台风移行速度与登陆角度对风暴潮的影响:一个理想模型数值实验

The effects of hurricane forward speed(V) and approach angle(θ) on storm surge are important and a systematic investigation covering possible and continuous ranges of these parameters has not been done before. Here we present such a study with a numerical experiment using the Finite Volume Community Ocean Model(FVCOM).The hurricane track is simplified as a straight line, such that V and θ fully define the motion of the hurricane. The maximum surge is contributed by both free waves and a forced storm surge wave moving with the hurricane.Among the free waves, Kelvin-type waves can only propagate in the down-coast direction. Simulations show that those waves can only have a significant positive storm surge when the hurricane velocity has a down-coast component. The optimal values of V and θ that maximize the storm surge in an idealized semi-circular ocean basin are functions of the bathymetry. For a constant bathymetry, the maximum surge occurs when the hurricane approaches the coast from the normal direction when the free wave generation is minimal; for a stepped bathymetry, the maximum surge occurs at a certain acute approach angle which maximizes the duration of persistent wind forcing; a step-like bathymetry with a sloped shelf is similar to the stepped bathymetry, with the added possibility of landfall resonance when the free and forced waves are moving at about the same velocity. For other cases, the storm surge is smaller, given other parameters(hurricane size, maximum wind speed, etc.)unchanged.     

Truss Spar平台在波流联合作用下运动响应预报方法比较

基于细长体水动力模型比较了Truss Spar平台在波流联合作用下运动响应预报的三种方法。分别采用波流耦合、速度叠加及力叠加计算Truss Spar平台在波流联合作用下的水动力载荷,根据流场水质点运动规律和Truss Spar外部形状特点,分段高效计算水动力载荷。利用Runge-Kutta-Fehlberg方法求解刚体非线性运动方程得Truss Spar在波流场中的运动响应。研究结果表明力叠加法所预报的Truss Spar纵荡和纵摇运动明显大于其他两种方法的相应运动响应预报结果,而波流耦合法与速度叠加法所预报的纵荡与纵摇运动响应幅值相当,三种方法所预报的垂荡运动响应的大小取决于具体波流参数。     

Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method

A 3D time-independent finite difference method is developed to solve for wave sloshing in a three-dimensional tank excited by coupled surge and sway motions. The 3D equations of fluid motion are derived in a moving coordinate system. The three-dimensional tank, with an arbitrary depth and a square base, is subjected to a range of excitation frequencies with motions that exhibit multiple degrees of freedom. For demonstration purposes the numerical scheme is validated by a benchmark study. Five types of sloshing waves were observed when the tank is excited by various excitation frequencies. A spectral analysis identified the resonant frequencies of each type of wave and the results show a strong correlation between resonant modes and the occurrence of the sloshing wave types. The method can be used to simulate fluid sloshing in a 3D tank with six-degrees of freedom.     

Higher order Boussinesq equations

A new form of Boussinesq-type equations accurate to the third order are derived in this paper to improve the linear dispersion and nonlinearity characteristics in deeper water. Fourth spatial derivatives in the third order terms of the equations are transformed into second derivatives and present no difficulty in numerical computations. With the increase in accuracy of the equations, the nonlinear and dispersion characteristics of the equations are of one order of magnitude higher accuracy than those of the classical Boussinesq equations. The equations can serve as a fully nonlinear model for shallow water waves. The shoaling property of the equations is also of high accuracy through shallow water to deep water by introducing an extra source term into the second order continuity equation. An approach to increase the accuracy of the nonlinear characteristics of the new equations is introduced. The expression for the vertical distribution of the horizontal velocities is a fourth order polynomial.     

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second-order random wave solutions of water wave equations in tinite water depth, statistical distributions of the depth-integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all detemained by the water depth and the wavenumber spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.     

The dragged surge motion of tension-leg type fish cage system subjected to multi-interactions among wave and structures

In this paper, a typical tension-leg type net cage system is analyzed, and a set of motion equations for the cage system in the simplified two-dimensional case is derived. Subsequently, a close form analytical solution is obtained when all of the multi-interactions between the top platform structure, the incident wave, and the motion of both the tether and net are considered. The parameter of solidity as a ratio of the twine diameter to the mesh size of the cage is also taken into account in the analysis. The purpose of this paper is to investigate the dragged surge motion of the tension-leg type cage system when subjected to incident waves and flow drags on the net-cages. Furthermore, the dynamic behavior of the platform is compared to the case when the net-cage drag is not considered. Numerical examples are carried out in a range of periods of waves, and the results are discussed focusing on the motion of both the platform and cage. It was found that there is a significant influence of the net-cage drag on the surge motion of the entire structural system. Various parameters such as the material property, twine diameter, mesh size and the dimension of the net-cages were considered. It was found that the vibration of the net-cage system might be significantly overestimated if the drag effect of the net and tethers is neglected.     

Application of higher-level GN theory to some wave transformation problems

Recently derived (Webster et al., 2011), simplified higher-level Green–Naghdi equations (GN-3, GN-5 and GN-7) are used in this work to simulate the transformation of two-dimensional, shallow-water wave problems. The spatial derivatives are discretized through a five-point difference scheme. A new algorithm is developed to solve the resulting block-pentadiagonal matrix. These high-level GN equations are then utilized to develop a numerical wave tank. A wave-maker is placed at the forcing boundary of the tank that uses the stream-function theory to generate nonlinear incident waves. The numerical wave tank is used to analyze the effects of large-amplitude waves passing over a submerged bar. A damping zone is placed near the wave-maker (up-wave side) to absorb the reflected waves from the front side of the submerged bar. Another damping zone is placed at the down-wave side of the computational domain to absorb the radiated waves. In the first test case, the front and back slopes of the bar are both mild (Luth et al., 1994). The waves that evolved over the bar are simulated by using the GN-3, GN-5 and GN-7 equations. The GN-3 equations provide time histories that compare well with the experimental data at different wave gauges, except at the ones behind the bar. The results of the GN-5 and GN-7 equations compare very well with all the experimental data considered here. In the second test case, the front and back slopes of the bar are both steep (Ohyama et al., 1995). The GN-5 equations predict the wave elevation well. In the third test case, the front and back slopes of the bar alternate, one of them being mild and the other one being steep (Zou et al., 2010). Again, the predictions of the GN-5 equations agree with the experimental data well. In all the test cases considered in this work, there are some differences between the GN-3 and GN-5 results after the crest of the bar. Numerical results obtained by the GN-5 and GN-7 equations are almost the same along the wave flume, but the GN-7 equations require more computational time. Therefore, the GN-5 results are accepted here as the converged GN theory results. The numerical validations show that the GN-5 equations can simulate the strongly nonlinear and dispersive waves observed behind the submerged bar crest satisfactorily.     

Diffraction of Water Waves by A Vertically Floating Cylinder in A Two-Layer Fluid

In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.     

Third order wave force on axisymmetric bodies

The third order triple-frequency wave load on fixed axisymmetric bodies by monochromatic waves is considered within the frame of potential theory. Waves are assumed to be weak non-linearity and a perturbation method is used to expand velocity potentials and wave loadings into series according to a wave steepness of kA. Integral equation method is used to compute velocity potentials up to second order in wave steepness. The third order triple-frequency wave loads are computed by an indirect method and an efficient method is applied to form the third order forcing term on the free surface quickly. The method can be used to compute third order triple-frequency surge force, heave force and pitch moment on any revolution bodies with vertical axes. The comparison with Malenica and Molin's results is made on surge force on a uniform cylinder, and comparison with experimental results is made on third order surge force, heave force and pitch moment on a truncated cylinder. More numerical computations are carried out for third order forces and moments on a uniform cylinder, truncated cylinders and a hemisphere.     

Resonant interaction of waves of continuous and discrete spectra in the simplest model of a stratified shear flow

The equations of dynamics of eddy—wave disturbances of two-dimensional stratified flows in an ideal incompressible fluid that are written in a Hamiltonian form are used to study the resonant interaction of waves of discrete and continuous spectra. A gravity—shear wave generated at a jump of the density and vorticity of the undisturbed flow and a wave generated at a weak vorticity jump, which is similar to a wave of a continuous spectrum, participate in the interaction. The equations are written in terms of normal variables to obtain the system of evolution equations for the amplitudes of the interacting waves. The stability condition for eddy—wave disturbances is derived within the framework of the linear theory. It is shown that a cubic nonlinearity may lead to the stabilization of unstable disturbances if the coefficient of the nonlinear term is positive.     

浮式塔的动力计算

采用频域二阶摄动法研究了浮式塔在给定环境条件下的动力响应.计算了浮式塔在不规则波上的一阶运动响应函数和运动谱以及张力谱,同时进行了相应的模型试验.由结果的比较可以看出,试验结果与理论方法计算得到的结果吻合较好.计算结果表明,波浪的二阶作用对浮式塔的低频纵荡有影响.计算结果与试验结果的比较说明频域二阶摄动法可以用于浮式塔的动力分析.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation,a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper.For special case of slope angle β=π/2,this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline.Interactions between two edge waves including progressive,standing and partially reflected standing waves are also discussed.The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given.The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated,and the corresponding theoretical autocorrelation and spectral density functions of the first and the second orders are derived.The boundary conditions for the determination of the parameters of short edge wave are suggested,that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory.Finally some computation results are demonstrated.     

Numerical analysis of effects of tidal variations on storm surges and waves

This study examines the effects of tides on surges, wave setups and waves, in terms of tidal amplitudes and phases, by using a coupled numerical model of Surge, WAve and Tide (called as SuWAT). The SuWAT model, composed of depth integrated nonlinear shallow water equations and Simulating WAves Nearshore (SWAN) model, is able to simultaneously run with an arbitrary number of nested domains by using the Message Passing Interface. The results for an idealized case indicate that surge and wave setup are increased in the phase of low water and decreased in the high water phase; on the other hand, waves change in a reverse manner. Such changes are enhanced by large tidal variations. The conventional method (e.g., surge plus tide independently) has the possibility of overestimation for the total water level. The hindcast results for Typhoon Ewiniar in 2006 show that the run with tides is more accurate 10% than that without tides in coastal areas of Korea. The nested scheme improves the accuracy up to 40% for the prediction of water levels in the simulations. It is shown that the present coupled model, SuWAT, is capable of predicting both water levels and waves under storm events with reasonable accuracy against the observations.     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

Effect of the damping and excitation on the identification of the hydrodynamic parameters for an underwater robotic vehicle

The main objective of this work is to investigate the effects of the damping level as well as different excitation forms on the overall prediction of the hydrodynamic parameters in the equations describing the coupled heave and pitch motions for an Underwater Robotic Vehicle (URV) sailing near the sea surface in random waves. The response of an underwater vehicle heaving and pitching in random waves having wide-band and narrow-band spectra are generated. The RDLRNNT technique is used to identify the hydrodynamic parameters in the equations. The technique is based on a combination of a multiple linear regression algorithm and a neural networks technique. The combination of the classical parametric identification techniques and the neural networks technique provides robust results and does not require a large amount of computer time. The identification technique would be particularly useful in identifying the parameters for both moderately and lightly damped motions under the action of unknown excitations effected by a realistic sea. It is shown that the developed technique produces reliable results for the parameters in the equations describing the coupled heave and pitch motions for a URV.     

System Analysis of Disaster Prevention Design Criteria for Coastal and Estuarine Cities

—In China,estuarine and coastal cities are mostly regional economic development centers.Thedisasters by combined effect of upper reach flood,storm surge and typhoon waves are primary obstaclesto the economic development of such cities.Thus the risk analysis and system analysis of flood-stormsurge-wave disaster,economic loss and flood-storm surge control measures play a very important role inthe sustainable development of coastal cities.There are three types of coastal cities for consideration.Thefirst type of city is like Tianjin.The most significant damage is from the upper reach flood.The effect ofstorm surge is negligible,because in the estuary of the Haihe River,tidal locks are built.The Grey MarkovModel(GMM)is used to forecast the flood peak level.GMM combines the Grey system and the Markovtheory into a high-precision model.The predicted flood peak levels are close to the measured data.A syn-thetic model is established for economic assessment,risk analysis and flood-control benefit estimation.Asa n     

Green functions with pulsating sources in a two-layer fluid of finite depth

The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.     

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.