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1.
Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (CB=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow
, and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when
, the frequency dispersion can be neglected in supercritical flows. 相似文献
2.
A coupled discontinuous–continuous Galerkin (DG–CG) shallow water model is compared to a continuous Galerkin generalized wave-continuity equation (GWCE) based model for the coastal ocean, whereby local mass imbalance typical of GWCE-based solutions is eliminated using the coupled DG–CG approach. Two mass imbalance indicators for the GWCE-based model are presented and analyzed. The indicators motivate discussion on the suitability of using a GWCE-based model versus the locally conservative coupled DG–CG model. Both realistic and idealized test problems for tide, wind, and wave-driven circulation form the basis of the study. For the problems studied, coupled DG–CG solutions retain the robustness of well-documented solutions from GWCE-based models and also capture the dynamics driven by small-scale, highly advective processes which are problematic for GWCE-based models. Issues associated with the coupled DG–CG model are explored, including increased cost due to increased degrees of freedom, the necessary application of slope limiters, as well as the actual coupling process. 相似文献
3.
A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia. 相似文献
4.
Emanuele Di Lorenzo Andrew M. Moore Hernan G. Arango Bruce D. Cornuelle Arthur J. Miller Brian Powell Boon S. Chua Andrew F. Bennett 《Ocean Modelling》2007,16(3-4):160-187
We describe the development and preliminary application of the inverse Regional Ocean Modeling System (ROMS), a four dimensional variational (4DVAR) data assimilation system for high-resolution basin-wide and coastal oceanic flows. Inverse ROMS makes use of the recently developed perturbation tangent linear (TL), representer tangent linear (RP) and adjoint (AD) models to implement an indirect representer-based generalized inverse modeling system. This modeling framework is modular. The TL, RP and AD models are used as stand-alone sub-models within the Inverse Ocean Modeling (IOM) system described in [Chua, B.S., Bennett, A.F., 2001. An inverse ocean modeling system. Ocean Modell. 3, 137–165.]. The system allows the assimilation of a wide range of observation types and uses an iterative algorithm to solve nonlinear assimilation problems. The assimilation is performed either under the perfect model assumption (strong constraint) or by also allowing for errors in the model dynamics (weak constraints). For the weak constraint case the TL and RP models are modified to include additional forcing terms on the right hand side of the model equations. These terms are needed to account for errors in the model dynamics.Inverse ROMS is tested in a realistic 3D baroclinic upwelling system with complex bottom topography, characterized by strong mesoscale eddy variability. We assimilate synthetic data for upper ocean (0–450 m) temperatures and currents over a period of 10 days using both a high resolution and a spatially and temporally aliased sampling array. During the assimilation period the flow field undergoes substantial changes from the initial state. This allows the inverse solution to extract the dynamically active information from the synthetic observations and improve the trajectory of the model state beyond the assimilation window. Both the strong and weak constraint assimilation experiments show forecast skill greater than persistence and climatology during the 10–20 days after the last observation is assimilated.Further investigation in the functional form of the model error covariance and in the use of the representer tangent linear model may lead to improvement in the forecast skill. 相似文献
5.
6.
Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method 总被引：1，自引：0，他引：1
This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler’s equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed. 相似文献
7.
特征线计算格式下共轭方程两种导出途径的比较 总被引：1，自引：0，他引：1
共轭方程的导出是建立资料同化模型的关键，其导出方式有两种途径：AFD形式与FDA形式。在特征线计算格式基础上针对一类较广泛海洋动力控制方程分析了其两种共轭方程（AFD形式与FDA形式）之间的关系，并将理论结果应用于波谱共轭方程的讨论。 相似文献
8.
We implement an approach for the accurate assimilation of Lagrangian data into regional general ocean circulation models. The forward model is expressed in Lagrangian coordinates and simulated float data are incorporated into the model via four-dimensional variational data assimilation. We show that forward solutions computed in Lagrangian coordinates are reliable for time periods of up to 100 days with phase speeds of 1 m/s and deformation radius of 35 km. The position and depth of simulated floats are assimilated into the viscous, Lagrangian shallow water equations. The weights for the errors in the model and data are varied and the assimilation results react appropriately. We show the effect of different spatial and temporal samplings of float data on all Lagrangian trajectories in the computational domain. At the end of the assimilation period, results from the Lagrangian shallow water equations could be interpolated and used as initial and boundary conditions in an Eulerian general ocean circulation model. 相似文献
9.
ADCIRC, a finite element circulation model for shelves, coasts and estuaries, will be used for variational data assimilation. The nonlinear Euler–Lagrange (EL) problem will be solved using the iterated indirect representer algorithm. This algorithm makes such large, nonlinear but functionally smooth optimization problems feasible by iterating on linear approximations of the nonlinear problem (Picard iterations) and by making preconditioned searches in the “data subspace” at each iterate. Before solving the nonlinear EL using such Picard iterations, it essential that the iteration scheme be carefully examined within the framework of the nonassimilative or forward problem.The purpose of this paper is (1) to detail a Picard iteration procedure for ADCIRC, including the problematic bottom friction term; (2) to examine the ability of the iteration scheme to recover the nonlinear forward solution from deficient background fields; and (3) to present a study of different interpolation methods for reducing the memory/disk requirements of the iteration scheme. The iteration scheme is shown to be quite robust in its ability to recover the nonlinear solution from a variety of deficient background fields. A new cubic Hermitian interpolation method is shown to be a more effective alternative to standard linear interpolation for reducing memory/disk requirements, especially for high frequency overtides. 相似文献
10.
A new method of assimilating sea surface height (SSH) data into ocean models is introduced and tested. Many features observable by satellite altimetry are approximated by the first baroclinic mode over much of the ocean, especially in the lower (but non-equatorial) and mid latitude regions. Based on this dynamical trait, a reduced-dynamics adjoint technique is developed and implemented with a three-dimensional model using vertical normal mode decomposition. To reduce the complexity of the variational data assimilation problem, the adjoint equations are based on a one-active-layer reduced-gravity model, which approximates the first baroclinic mode, as opposed to the full three-dimensional model equations. The reduced dimensionality of the adjoint model leads to lower computational cost than a traditional variational data assimilation algorithm. The technique is applicable to regions of the ocean where the SSH variability is dominated by the first baroclinic mode. The adjustment of the first baroclinic mode model fields dynamically transfers the SSH information to the deep ocean layers. The technique is developed in a modular fashion that can be readily implemented with many three-dimensional ocean models. For this study, the method is tested with the Navy Coastal Ocean Model (NCOM) configured to simulate the Gulf of Mexico. 相似文献
11.
This note provides a detailed theoretical derivation for the removal of non‐physical finite‐amplitude computational oscillations from the solution of the adjoint of a discretized model using the leapfrog finite‐difference scheme. Numerical results are shown using a 1‐dimensional shallow water equation model. 相似文献
12.
将基于二维简化浅水波模型的间断Galerkin有限元与连续Galerkin有限元耦合方法推广至形式更为复杂的浅水波方程,并给出了误差分析以及模型问题的数值算例。 相似文献
13.
Tidal data inversion: interpolation and inference 总被引：1，自引：0，他引：1
Gary D. Egbert 《Progress in Oceanography》1997,40(1-4)
Initial efforts in applying inverse methods to studies of ocean tides have focused on making the best use of a small number of observations to map tidal fields in a large area. As such, inversion can be viewed as an objective analysis scheme which uses a dynamically appropriate spatial covariance, derived from the shallow water equations, to interpolate and smooth a sparse data set. Data from recent altimetry missions are not sparsely distributed relative to tidal wavelengths in the open ocean, apparently reducing the need for complicated dynamically based interpolation schemes. Altimetric data sets are also quite large, making application of rigorous inversion methods to global tidal modeling a challenging computational problem. We describe here a new iterative solution scheme which allows us for the first time to fit the full set of TOPEX/Poseidon cross-over differences. The resulting solution (TPXO.3) fits validation tide gauges significantly better than previous inverse solutions. TPXO.3 also reduces residual cross-over variances relative to other recent inverse and empirical solutions, particularly in shallow water where improvements are dramatic. With the new solution approach very significant improvements in global tidal models should be possible in shallow areas and in the vicinity of complex bathymetry, where high-accuracy tidal modeling remains a challenging problem. With the recent improvements in the definition of tidal elevations in the open ocean it should now also be possible to resolve some long unanswered questions about tidal energetics and dynamics. Inverse methods provide a natural framework for addressing these issues, and making inferences about tidal dynamics. In particular, by bringing data and dynamics together in a single solution, we can rigorously test the consistency of the two. We present results of global and local inversions which suggest that over elongated bathymetric features oriented perpendicular to tidal flows, energy dissipation in the open ocean is significantly enhanced, presumably due to conversion of barotropic tidal motions into baroclinic modes. For the M2 tide our preliminary results suggest that perhaps as much as 0.5 TW of energy is dissipated in this manner. However, due to the simplified linear dynamics and limited spatial resolution used for our inversion, there are significant uncertainties associated with these results. A more careful application of inverse methods to make more rigorous inferences about tidal energetics, including use of more reasonable prior dynamics, and the highest possible spatial resolution, should allow for closure of the tidal energy budget within the next few years. 相似文献
14.
A method to reduce the spin-up time of ocean models 总被引：2，自引：2，他引：0
The spin-up timescale in large-scale ocean models, i.e., the time it takes to reach an equilibrium state, is determined by the slow processes in the deep ocean and is usually in the order of a few thousand years. As these equilibrium states are taken as initial states for many calculations, much computer time is spent in the spin-up phase of ocean model computations. In this note, we propose a new approach which can lead to a very large reduction in spin-up time for quite a broad class of existing ocean models. Our approach is based on so-called Jacobian–Free Newton–Krylov methods which combine Newton’s method for solving non-linear systems with Krylov subspace methods for solving large systems of linear equations. As there is no need to construct the Jacobian matrices explicitly the method can in principle be applied to existing explicit time-stepping codes. To illustrate the method we apply it to a 3D planetary geostrophic ocean model with prognostic equations only for temperature and salinity. We compare the new method to the ‘ordinary’ spin-up run for several model resolutions and find a considerable reduction of spin-up time. 相似文献
15.
A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model. 相似文献
16.
The adjoint approach, one of the variational data assimilation (VDA) methods, is now widely used for fitting numerical models of meteorology and oceanography tO the observaions. The fundamental idea is to minimize a cost function, which is sum of Squares in the differences betweenthe data and their model counterparts, by adjllsting the independent model variables such as initialvalue, boundary value and Parameters. The numerical model is an operator maPPing the independent model variables i… 相似文献
17.
This paper describes the simulation of the flow of a viscous incompressible Newtonian liquid with a free surface. The Navier–Stokes equations are formulated using a streamline upwind Petrov–Galerkin scheme, and solved on a Q-tree-based finite element mesh that adapts to the moving free surface of the liquid. Special attention is given to fitting the mesh correctly to the free surface and solid wall boundaries. Fully non-linear free surface boundary conditions are implemented. Test cases include sloshing free surface motions in a rectangular tank and progressive waves over submerged cylinders. 相似文献
18.
A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave surface elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial derivatives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor–corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in literature. The comparison demonstrates that the new form of the equations is capable of calculating wave transformation from relative deep water to shallow water. 相似文献
19.
In the present study, a Fourier analysis is used to develop expressions for phase and group speeds for both continuous and discretized, linearized two-dimensional shallow water equations, in Cartesian coordinates. The phase and group speeds of the discrete equations, discretized using a three-point scheme of second order, five-point scheme of fourth order and a three-point compact scheme of fourth order in an Arakawa C grid, are calculated and compared with the corresponding values obtained for the continuous system. The three-point second-order scheme is found to be non-dispersive with grid resolutions greater than 30 grids per wavelength, while both the fourth-order schemes are non-dispersive with grid resolutions greater than six grids per wavelength. A von Neumann stability analysis of the two- and three-time-level temporal schemes showed that both schemes are stable. A wave deformation analysis of the two-time-level Crank–Nicolson scheme for one-dimensional and two-dimensional systems of shallow water equations shows that the scheme is non- dispersive, independent of the Courant number and grid resolution used. The phase error or the dispersion of the scheme decreases with a decrease in the time step or an increase in grid resolution. 相似文献
20.
A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows 总被引：2，自引：0，他引：2
A set of weakly dispersive Boussinesq-type equations, derived to include viscosity and vorticity terms in a physically consistent manner, is presented in conservative form. The model includes the approximate effects of bottom-induced turbulence, in a depth-integrated sense, as a second-order correction. Associated with this turbulence, vertical and horizontal rotational effects are captured. While the turbulence and horizontal vorticity models are simplified, a model with known physical limitations has been derived that includes the quadratic bottom friction term commonly added in an ad hoc manner to the inviscid equations. An interesting result of this derivation is that one should take care when adding such ad hoc models; it is clear from this exercise that (1) it is not necessary to do so – the terms can be included through a consistent derivation from the viscous primitive equations – and (2) one cannot properly add the quadratic bottom friction term without also adding a number of additional terms in the integrated governing equations. To solve these equations numerically, a highly accurate and stable model is developed. The numerical method uses a fourth-order MUSCL-TVD scheme to solve the leading order (shallow water) terms. For the dispersive terms, a cell averaged finite volume method is implemented. To verify the derived equations and the numerical model, four cases of verifications are given. First, solitary wave propagation is examined as a basic, yet fundamental, test of the models ability to predict dispersive and nonlinear wave propagation with minimal numerical error. Vertical velocity distributions of spatially uniform flows are compared with existing theory to investigate the effects of the newly included horizontal vorticity terms. Other test cases include comparisons with experiments that generate strong vorticity by the change of bottom bathymetry as well as by tidal jets through inlet structures. Very reasonable agreements are observed for the four cases, and the results provide some information as to the importance of dispersion and horizontal vorticity. 相似文献