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1.
Francis Auclair Claude Estournel Jochem W. Floor Marine Herrmann Cyril Nguyen Patrick Marsaleix 《Ocean Modelling》2011,36(1-2):49-70
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
2.
Numerical ocean modelling is computationally very demanding. Traditionally, the hydrostatic approximation has been applied to reduce the computational burden. This approximation is valid in large scale studies with coarse grid resolution. With faster computers and gradually smaller grid sizes, we may expect that more studies will be performed with non-hydrostatic ocean models. In recent papers several methods for including non-hydrostatic pressure in σ-coordinate models have been suggested. In this paper the sensitivity of the non-hydrostatic pressure field, the velocity fields, and the density fields to changes in the method for computing non-hydrostatic pressure in σ-coordinate ocean models is addressed.The first test case used involves the propagation and breaking of an internal wave at an incline in a tank. The other test case concerns tidally driven flow over a sill in a stratified fjord. The results from our numerical exercises suggest that the velocity and density fields are very robust to the model choices investigated here. The differences between the model results are of the same order as the uncertainty due to the internal pressure gradient error, and they are smaller than an estimate of the uncertainty due to subgrid scale closure. 相似文献
3.
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
4.
A two-dimensional non-hydrostatic ocean model and a hydrostatic version of the same model are used to simulate convective adjustment, without the use of an instantaneous adjustment parameterization. The model geometry is a domain on the vertical plane of width 40 km and depth 500 m. Model results for four cases are examined: hydrostatic and non-hydrostatic, at 0.1 and 1 km spatial resolution. The convectively adjusted stable state obtained in all four cases are qualitatively similar; thus the hydrostatic approximation does not eliminate convective adjustment. The details of the simulated convective plumes depend on resolution and whether the hydrostatic approximation is made. The adjusted state has significant stratification which cannot be captured by the conventional instantaneous adjustment or diffusion-based parameterizations. We also compare the results to the case when an instantaneous adjustment parameterization is used. 相似文献
5.
We explore the efficacy of “super parameterization” (SP) in ocean modeling in which local 2-d non-hydrostatic plume-resolving fine-grained (FG) models are embedded at each vertical column of a coarse-grained (CG) hydrostatic model. A general multi-scale algorithm is described in which tendencies from the FG models are projected onto the CG model which in turn constrains the average state of the FG models, coupling the two models together. The approach is tested in the context of models of open ocean deep convection and compared with a pure hydrostatic, coarse resolution model using convective adjustment (HYD) and a full 3-d non-hydrostatic plume-resolving simulation (NH). The SP model is found to be greatly superior to HYD at much less computational cost than the fully non-hydrostatic calculation. 相似文献
6.
《Ocean Modelling》2011,39(3-4):203-216
A fully nonlinear, non-hydrostatic model, MITgcm, is used to investigate internal solitary waves (ISWs) from the Luzon Strait (LS). As the ISWs in the South China Sea (SCS) have drawn more and more attention in recent years, they are studied in various ways, i.e., via remote sensing images, in situ measurements, and numerical simulations. The inspiration of this paper derived from the potential flaws of different numerical models that were employed to examine ISWs. In this study, we performed three-dimensional (3D) experiments with realistic topography and stratification, as well as with fully non-hydrostatic terms in the model, which was rather important for investigating the ISWs.Modeling results showed that baroclinic tides in the LS were essentially three-dimensional (3D), and that wave structures around two ridges in the strait were complicated with interesting internal oceanic phenomena. Several zonal cross-sections were chosen to illustrate vertical structures of zonal velocity field, and to show their meridional variances together with surface horizontal velocity gradients in order to highlight the advantages of 3D modeling with fully nonlinear, non-hydrostatic terms. Following Vlasenko et al. (2005), analysis of two parameters (Froude number and slope parameter that is defined as the ratio of inclination of topography to slope of radiated rays) that govern generation regime indicated that internal waves produced in the LS were subject to a mixed lee wave regime rather than baroclinic tide regime or unsteady lee wave regime.The propagation of ISWs beyond the generation area showed that manifestation of 3D effects was not very obvious, which, through further analysis, was mainly attributed to homogeneity of topography, inaccuracy of barotropic forcing, and Kuroshio intrusion in the LS. To better understand the necessity of 3D modeling, we chose several zonal cross-sections and performed various sensitivity experiments to show discrepancies between 2D and 3D cases. 相似文献
7.
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
8.
Motoyasu Miyata 《Journal of Oceanography》1979,35(1):43-46
A theory of the coastal Kelvin wave is presented in which the pressure is assumed not to be hydrostatic. The results show that the non-hydrostatic Kelvin wave is dispersive and that the e–1 decay distance of the wave amplitude from the coast decreases as the wave length becomes shorter. Similar conclusions can be drawn on the equatorial Kelvin wave. 相似文献
9.
This paper presents CCHE2D-NHWAVE, a depth-integrated non-hydrostatic finite element model for simulating nearshore wave processes. The governing equations are a depth-integrated vertical momentum equation and the shallow water equations including extra non-hydrostatic pressure terms, which enable the model to simulate relatively short wave motions, where both frequency dispersion and nonlinear effects play important roles. A special type of finite element method, which was previously developed for a well-validated depth-integrated free surface flow model CCHE2D, is used to solve the governing equations on a partially staggered grid using a pressure projection method. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed based on the partially staggered grid. In addition, a simple and efficient wetting and drying algorithm is implemented to deal with the moving shoreline. The model is first verified by analytical solutions, and then validated by a series of laboratory experiments. The comparison shows that the developed wave model without the use of any empirical parameters is capable of accurately simulating a wide range of nearshore wave processes, including propagation, breaking, and run-up of nonlinear dispersive waves and transformation and inundation of tsunami waves. 相似文献
10.
基于ROMS(Regional Ocean Modeling System)模式,设计了9组理想数值实验,研究了内潮的产生对地形和背景层结环境的敏感性。结果表明:高斯海脊两侧地形梯度较大的超临界坡面处是内潮的主要源区;地形和层结环境的变化对内潮生成有很大影响;如地形和层结保持不变,不同的网格水平分辨率和垂向层数条件下估算的内潮转换率存在差别;地形和跃层的相对空间关系对内潮生成及其引起的水体混合强度存在影响。高分辨率的地形和合适的背景层结是内潮模拟的关键。该结论对于内潮形成的数值模拟研究有一定参考价值。 相似文献
11.
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
12.
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. 相似文献
13.
The pycnocline in a closed domain is tilted by external wind forcing and tends to restore to a level posi- tion when the wind falls. An internal seiche oscillation exhibits if the forcing is weak, otherwise internal surge and internal solitary waves emerge, which serve as a link to cascade energy to small-scale processes. A two-dimensional non-hydrostatic code with a turbulence closure model is constructed to extend previous laboratory studies. The model could reproduce all the key phenomena observed in the corresponding labo- ratory experiments. The model results further serve as a comprehensive and reliable data set for an in-depth understanding of the related dynamical process. The comparative analyses indicate that nonlinear term favors the generation of internal surge and subsequent internal solitary waves, and the linear model predicts the general trend reasonably well. The vertical boundary can approximately reflect all the incoming waves, while the slope boundary serves as an area for small-scale internal wave breaking and energy dissipation. The temporal evolutions of domain integrated kinetic and potential energy are also analyzed, and the results indicate that about 20% of the initial available potential energy is lost during the first internal wave breaking process. Some numerical tactics such as grid topology and model initialization are also briefly discussed. 相似文献
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15.
In the present study,a semi-implicit finite difference model for non-bydrostatic,free-surface flows is analyzed and discussed.The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general,irregular domain of arbitrary scale.At outflow,a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection.The equations are solved with the fractional step method where the hydrostatic pressure component is determined first,while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric.The advectiou and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach.The resulting model is computationally efficient and unrestricted to the CFL condition.The developed model is verified against analytical solutions and experimental data,with excellent agreement. 相似文献
16.
Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure 总被引：2，自引：0，他引：2
A numerical method for non-hydrostatic, free-surface, irrotational flow governed by the nonlinear shallow water equations including the effects of vertical acceleration is presented at the aim of studying surf zone phenomena. A vertical boundary-fitted grid is used with the water depth divided into a number of layers. A compact finite difference scheme is employed for accurate computation of frequency dispersion requiring a limited vertical resolution and hence, capable of predicting the onset of wave breaking. A novel wet–dry algorithm is applied for a proper handling of moving shoreline. Mass and momentum are strictly conserved at discrete level while the method only dissipates energy in the case of wave breaking. The numerical results are verified with a number of tests and show that the proposed model using two layers without ad-hoc assumptions enables to resolve propagating nonlinear shoaling, breaking waves and wave run-up within the surf and swash zones in an efficient manner. 相似文献
17.
进动(precession)共振是一种非线性共振相互作用,2016年才有学者对这一现象进行研究。采用非静压二维自由表面流模型模拟了深水条件下重力波的进动共振现象。通过边界造波的方法产生双色波,分析了触发进动共振的初始条件;探讨了进动共振在小振幅前提条件下发生的简化初始条件。数值模拟分析两组对称测点,对不同测点的波面、能量谱进行对比分析。数值结果表明:非静压二维自由表面流模型可以模拟进动共振现象,并且可以采用双色波作为条件来研究深水五波进动共振现象,进动共振需要一定的能量转化时间,进动共振发生的条件是三波组合的进动频率等于一个系统存在的非线性频率。 相似文献
18.
Baroclinic terms have been implemented in a three-dimensional fully hydrodynamic model developed by Badiei et al. [2008. A three-dimensional non-hydrostatic boundary fitted model for free surface flows. International Journal for Numerical Methods in Fluids, 56(6), 607-627] modifying its momentum equations to account for density gradients and utilizing the scalar (salinity, temperature, etc.) conservation equation (SCE) and a state equation for the calculation of density. In the solution of advection-diffusion terms of the governing Navier-Stokes equations (NSE) and SCE, a symmetric splitting method was applied to ensure the long-term stability of simulations. Correction terms proposed by Ruddic et al. (1995) were applied to SCE to ensure the conservation of the scalar quantity. In the presence of baroclinic terms, the zero gradient pressure in the vertical direction in the vicinity of surface and bottom boundaries assumed by Badiei et al. [2008. A three-dimensional non-hydrostatic boundary fitted model for free surface flows. International Journal for Numerical Methods in Fluids, 56(6), 607-627] created spurious currents. This problem was solved by assuming a hydrostatic pressure variation at those boundaries. The ability of extended model was validated by comparing its results with an experimental test case. The simulation of hydrodynamic and salt intrusion at Anzali Port located at the southern coasts of Caspian Sea in Iran was carried out by the model with both barotropic and baroclinic modes. The simulated results with baroclinic mode show a better agreement with measured data as compared to the results of barotropic mode that clearly demonstrate the significance of baroclinic terms in the simulation of cyclic intrusion of salt wedge into the Port Basin. 相似文献
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20.
The problem of static three-dimensional, nonlinear, large deformation response of a marine riser is formulated within small strain theory and solved numerically. This type of analysis is necessary, for the new generation of drilling and production risers. The mathematical model takes properly into account the effects of internal and external pressure and the complete nonlinear boundary conditions, without linearizing the follower forces. The extensibility or inextensibility condition is used as the constitutive relation in the tangential direction. Torsion and bending are coupled. The external load and the boundary conditions are deformation dependent. A solution method is developed based on an incremental finite element algorithm, which involves a prediction-correction scheme. In the correction phase deformation dependent quantities are updated. The extensibility or inextensibility condition is used to reduce the degrees of freedom of the system. The numerical results of the developed computer code compare very well with available semi-analytical and numerical solutions. Three numerical applications are used to demonstrate the importance of large deformation, nonlinear and three-dimensional analyses. 相似文献