A SPH numerical wave basin for modeling wave-structure interactions

Based on a parallel SPH-LES model, a three dimensional numerical wave basin is developed to study wave interaction with coastal structures. The OpenMP programming technology combined with an existing MPI program contained in the parallel version of SPHysics code has been implemented to enable the simulation of hundred millions of particles running on a computer cluster. As part of the numerical basin development work an active absorbing wave maker and a sponge layer are introduced. The dynamic boundary conditions are also corrected to reduce the spurious effects. Wave generation and propagation in the numerical wave basin is first tested and confirmed with analytical results. Then, the model is applied to simulate wave interactions with a vertical breakwater and a vertical cylinder in order to further assess the capability of the numerical wave basin. The predicted free surface elevation near the vertical breakwater is compared with the experimental data while the horizontal forces and overturning moments acting on the vertical cylinder are verified with the analytical results. In all these cases the model results show excellent agreement with the validation data.     

Observations of wave-structure interaction for a multi-legged concrete platform

This paper presents the results of a physical model study of waves around the Brent Bravo gravity based structure. The work arose as a result of a recent incident in which significant amounts of water were projected upwards, thus causing damage to ancillary steelwork and pipework. Measurements of the water surface elevation in the vicinity of the model structure show that the three large, closely spaced legs give considerable wave-structure interaction. In particular, if the incident waves are relatively short and steep, this wave-structure interaction produces high-frequency waves which radiate outwards from the centre of the structure. Nonlinear interaction of these waves with the incoming wave field leads to enhancement of their height and steepness, and explains the very high water surface elevations experienced at Brent Bravo.

Although the present data specifically relate to this structure, similar behaviour may arise in other types of structures with large, closely spaced legs. The observed nonlinear wave-structure interaction is also relevant for the study of ‘ringing’, or the highfrequency response of relatively flexible structures, but in the case of very stiff structures such as Brent Bravo, this leads to excitation of the fluid rather than the structure. For structures where nonlinear interaction with waves may occur, it cannot be assumed that the crest elevation in the open sea provides a good estimate for the air-gap. However, it must be stressed that given the nature of the interaction, any wave impact will be local rather than global and will therefore not threaten the overall integrity of the structure. On the basis of the test results, practical guidance was developed for the assessment of loads on items in the air-gap of Brent Bravo.     

二维自由面条件和辐射条件的数值模拟

在时域内对二维自由面条件和远方辐射条件进行数值模拟,自由面条件采用先积分后离散的处理方式,远方条件采用匹配积分方程的方法和透射理论的人工边界方法处理。分别计算了圆柱与水面直交和斜交时的水动力系数以及摇板造波问题的速度势,计算结果与文献值和理论值符合程度良好。     

地转条件下的浪致辐射应力

首先将Longuet-Higgins提出的海浪辐射应力拓广为自海面至任意深度的单位面积铅直水柱承受的海浪辐射应力,并在此基础上首次给出地转条件下单位水体承受的海浪辐射应力计算式.最后给出单位水体承受的浪致作用力,为在海流数值模拟中便利的考虑海浪对流的驱动作用提供必要的条件.     

A time-dependent numerical model of the mild-slope equation

On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time-dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin’s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin’s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin’s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real-time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area.     

Numerical modelling of wave-structure interaction by a three-dimensional nonlinear boundary element method: A step towards the numerical wave tank

A three-dimensional numerical model for determination of the interaction between non-linear water waves and a structure is developed. The model is based on a boundary integral equation method for the spatial solution of a potential theory problem, combined with a time-stepping method based on the fully non-linear free surface conditions for temporal updating of moments on a structure in the fluid domain. Comparison with experimental results shows good agreement. The present model is considered to be one of the steps towards a three-dimensional numerical model in which the wave-structure interaction in a wave tank can be simulated.     

A condition index for African penguin Spheniscus demersus chicks

The body condition of altricial seabird chicks is directly related to the amount of food received from their parents, which depends on feeding conditions at sea. An index of body condition is therefore a useful tool for assessing variation in food availability between different breeding colonies. Quantile regression techniques were used to develop a body condition index for African penguin Spheniscus demersus chicks, based on maximum and minimum growth relative to structural size. This is considered the most appropriate index for comparing the body condition of groups of chicks, varying in size and of unknown age, between breeding colonies. Based on this study, recommendations are made with regard to morphometric measurements, sample size and the sampling interval required to compare effectively the condition of African penguin chicks between breeding colonies throughout their distributional range.     

A B-spline-based method for radiation and diffraction problems

An open uniform B-spline-based panel method is developed for solution of potential flow problems. In this method, both geometry as well as the field variables are represented by the same open uniform B-spline basis function. The method is initially applied for the radiation problem in unbounded fluid. Computed results for a spheroid of different aspect ratio are found to be in excellent agreement with analytical results. The method is then applied for diffraction problem formulated based on the transient (time-domain) Green's function. Computed results for a hemisphere and Wigley hull are compared with published results and the comparison shows good agreement.     

Comparison of time-dependent extended mild-slope equations for random waves

The extended mild-slope equations of Suh et al. [Suh, K.D., Lee, C., Park, W.S., 1997. Time-dependent equations for wave propagation on rapidly varying topography. Coastal Eng., 32, 91–117] and Lee et al. [Lee, C., Kim, G., Suh, K.D., 2003. Extended mild-slope equation for random waves. Coastal Eng., 48, 277–287] are compared analytically and numerically to determine their applicability to random wave transformation. The geometric optics approach is used to compare the two models analytically. In the model of Suh et al., the wave number of the component wave with a local angular frequency ω is approximated with an accuracy of O(ω − ω¯) at a constant water depth, where ω¯ is the carrier frequency of random waves. In the model of Suh et al., however, the diffraction effects and higher-order bottom effects are considered only for monochromatic waves, and the shoaling coefficient of random waves is not accurately approximated. This inaccuracy arises because the model of Suh et al. was derived for regular waves. In the model of Lee et al., all the parameters of random waves such as wave number, shoaling coefficient, diffraction effects, and higher-order bottom effects are approximated with an accuracy of O(ω − ω¯). This approximation is because the model of Lee et al. was developed using the Taylor series expansion technique for random waves. The result of dispersion relation analysis suggests the use of the peak and weighted-average frequencies as a carrier frequency for Suh et al. and Lee et al. models, respectively. All the analytical results are verified by numerical experiments of shoaling of random waves over a slightly inclined bed and diffraction of random waves through a breakwater gap on a flat bottom.     

A simulation of radiation imagery for ocean color satellite

The ocean color satellite is mainly applied to measure the water constituents such as chlorophyll, suspended material and yellow substance. The leaving water radiance is very small part of the total radiance arrival at the sensor about 3%-15%,and depends on the properties of the orbit and sensor. Before the satellite is launched on the orbit, it needs to simulate the radiation imagery in order to evaluate the quality and availability of the satellite data.
If the parameters of satellite orbit, the properties of sensor as well as the characteristics of the atmosphere and water have been known, the radiation scattered by air molecule and aerosol, reflected solar radiation, water leaving and total radiation arriving at the sensor can be simulated by the models of radiation transfer in the atmosphere, air/water and subsurface water. In this paper, the mechanism, models and procedures of the radiation simulation are first discussed and employed to simulate a series of imageries for the Chinese satellites FY-lA, FY-1B, and ROCSAT-1 (Taiwan, China), and American satellite Ses STAR. Their results show that the solar irradiance arrived at water surface and the sun glitter mainly affect the quality and availability of satellite data, which depend on the orbit properties. Finally, some suggestions are proposed to improve the quality and availability of a:ean color satellite data.     

Time-domain simulation of wave–structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition

Based on the Rankine source, this paper proposed a time-domain method for analyzing the three-dimensional wave–structure interaction problem in irregular wave. A stable integral form of the free-surface boundary condition (IFBC) is employed to update the velocity potential on the free surface. A multi-transmitting formula, with an artificial wave speed, is used to eliminate the wave reflection for radiation condition on the artificial boundary. An effective multi-transmitting formula, coupled with damping zone method, is further used to analyze the irregular wave diffraction at the artificial boundary. We investigate hydrodynamic forces on floating structure and compare our solution to the frequency-domain solution. It is shown that long time simulation can be done with high stability and the numerical results agree well with the solution obtained under the frequency domain. The efficiency of the proposed multi-transmitting formula and the coupled methods for radiation boundary make them promising candidates in studying the irregular water wave problem in time domain.     

A panel-free method for time-domain analysis of the radiation problem

A panel-free method (PFM), based on the desingularized Green’s formulae proposed by Landweber and Macagno, has been developed to solve the radiation problem of a floating body in the time domain. The velocity potential due to a non-impulsive velocity is obtained by solving the boundary integral equation in terms of source strength distribution. The singularity in the Rankine source term of the time-dependent Green function is removed. The geometry of a body surface is mathematically represented by NURBS surfaces. The integral equation can be globally discretized over the body surface by Gaussian quadratures. No assumption is needed for certain degree of approximation of distributed source strength on the body surface. The accuracy of PFM was demonstrated by its application to a classical problem of uniform flow past a sphere. The response function of a hemisphere at zero speed was then computed by PFM. The computed response function, added-mass and damping coefficients are compared with other published results.     

A low-scattering approximation for the hydrodynamic interactions of small wave-power devices

This paper concerns mathematical modelling of the hydrodynamic interaction forces between small vertically axisymmetric wave-power devices. The model takes into account small-body approximations for the first order scattered waves but neglects multiple scattering. Further, the local wave fields are neglected, making the model inapplicable for very closely spaced bodies.The model, which is called the low-scattering approximation, comprises analytical formulae for the forces in any of the translation modes surge, sway and heave. It requires, however, that the following isolated-body parameters are known or externally supplied: the added mass and the force coefficients for both heave and surge motion.Comparison with accurate numerical results of a two-buoy system indicates that the present approach is fairly good even when the buoy diameter is as large as 1/6 of the wavelength and the buoy spacing is as small as 5 buoy radii.     

A new facility for studying ocean-structure–seabed interactions: The O-tube

This paper describes a unique new physical testing facility for studying ocean-structure–seabed interactions, and in particular pipeline on-bottom stability on erodible seabed under hydrodynamic loading. The facility, named the O-tube due to its shape, is a fully enclosed flume in which ambient and storm-induced near-seabed flows are generated by a computer-controlled flow pump. Combined steady and oscillatory flow can be generated by alternating pump flow directions in a controlled manner, and computer control also allows irregular flow to be generated. The design of the O-tube combines the capabilities of a conventional open channel flume (which provides steady current) with a U-tube (which provides oscillatory flow). The facility is designed to physically model severe storm conditions, as well as ambient or tidal flows. When studying pipeline stability on erodible seabed under severe hydrodynamic loading conditions, tests can be performed at a relatively large scale (typically 1/5) for large diameter pipelines (e.g. 40 in. gas trunklines) and at full scale for small diameter pipelines (< 8 in.) to minimize potential scaling effects associated with movable bed model tests. The specifications of the O-tube, a model pipe and an actuator system that supports the model pipe are given in detail. Preliminary model testing results show that the facility has met its design expectations.     

Moving shoreline boundary condition for nearshore models

The paper develops and analyzes two fully nonlinear boundary conditions that incorporate the motion of the shoreline in nonlinear time domain nearshore models. A moving shoreline essentially means the computational domain is changing with the solution of the flow. The problem is solved in two steps. The first is to establish an equation that determines the motion of the shoreline based on the local momentum balance. The second is to develop and implement into a shoreline model the capability of accommodating a changing computational domain. The two models represent two different ways of addressing this step: one is to track the position of the shoreline in a fixed grid by establishing a special shoreline point which generally is not a fixed grid point. The second is by a coordinate transformation that maps the changing domain onto a fixed domain and solves the basic equations in the mapped domain. The two shoreline conditions are tested against three known solution for nonlinear shoreline motion. Two are the 1-D solutions to the nonlinear shallow water (NSW) equations by Carrier and Greenspan [J. Fluid Mech. 4 (1958) 97], one representing the response to a transient change in the offshore water level, the other the motion due to a periodic standing wave, both on slopes steep enough to allow full reflection. The third is the 2-D horizontal (2DH) computational solution by Zelt [Coast. Eng. 15 (1991) 205] for the run-up of a solitary wave on a cusped beach. In all cases, both models are shown to behave well and give high accuracy results for suitably chosen grid and time spacings.     

Extended KdV equation for transient axisymmetric water waves

The equation for non-linear water waves in shallow water with cylindrical symmetry is established in the form of the Extended KdV (EKdV) equation. The method of solution is based on the Split Step Fourier Algorithm. It is applicable in both directions; that is, given a wave record near the origin, the theory predicts the wave evolution. Similarly, given a wave record at a distance from the origin, the method is able to predict the original wave near the origin. Theory is applied to and verified by transient wave records obtained from underwater explosions and by dropping a large cylindrical plate in very shallow water. The difference between the KdV and the Extended KdV equation is emphasized for small valuev of Ursell parameter.     

斜入射分层线性各向异性等离子体电磁散射时域有限差分方法分析

提出了斜入射分层线性各向异性等离子体电磁散射的时域有限差分(FDTD)方法,通过将二维麦克斯韦方程等价地转换为一维麦克斯韦方程,避免了用二维时域有限差分方法分析该散射问题,极大地提高了计算效率.分析推导了TE_z和TM_z波斜入射线性分层各向异性等离子体电磁散射的FDTD方法,然后通过该方法计算不同入射角的各向异性等离子板的电磁波反射系数,并与其解析解进行比较,结果表明该方法的准确性和有效性.最后,将该算法应用于计算涂覆分层各向异性等离子     

Improved coastal boundary condition for surface water waves

Surface water waves in coastal waters are commonly modeled using the mild slope equation. One of the parameters in the coastal boundary condition for this equation is the direction at which waves approach a coast. Three published methods of estimating this direction are examined, and it is demonstrated that the wave fields obtained using these estimates deviate significantly from the corresponding analytic solution. A new method of estimating the direction of approaching waves is presented and it is shown that this method correctly reproduces the analytic solution. The ability of these methods to simulate waves in a rectangular harbor is examined.