均质地基上浅埋矩形基础极限承载力上限分析

基于土体塑性极限分析理论,推导一般黏性土地基上矩形基础承载力的上限解。为了证实上限解的合理性与适用性,采用大型通用有限元分析软件ABAQUS进行数值分析,并分别与Vesic理论解和Salgado et al理论解进行了对比。结果表明,推导的三维矩形基础上限解能较好地计算黏性土地基的极限承载力。     

一种随时间变化的近区稀释的半解析解

根据基本的扩散方程，以污染物质输入量为已知条件，给出了一种近区稀释的半解析解。该半解析解摆脱了流速是单向的、持续的和定常的条件限制，反映了近区稀释在以潮流场为背景场的状态下，随时间的可变性。     

JZ9-3油田水质对聚合物3640C溶液黏度的影响分析

实验研究了JZ9-3油田的3种水质（水源水、污水、清污混合水）对聚合物溶液剪切前后黏度的影响。结果显示：在相同浓度条件下,清污混合水配制的聚合物溶液黏度最高,其次是污水配制的聚合物溶液,水源水配制的聚合物溶液黏度最低;聚合物溶液经WARING搅拌器（1档3 500 rpm,20 s）剪切后的黏度保留率数据显示,污水配制的聚合物溶液剪切后黏度保留率最高,当浓度大于1 000 mg/L时,保留率在90%左右;最低的是水源水配制的聚合物溶液,保留率在55%左右。分析发现二价阳离子除了对聚合物溶液的黏度存在一定的影响外,对聚合物溶液剪切后的黏度保留率影响更大。     

基于矩阵分解的平差解算方法研究

首先分析了法方程稳定性对平差解算结果的影响。为减弱法方程对平差解算结果的影响,采用矩阵分解方法直接对系数矩阵进行矩阵分解,以求解最小二乘最小范数解替代原来最小二乘的法矩阵求逆运算,从而克服法方程求逆造成的解算稳定性差和病态性问题。实验分析结果表明基于矩阵分解的平差解算精度和可靠性较优。     

Simplified Method and Improved Solution for Deriving Fifth Order Stokes Wave

As the solution of the two equations for determining the existing fifth order Stokes wave de-rived by Skjelbreia is complex and tedious,the two equations are simplified into one equation for deter-mining d/L,i.e.,f(H,T,d/L)=0.According to this simplified method,three cases of the solution forthe Skjelbreia equations have been found:one accurate solution;more than one accurate solution and noaccurate solution(but there exists the optimum approximate solution in the area of satisfying Skjelbreiaequations).As to the case of more than one accurate solution,the reasonable solution can be judged fromthe method of variational principle,by means of which an optimum solution improved from the solutionof Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex andnonlinear wave theory,i.e.,the optimum fifth order Stokes wave,is given.     

An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit

An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457–459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunt's solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed.     

Calculation of the initial elevation at the tsunami source using analytical solutions

We have obtained an analytical solution to the problem of determining the initial elevation at the tsunami source, which was formed by small residual deformations of a flat sloping bottom. This solution, which is newly derived, is compared with the known analytical solution of an equivalent problem over a horizontal bottom. It is shown that applying an analytical solution over a horizontal bottom for calculating the initial perturbations in the sources of realistic tsunami provides sufficient accuracy.     

On the heave radiation of a rectangular structure

In this paper, an analytic solution to the heave radiation problem of a rectangular structure is presented. To solve the problem analytically, the nonhomogeneous boundary value problem is linearly decomposed into homogeneous ones, which can be readily solved. To provide further comparisons to the present analytic solution, a boundary element method is also presented to solve the problem. The present analytic solution is compared with the result by Black et al. [(1971)] Radiation and scattering of water waves by rigid bodies. J. Fluid Mech. 46, 151–164], and the boundary element solution, and the comparisons show very good agreements. Upon examination of the present analytic solution, it is shown that the solution satisfies the nonhomogeneous boundary condition in a sense of series convergence. Using the present analytic solution, the generated waves, the added mass and the radiation damping coefficients, as well as the hydrodynamic effects of the submergence and the width of the structure, are investigated.     

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear (1961), confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.     

Analysis of orthogonal wave reflection by a caisson with open front chamber filled with sloping rubble mound

A new combined caisson, including an open window on the front wall and an internal rubble mound with a slope, has been proposed and used in Italy. This study presents a semi-analytical solution to estimate the wave absorbing performance of the new combined caisson with regard to orthogonal wave attack. The internal slope of the rubble mound is assumed to be a series of horizontal steps. Then the matched eigenfunction expansions are used to develop the semi-analytical solution. The square-root singularity of fluid velocity at the upper tip of the front submerged wall is incorporated into the solution to enhance the convergence of calculated results. The new semi-analytical solution is confirmed by an independently developed multi-domain boundary element method solution. Also the predictions of the semi-analytical solution agree reasonably well with experimental data. Based on both the calculations and the experimental data, some useful results are presented for practical engineering.     

A new approximate analytic solution for water wave scattering by a submerged horizontal porous disk

This study gives a new approximate analytic solution for water wave scattering by a submerged horizontal porous disk in the context of the linear potential theory. The solution is based on the domain decomposition method. The velocity potentials are determined by two different approaches. One approach is to adopt decompositions for velocity potentials, and the other is to expand the vertical derivative of the velocity potential on the porous disk along the radial direction. Hence the velocity potentials are determined by the matched eigenfunction expansions. Differing from previous solutions with respect to the porous disk, the present solution needs no complex dispersion relations. Thus the new solution is easier for numerical implementation. According to numerical examples, the convergence of the present solution is satisfactory. In addition, the present predictions of the wave surface elevation and the vertical wave force on the disk agree very well with previous results by different approaches. The present solution can also be extended to other structures involving disks, such as a fish cage, a porous disk with finite thickness, and a submerged elastic disk.     

潮波方程数值格式与摩阻系数选取

基于一维阻尼潮波传播方程解析解,从求解数值格式及Heuristic稳定性分析方面,讨论了数值解的精度、计算耗时和摩阻系数选取等问题。研究结果表明:1)Courant数小于1时,潮波方程显格式解的精度略高于隐格式解,计算耗时少于隐格式解;2)为减少计算耗时,潮波方程的隐格式解允许较大的时间步长,但解的精度有所降低,须通过减小底床摩阻系数以保证计算精度;3)隐格式解摩阻系数的选取与Courant数有关,Courant数越大,摩阻系数的选取值比实际值越小,通过理论分析结合数值试验得到了相应的关系式。这些研究结论对实际海域的潮波传播的数值模拟具有重要的应用价值。     

ANALYTICAL SOLUTION FOR THE VELOCITY POTENTIAL OF LINEAR WAVES OVER SLOPING BEACHES

An analytical solution for the velocity potential of linear waves traveling over sloping beaches is obtained in the present paper, the restriction to the solution, i. e. the cube of bottom slope a being negligible. When the terms of order of a2 are neglected, the solution is the same as that presented by Biesel in 1951[1]. When the terms of order of a2 are retained, the wave dispersion relation is corrected. Forthermore, the solution corrected to any higher order of a can be obtained without difficulty by means of the disturbation method given by this paper".     

Linear wave reflection by trench with various shapes

Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed.     

An approximate solution of wave-modified Ekman current for gradually varying eddy viscosity

An approximate steady solution of the wave-modified Ekman current is presented for gradually varying eddy viscosity by using the WKB method with the variation of parameters technique. The parameters involved in the solution can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water. The solution reduces to the exact solution when the eddy viscosity is taken as a constant. As illustrative examples, for a fully developed wind-generated sea with different wind speeds and a few proposed gradually varying eddy viscosities, the current profiles calculated from the approximate solutions are compared with those of the exact solutions or numerical ones by using the Donelan and Pierson wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. It is shown that the approximate solution presented has an elegant form and yet would be valid for any given gradually varying eddy viscosity. The applicability of the solution method to the real ocean is discussed following the comparisons with published observational data and with the results from a large eddy simulation of the Ekman layer.     

The time-dependent motion of a floating elastic or rigid body in two dimensions

The linear time-dependent motion of a floating elastic or rigid body, subject to some initial displacement, which subsequently evolves freely is considered. The solution is derived by a Fourier transform and by the generalized eigenfunction method. Compared to other solutions, such as the Cummins method, the present solution requires neither time-stepping nor high-frequency calculations. A series of new identities for the frequency-domain problem are also presented. The Fourier transform solution allows an approximate solution to be calculated by an expansion over the complex resonances known as the singularity expansion method. Simple expressions for the singularity expansion method approximation are given. The method is illustrated with a series of numerical calculations.     

Theoretical solution for wave diffraction by wedge or corner with arbitrary reflection characteristics

An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral representations, corresponding recurrence relation and asymptotic expressions are also derived. The solution is simplified for some special cases of rπ. For Rr= R0,r= 1/N and Rr≠R0,r = 1/2N, the solution can be reduced to linear superpositions of incident and partially reflected waves, hence a nonlinear solution of forth order for this problem can be obtained by using the author's theory of nonlinear interaction among gravity surface waves. The given solution is related to inhomogeneous Robin boundary conditions, which include the Neumann boundary conditions usually accepted in wave diffraction theory.     

The Transient Solution of Plane Progressive Waves

- Generated by an ideal sinusoidal motion of the vertical plate, the simplest linear solution in time domain for two-dimensional regular waves is derived. The solution describes the propagation process of the plane progressive wave with a front, and will approach the linear steady- state solution as the oscillation time of the plate approaches infinity. The solution presented in this paper can be used to provide an incident wave model with analytical expression for solving the problems of diffraction and response of floating bodies in time domain.     

Notes on linear and nonlinear barotropic flows in a polar circular basin

Barotropic flows in a circular ocean are studied. Flows are driven by an inflow and an outflow through openings at the circumference. A linear, steady state solution is interpreted in terms of dissipating planetary waves. A weakly nonlinear, steady state solution is obtained numerically. It differs remarkably from the linear solution; an intense anticyclonic polar gyre extending over the whole basin is formed. The nonlinear term is essential to the gyre and can not be neglected, although the Rossby number is small.     

Analytical and Experimental Studies on Hydrodynamic Performance of Semi-Immersed Jarlan-Type Perforated Breakwaters

The present study proposes a new semi-immersed Jarlan-type perforated breakwater including a perforated front wall, a solid rear wall, and a horizontal perforated plate connecting the lower tips of the two walls. An analytical solution is developed to estimate the hydrodynamic performance of the new breakwater. The analytical solution is confirmed by solutions for special cases, an independently developed multi-domain boundary element method solution and experimental data. Numerical examples based on the analytical solution indicate that compared with previous semi-immersed breakwaters, the new breakwater may have better wave-absorbing performance and smaller wave forces. Some useful results are presented for practical designs of semi-immersed Jarlan-type perforated breakwaters.