Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient （CG） method with a symmetric successive overelaxlation （SSOR） preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.

Fully Nonlinear Shallow Water Waves Simulation Using Green-Naghdi Theory

Green-Naghdi （G-N） theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by ＂levels＂ where the higher the level, the more complicated and presumably more accurate the theory is. In the research presented here a comparison was made between two different levels of G-N theory, specifically level II and level III G-N restricted theories. A linear analytical solution for level III G-N restricted theory was given. Waves on a planar beach and shoaling waves were both simulated with these two G-N theories. It was shown for the first time that level III G-N restricted theory can also be used to predict fluid velocity in shallow water. A level III G-N restricted theory is recommended instead of a level II G-N restricted theory when simulating fullv nonlinear shallow water waves.

Different responses of two adjacent artificial beaches to Typhoon Hato in Zhuhai,China

Major differences in beach erosion between two neighboring artificial beaches Xiangluwan Beach(XL beach)and Meiliwan Beach(ML beach)in Zhuhai,China,were studied after Super Typhoon Hato.In this study,a fully nonlinear Boussinesq wave model(FUNWAVE)-Total Variation Diminishing(TVD)was used to distinguish the main impact factors,their relative contributions,and the hydrodynamic mechanisms underlying the different beach responses.Results show that compared to the ML beach,the main reason for the relatively weak erosion on Xiangluwan(XL)beach was the smaller beach berm height(accounting for approximately 75.9%of the erosion response).Regarding the beach with a higher berm,the stronger wave-induced undertow flow,along with the higher sediment concentration,led to a higher offshore sediment transport flux,resulting in more severe erosion relative to the beach with a smaller berm height.The second most important reason explaining the weak erosion on XL beach was the absence of seawalls(accounting for approximately 17.9%of the erosion response).Wave reflection induced by the seawall could cause higher suspended sediment concentration,resulting in a toe scouring near the seawall.The offshore submerged breakwater protected XL beach slightly(accounting for approximately 6.1%of the erosion response).Due to the higher water level induced by storm surge,most of the wave energy could penetrate through the submerged breakwater.The effect of the larger berm width of XL beach was negligible.Compared to the beach with a larger berm width,the erosion/deposition regions in the beach with a narrower berm width showed shoreward migration,without significant changes in the erosion/deposition extent.Despite of this,the larger berm width could reduce the wave energy reaching the shoreline.This study of the storm stability of artificial beaches may be applied to beach restoration design.

全非线性波的高阶谱方法

Efficient generation of an accurate numerical wave is an essential part of the Numerical Wave Basin that simulates the interaction of floating structures with extreme waves.computational fluid dynamics(CFD)is used to model the complex free-surface flow around the floating structure.To minimize CFD domain that requires intensive computing resources,fully developed nonlinear waves are simulated in a large domain that covers far field by more efficient potential flow model and then coupled with the CFD solution nearfield.Several numerical models have been proposed for the potential flow model.the higher-level spectral(HLS)method presented in this paper is the extended version of HLS model for deep water recently been derived by combining efficiency and robustness of the two existing numerical models–Higher-Order Spectral method and Irrotational Green-Naghdi model(Kim et al.2022).The HLS model is extended for the application of finite-depth of water considering interaction with background current.The verification of the HLS model for finite depth is made by checking the qualification criteria of the generated random waves for a wind-farm application in the Dong-Hae Sea of Korea.A selected wave event that represents P90 crest height is coupled to a CFD-based numerical wave tank for the future air-gap analysis of a floating wind turbine.

A fully nonlinear and weakly dispersive water wave model for simulating the propagation,interaction,and transformation of solitary waves

This paper presents the development of a theoretical model of fully nonlinear and weakly dispersive(FNWD)waves and numerical techniques for simulating the propagation,interaction,and transformation of solitary waves.Using the standard expansion method and without the limit of small nonlinear parameter defined as the ratio of the wave height versus water depth,a set of model equations describing the FNWD waves in a domain of moderately varying bottom topography are formulated.Exact solitary wave solutions satisfying the FNWD equations are also derived.Numerically,a time-accurate and stabilized finite-element code to solve the governing equations is developed for wave simulations.The solitary wave solutions of FNWD,weakly nonlinear and weakly dispersive(WNWD),and Laplace equations based models in terms of wave profile and phase speed are compared to examine their related features and differences.Investigations on the overtaking collision of two unidirectional solitary waves of different amplitudes,i.e.,ax and a2 where a1>a2,are carried out using both the FNWD and WNWD water wave models.Selected cases by running the FNWD and WNWD models are performed to identify the critical values of a1/a2 for forming a flattened merging wave peak,which is the condition used to determine if the stronger wave is to pass through the weaker one or both waves are to remain separated during the encountering process.It is interesting to note the critical values of a1/a2 obtained from the FNWD and WNWD models are found to be different and greater than the value of 3 proposed by Wu through the theoretical analysis of the Korteweg-de Vries(KdV)equations.Finally,the phenomena of wave splitting and nonlinear focusing of a solitary wave propagating over a three-dimensional semicircular shoal are simulated.The results obtained from both the FNWD and WNWD models showing the fission process of separating a main solitary wave into multiple waves of decreasing amplitudes are presented,compared,and discussed.

SECOND ORDER TRANSIENT WAVES AROUND A VERTICAL CYLINDER IN A TANK

The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The results are compared with those obtainal from the fully nonlinear theory based on a finite element formulation.It is found that the second order solutiongives a fsr better agreement with the fully nonlinear solution.