Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate from the Lagrangian Viewpoint

By using the Euler-Lagrangian method, we examine water movements within the layer of minimum oxygen concentration and estimate local oxygen consumption rates for 15 regions of the global ocean. To do this, a number of labeled particles (which represent water parcels) are deployed at the center of a grid with 15 depth levels and tracked backward in time for 50 years in a three-dimensional velocity field. We assume that a particle picks up oxygen when it encounters the point of maximum oxygen concentration along the 50 years segment of its path. We introduce a contribution rate from waters distributed throughout the global ocean to the oxygen concentration of a local layer under consideration. Water parcels which are assumed to pick up oxygen within the oxygen minimum layer of an oceanic region under consideration make a very small contribution to the overall oxygen concentration of this layer. In addition, these parcels move out of the layer and water parcels from the upper layers take their place. The averaged Lagrangian local oxygen consumption rate is 0.033 ml/l/yr for the depth of the oxygen minimum layer, 0.20 ml/l/yr at 100 m depth (euphotic layer), 0.043 ml/l/yr for layers from 150 m to 800 m depth and 0.012 ml/l/yr for deep layers from 800 m to 3000 m. The present Lagrangian numerical experiment produces a maximum difference between observed and calculated concentrations of oxygen and, therefore, a maximum oxygen consumption rate. Although the present method has an ambiguity as to how oxygen is picked up, we nevertheless were able to identify regions in which the water parcels pick up oxygen of maximum concentration. We found that the South Equatorial Current (SEC) transports oxygen of higher concentration to the middle latitude regions of both the North Atlantic and the North Pacific across the equator.     

Application of an improved semi-Lagrangian procedure to fully-nonlinear simulation of sloshing in non-wall-sided tanks

The semi-Lagrangian procedure is widely used for updating the fully-nonlinear free surface in the time domain. However, this procedure is only available to cases when the body surface is vertical near the waterline. Present study introduces an improved semi-Lagrangian procedure which removes this ‘vertical-wall’ limitation. Coupling with the boundary element method, the improved semi-Lagrangian procedure is applied to the simulation of fully-nonlinear sloshing waves in non-wall-sided tanks. From the result comparison with the open source CFD software OpenFOAM, it is confirmed that this numerical scheme could guarantee a sufficient accuracy. Further series studies on 2D and 3D fully-nonlinear sloshing waves in wedged tanks are performed. Featured phenomena are observed which are distinct from those in wall-sided tanks.     

Numerical Simulation of Wave Field near Submerged Bars by PLIC-VOF Model

Investigating the wave field near structures in coastal and offshore engineering is of increasing significance. In the present study, simulation is done of the wave profile and flow field for waves propagating over submerged bars, using PLIC-VOF （Pieeewise Linear Interface Construction） to trace the free surface of wave and finite difference method to solve vertical 2D Navier-Stokes （N-S） equations. A comparison of the numerical results for two kinds of submerged bars with the experimental ones shows that the PLIC-VOF model used in this study is effective and can compute the wave field precisely.     

Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

洋浦近岸海域污染控制规划方案优化——Ⅰ.排污口位置优选

在洋浦近岸海域计算潮流场基础上,计算预选排污口附近海水质点运动轨迹及预测污染物浓度分布,最后,从环保角度出发,推荐了洋浦地区各开发区的排污口位置,为洋浦近岸海域污染控制规划方案的制定及其优化提供了依据。     

数字海底地形分割算法

根据不同海底地形特征,提出了基于多波束测量数据进行海底地形分割的"三态值模型"法,其步骤包括:将地形数据滤波和网格化;利用"3×3"差分算子计算各节点的梯度;利用最大梯度追踪算法检测正负地形与平缓地形的分界线;利用"三态值"算法识别正、负和平缓地形。应用该方法对胶州湾实验海区多波束实测数据处理结果表明,该方法切实可行,能够对数字海底地形准确地进行快速分割。     

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast.     

Third order contribution to the wave-making resistance of a ship at finite depth of water

This paper presents a potential based boundary element method for solving a nonlinear free surface flow problem for a ship moving with a uniform speed in finite depth of water. The free surface boundary condition is linearized by the systematic method of perturbation in terms of a small parameter up to third order. The surfaces are discretized into flat quadrilateral elements and the influence coefficients are calculated by Morino's analytical formula. Dawson's upstream finite difference operator is used in order to satisfy the radiation condition. The second order solution gives better result than the first or third order solution. So the present method with the second order solution can be adopted as a powerful tool for the hydrodynamic analysis of the thin ship in finite depth of water.     

Second-order resonance of sloshing in a tank

Sloshing in a two-dimensional rectangular tank in horizontal motion is analysed based on the velocity potential theory. It is found that even when the first-order excitation is away from all the natural frequencies of the tank, second-order resonance can still occur when the sum-frequency or the difference-frequency is equal to one of the natural frequencies corresponding to the even mode. However, such resonance is not excited when the sum or difference frequency is equal to the natural frequency of an odd mode.