin scale mixing.  相似文献   

18.
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19.
A three-dimensional σ-coordinate ocean model with realistic forcing is used to derive and compare flushing time, residence time and water age distributions in Bass Strait, a broad shallow shelf sea in south-eastern Australia which exhibits seasonal variation in water mass properties and circulation. Results illustrate flushing out of most old water occurs each winter–spring period and the circulation in summer increases age of remnant older water in the Strait. A correlation between water age and salinity is found in winter which is the result of advective “erosion” of the interior water mass. The presence of an area in the south-eastern part of the interior with low flushing is suggested to result from a number of physical factors including the presence of quasi-stationary eddies which entrain age, leading to relatively older water residing there.  相似文献   

20.
A two-equation k– turbulence model is used in this paper to simulate the propagation of cnoidal waves over a submerged bar, where the free surface is handled by the volume-of-fluid (VOF) method. Using a VOF partial-cell variable and a donor–acceptor method, the model is capable of treating irregular boundaries, including arbitrary bottom topography and internal obstacles, where the no-slip condition is satisfied. The model also allows the viscous sublayer to be modeled by a wall function approximation implemented in the grid nodes that are immediately adjacent to a wall boundary. The numerical model applied to the propagation of cnoidal waves over a submerged bar can produce results that are in general agreement with some laboratory measurements. Some remarks arising from the comparison between the computational and experimental results are presented.  相似文献   

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