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.     

A laboratory study of directional spectra with maximum likelihood method-Ⅰ Developing wind wave

measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likelihood method The investigations reveal that the angular spreading of the wave energy is consistent with cos^2s(θ/2) proposed by Longuet-Higgins et al.(1963, Ocean Wave Spectra, 111-136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole resalts. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al.(1975, Journal of Physical Oceanography, 5, 750-760) and Hasselmann et al.(1980, Journal of Physical Oceanography, 10, 1264-1280) in the field, and the relationship between the four nondimensional parameters s_m, f_o, b₁ and b₂, determining the directional width, and ū₁₀ (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al.(1985, Philosophical Transaction of Royal Society of London, A315, 509-562) when applied to field waves.     

支持向量机在海洋随机资料分析中的应用

在随机海洋资料的分析中,需要从大量的实际数据中提取出有用的信息来建立或检验各种海洋理论模型,因此我们要正确运用适当的手段来分析处理各种实际数据。文中简要介绍了数据挖掘中一项新的技术支持向量机,着重介绍了最优化问题的求解算法,以及如何应用于海洋资料的分析处理。     

Semi-analytical solution for the water wave diffraction by arrays of truncated circular cylinders in front of a vertical wall

The present study investigates the combined wave field that is induced by the continuous interaction of plane waves with an array of truncated circular cylinders in front of a rigid wall. The long-term goal of the study is the investigation of possible increase in the efficiency of cylindrical Wave Energy Converters (WECs) by putting in the vicinity of the array a barrier to propagation, a wall, that could assist the reflection of the incoming waves. The main task is to develop a generic solution method that is free of conceptual simplifications employed, e.g. by the method of images and the assumption of “pure” wave reflection. To cope with the set task, the proposed method relies on the semi-analytical formulation of the velocity potentials, while the solution is sought by combined expressions that involve polar and elliptical harmonics. The wall is represented as an elliptical cylinder with zero semi-minor axis. This assumption has eventually a beneficial effect to the underlying formulation given that it simplifies significantly the expansions of the involved diffraction potentials.     

A rational approach to seepage flow effects on bottom friction beneath random waves

The bottom friction beneath random waves is predicted taking into account the effect of seepage flow. This is achieved by using wave friction factors for rough turbulent, smooth turbulent and laminar flow valid for regular waves together with a modified Shields parameter which includes the effect of seepage flow. Examples using data typical to field conditions are included to illustrate the approach. The analytical results can be used to make assessment of seepage effects on the bottom friction based on available wave statistics. Generally, it is recommended that a stochastic approach should be used rather than using the rms values in an otherwise deterministic approach.     

Granular experiments of thrust wedges: Insights relevant to methane hydrate exploration at the Nankai accretionary prism

The accumulation mechanism of methane hydrates has been a central issue in previous hydrate research regarding the Nankai accretionary prism, southwest of Japan. Expulsion of formation fluids is significant during the prism accretion process, and the migration of these methane-bearing fluids exerts a strong control on the accumulation of hydrates. Two types of fluid pathways, inter-granular porosity and faults, need to be evaluated to understand hydrate accumulation. Fluid migration along faults can be partly modeled by examining faulting activity. Our study modeled the accretion process by using two granular methods that approximated the geologic body as an assemblage of particles: (1) analog experiments using granular materials, and (2) a numerical simulation based on the distinct element method. The analog experiments closely reproduced the prism geometry observed in seismic profiles across the Nankai accretionary prism. Digital image correlation analysis indicated that the frontal thrust is generally active but older structures are also frequently reactivated. The numerical simulations produced prism geometries similar to those of the analog experiments. The velocity distributions of the particles showed evidence of episodic faulting and reactivation, but the internal stress field exhibited little change in the deeper part of the prism during deformation. The frequent and substantial changes in fault activity displayed by the models indicate episodic fluid flow along fault surfaces. Active frontal thrusting suggests that formation fluids generally migrate from deep within the prism to the deformation front, but may move along reactivated older faults. Inter-granular permeability also fluctuates, as it is controlled by temporal and spatial variations in the internal stress field. However, fluid flow is likely to be relatively stable in the deeper segment of the prism.     

Critical Top Tension for Static Equilibrium Configuration of A Steel Catenary Riser

This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser（SCR） by using the finite element method. The critical top tension is the minimum top tension that can maintain the equilibrium of the SCR. If the top tension is smaller than the critical value, the equilibrium of the SCR does not exist. If the top tension is larger than the critical value, there are two possible equilibrium configurations. These two configurations exhibit the nonlinear large displacement. The configuration with the smaller displacement is stable, while the one with larger displacement is unstable. The numerical results show that the increases in the riser＇s vertical distances, horizontal offsets, riser＇s weights, internal flow velocities, and current velocities increase the critical top tensions of the SCR. In addition, the parametric studies are also performed in order to investigate the limit states for the analysis and design of the SCR.     

海泥环境中阴极保护的边界元计算

根据阴极保护的特点,建立了用于数值计算的模型;采用边界元方法对海泥介质中的阴极保护系统进行了计算,获得了海泥中钢管表面以及海泥介质内部的电位分布。将计算的结果与测量的数据进行比较,两者具有较好的一致性。     

Estimation of Land Subsidence Based on Groundwater Flow Model

This article presents an approach for estimating land subsidence due to withdrawal of groundwater. The proposed method calculates the groundwater seepage in 3-D-condition and calculates the land subsidence one-dimensionally. The governing equation on groundwater seepage is based on the three-dimensional mass conservation law and the principle of effective stress. The land subsidence calculation method is derived based on the following assumptions: (1) displacements occur only in the vertical direction, and (2) in vertical direction the total stresses do not change. The governing equation is solved by numerical method, i.e., finite element method (FEM) in spatial discretization and finite difference method (FDM) in time series discretization. In FEM Galerkin method is adopted and in FDM, lumped matrix method is employed. The proposed method is calibrated via analyzing 1-D consolidation problem and the results are compared with those from Terzaghi's one-dimensional consolidation theory and oedometer test. The proposed method is employed to analyze the consolidation of a soft layer due to withdrawal of groundwater from an aquifer under it. Moreover, this method is also applied to a field case of land subsidence due to groundwater pumping in a gas production field in Japan. The analytical results are compared with the field observed data. The results show that this approach simulates the field case well.     

Evaluation of Bearing Capacity for Multi-Layered Clay Deposits with Geosynthetic Reinforcement using Discrete Element Method

A stability analysis of reinforced foundation soil is presented in this paper. A method based on the discrete element method (DEM) is suggested for calculating the bearing capacity on strip footings over multilayer soils reinforced with a horizontal layer of geosynthetics. The proposed method can estimate the ultimate bearing capacity and the distribution of tensile force developed in the geosynthetics of the footing system by Winkler springs to account for the compatibility between soil blocks and tensile elements to consider the tensile behavior between soil and geosynthetics. For footings on various multilayer soils with or without reinforcement of geosynthetics, the results of the method were compared to the field test results as well as to those obtained by various methods proposed by other researchers.