Damping long waves by a multi-channel structure

In this paper, a multi-channel structure was developed to attenuate waves with various wave periods. By ignoring energy losses and the factor of channel width, a simple and straightforward method was used to tackle this problem. The theoretical solution showed that a single reflected channel structure could attenuate waves of a certain wave period, while a multi-channel structure could attenuate waves with various wave periods. If an interval of 0.05<relative water depth<0.15 is concerned, a structure consisting of four reflected channels could provide a transmission coefficient of less than 0.2. Experimental tests were conducted to verify the theoretical solutions. Both theoretical solution and experimental data indicated that waves with various wave periods would be effectively attenuated after passing through the multi-channel structure. Although some factors are neglected in treating this problem, the method is applicable. An allowed transmission coefficient can be provided by a multi-channel structure only if the computed peak value is not larger than that value.     

The prediction of the dynamic and structural motions of a floating-pier system in waves

In this study, a two-dimensional floating pier consists of single rectangular impermeable pontoon with side supporting pile-columns is studied. The purpose of this study is to present a theoretical solution for the linearized problem of incident waves exerting on a floating pier with pile-restrained. All boundary conditions are linearized in the problem, which is incorporated into a scattering problem and radiation problem with unit displacement. The method of separation of variables is used to solve for velocity potentials. For the radiation problem with unit heave and pitch amplitude, the boundary value problem with non-homogeneous boundary condition beneath the structure is solved by using a solution scheme. By calculating the wave force from velocity potential and solving the equation of motion of the floating structure simultaneously a close form theoretical solution for the problem is developed. The finite element method was also applied to calculate the dynamic responses on the supporting piles subjected to the pontoon motions and incident waves.     

Numerical Modeling of a Round Jet Discharged into Random Waves

Coastal disposal of waste water can be idealized as the problem of a jet under random waves. Understanding of this phenomenon is important for engineering design and environmental impact assessment. The present study aims to simulate such phenomenon by using a 3D numerical model based on the solution of the spatially filtered and σ-transformed Navier–Stokes equations with dynamic sub-grid scale model of turbulence. The numerical solution procedures are split into three steps: advection, diffusion and pressure propagation, and a Lagrange–Euler method is used to track the free surface. Cases of vertical jet in stagnant water, pure random waves and vertical jet in random waves are simulated with the same grid system for comparative study. Different methods of generating jet inflow turbulence have been tested and the method of jet azimuthal modes is found to be the optimum. The numerical results reproduce the distinct characteristics of jet in waves, including faster decay of centerline velocity, wider lateral spreading and the occurrence of wave tractive mechanism.     

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.     

Irrotational,progressive surface gravity waves near the limiting height

Numerical solutions of irrotational, progressive surface gravity waves in water of a constant depth are obtained by means of an iterative method. Our results suggest that waves with the surface slope angle greater than/6 may exist. The calculated phase velocity of deep water waves near the wave steepness 0.14 is significantly smaller than the value given by the Stokes' fourth approximation.In order to check our method, we apply it to the problem proposed byDavies (1951), which is hypothetical but similar to the present problem, and for which the exact solution is known. In this case our results show good agreement with the exact solution.     

Singularity and Breaking of the Third Order Stokes Waves

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FPSO甲板上浪研究现状

浮式生产储油轮（FPSO）是当今海洋石油开发的主流设施。FPSO通常采用单点系泊系统,船首暴露在波浪作用下,定位于特定海域进行长达数年的长期作业,上浪的风险很大。甲板上浪及其产生的载荷已是当前国际FPSO工程和研究领域的热点之一。介绍了国内外在试验研究和理论研究两方面对FPSO甲板上浪研究的进展情况,并建议我国开展这方面的研究。     

On some stability properties of the discretization of damped propagation of shallow-water inertia–gravity waves on the Arakawa B-grid

We investigate a problem mentioned by Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2), who looked at the problem of the discretization of inertia–gravity waves in the staggered B-grid. We generalize this study by adding diffusion. General stability conditions are found with the help of Miller's theorem, and the paradox found in Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2) is discussed. It is argued that it stems from inappropriate application of boundary conditions in conjunction with a Coriolis force treatment which could produce mechanical work.     

Decomposing damped incident and reflected waves using correlation and quasi-linearization methods

Water waves propagating over a layer of soft mud or submerged aquatic vegetation can drastically attenuate over distances comparable to several wave lengths. The attenuation in the case of mud has been found previously to be reasonably described by an exponential decay. Waves reflect from beaches and any structures that they impact. The reflected waves affect wave heights measured in the field or laboratory wave basins.Decomposition of small amplitude waves into incident and reflected waves is a linear problem. However, the presence of the exponential damping introduces nonlinearity to the decomposition problem and requires an iterative process for solving the problem. Despite considerable experimental research on attenuation of waves over mud, none of the existing methods for decomposition of incident and reflected waves have accounted for this case.Here, the Newton Algorithm was used to account for the effect of wave decay over mud by quasi-linearizing the nonlinear equations. Also, a second method using a new error function and a commercial nonlinear solver was proposed in both time and frequency domain. The performance of both methods has been verified using artificial as well as laboratory data.     

Dynamic response of a poro-elastic soil to the action of long water waves: Determination of the maximum liquefaction depth as an eigenvalue problem

In this work, a theoretical analysis of the dynamic response of a poro-elastic soil to the action of long water waves is conducted. For some combinations of the physical parameters of the soil and the water waves, the vertical stress tends towards zero at a certain unknown depth in the soil, as measured from the top of that medium. Under this condition, the liquefaction of the soil is imminent, at which time the excess pore pressure is essentially equal to the overburden soil pressure. Physical problems of this type have been widely studied in the specialized literature. However, most major studies have focused on solving the governing equations together with a liquefaction criterion. Here, the maximum momentary liquefaction depth induced by long water waves is considered as part of the problem, which is treated as an eigenvalue problem. To solve this problem, the governing equations are written in dimensionless form. The theoretical results show that for long waves, the horizontal displacements are smaller in magnitude than the vertical displacements, and when the wavelength or wave period increases, the maximum liquefaction also increases. Analytical solutions for the excess pore pressure and the horizontal and vertical displacements are obtained. The analytical results for the pore pressure are found to be very close to the analytical results reported in the specialized literature.     

Stationary waves in the flow of a homogeneous fluid with vertical shear of the velocity

A plane problem of free stationary gravitational waves in a horizontal current with vertical shear of the velocity is studied in the linear statement. The determination of the parameters of waves is reduced to the solution of the Sturm–Liouville boundary-value problem. For some vertical distributions of current velocity, we obtain analytic solutions. We propose a numerical algorithm for finding the parameters of waves. On the basis of the performed analysis, we establish the possibility of existence of stationary surface waves in currents for certain ranges of the Froude number. As the Froude number decreases, the waves become shorter, which leads to a faster attenuation of waves disturbances with depth. Under the actual conditions, the waves are short and suffer the influence of shear currents only in the subsurface layer of the ocean.     

Nonlinear Analysis of Nearshore Wave Height Variation Due to Shoaling

Wave formulae derived from the dispersion relation for cnoidal waves are used to find an analytical solution to the problem of nearshore wave height variation on a simple topography, i. e., with an incrementally constant slope. The solution accounts for shoaling, frictional dissipation and will be sufficiently accurate for practical purposes considering the simplified assumptions which are necessary for the treatment of this problem by any method.     

Wave pressures on a vertical wall due to short-crested waves: fifth-order approximation

Non-linear wave pressure induced by short-crested waves on a vertical wall is an important factor to be considered in the design of coastal structures. The existing models to estimate the wave pressure in engineering design are limited to the third-order solution ([Hsu et al., 1979]). In this paper, an analytical solution up to the fifth-order is derived through perturbation approximation. This analytical closed-form solution is used to investigate the contributions of the higher-order components in short-crested waves. It is found that fifth-order components significantly affect the change of pressure, especially in shallow water and larger waves.     

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.     

考虑旋转向量水平分量的大洋内波方程的一个渐近解

对于考虑旋转向量水平分量的大洋内波方程,本文求出了满足该方程的波函数的一个渐近解.该渐近波函数的振荡特性得到研究,结果表明旋转向量水平分量对高模态(高波数)内波的影响是不可忽略的.     

Padé coefficients for the solution of the wave dispersion equation under ice

The equations governing the propagation of linear gravity waves in ice-covered waters of finite depth is delineated for the linear elastic deformation of the ice plates that are modeled as elastically supported. The possible limiting condition for the validity of the assumptions involved in the formulation of the problem is discussed. A solution procedure for the solution of the wave dispersion equation under ice is discussed and a set of coefficients synthesized using the properties of infinite series and Padé approximants. Direct application of these coefficients for the calculation of wave characteristics in ice-covered sea will eliminate the need for iterative procedure, and hence will reduce the computational time. The derived coefficients were used for the computation of the wave characteristics of laboratory simulated waves and compared with the values obtained through iteration and the error was found to be less than 2%.     

Short gravity waves on steady non-uniform currents obtained through up-/downwelling

Small amplitude water waves propagating in a medium with a steady non-uniform current are investigated. The non-uniform current is obtained by up- or downwelling through the horizontal bed. A new locally valid velocity potential correct to the second order is derived describing the combined wave–current motion. From this solution expressions for the local evolution of the wave amplitude and the wave number are extracted. These expressions are compared with the results found using the principle of wave action conservation and the linear dispersion relation, and good agreement is found at small distances compared to the wavelength. Unlike earlier works there is no restriction to deep water. The results valid for deep water are found as a special case of the general solution and agree with the solution found by Longuet-Higgins, M.S. and Stewart, R.W. (1961) The changes in amplitude of short gravity waves on steady non-uniform currents. Journal of Fluid Mechanics, 10(4), 529–549. Furthermore, it is shown that the principle of wave action conservation in fact holds for waves propagating in a medium with a steady non-uniform current maintained by up-/downwelling also on finite depth.     

On waves propagating over poro-elastic seabed

In this study, an analytical solution is developed for the problem of periodic waves propagating over a poro-elastic seabed of infinite depth. Water waves above the seabed are described using the linear wave theory. The poro-elastic seabed is modelled based on the Biot theory in which the inertia effect and Darcy's friction are added. Continuity of dynamic pressure and flow flux at the interfacial seabed surface are considered. Adopting an approach similar to Hsu et al. (1993), the governing equations for the pore pressure and displacements of the poro-elastic medium are derived. The present analytic solution compares favorably well with experimental results by Yamamoto et al. (1978), and analytical results by Song (1993) for the case of fine sand. Using the present theory, variations of the wavelength and fluid pressure caused by coupling of waves and the poro-elastic seabed are discussed. Results show that higher elasticity of the poro-elastic seabed induces larger interface pressure, but higher permeability causes smaller pressure on the seabed interface. The wave length is affected by the poro-elastic seabed and becomes shorter for softer seabed and shallower water depth.     

The effect of frequency dispersion on plane waves generated as a result of bed motions

Using a linear statement, the paper studies surface waves occurring due to minor shifts of the bottom sections. A plane case is considered. An analytical solution to the problem has been derived using Fourier transforms. Asymptotic laws for the degeneration of waves propagating over finite bottom deformations have been defined. Numerical analysis of the integrals is applied to study the effect of the horizontal extent of a wave generation area and bottom irregularities on the shape of waves and their amplitudinal and energetic parameters. Attention is focused on the manifestation of frequency dispersion at the stage of wave generation as a developed wave process. Translated by Vladimir A. Puchkin.