Theoretical Model and Random Simulation for Nonlinear Interaction of Irregular Waves with Vertical Wall

According to the theoretical solutions for the nonlinear three-dimensional gravity surface waves and their interactions with vertical wall previously proposed by the lead author, in this paper an exact second-order random model of the unified wave motion process for nonlinear irregular waves and their interactions with vertical wall in uniform current is formulated, the corresponding theoretical nonlinear spectrum is derived, and the digital simulation model suitable to the use of the FFT (Fast Fourier Tansform) algorithm is also given. Simulations of wave surface, wave pressure, total wave pressure and its moment are performed. The probability properties and statistical characteristics of these realizations are tested, which include the verifications of normality for linear process and of non-normality for nonlinear process; the consistances of the theoretical spectra with simulated ones; the probability properties of apparent characterstics, such as amplitudes, periods, and extremes (maximum and minimum, positive and negative extremes). The statistical analysis and comparisons demonstrate that the proposed theoretical and computing models are realistic and effective, the estimated spectra are in good agreement with the theoretical ones, and the probability properties of the simulated waves are similar to those of the sea waves. At the same time, the simulating computation can be completed rapidly and easily.     

Laboratory Study on the Interaction Between Regular Obliquely Incident Waves and Vertical Walls

The characteristics of wave forces are studied based on physical model tests with regular waves. The ratio of obliquely incident wave forces to normally incident wave forces on unit length of a vertical wall is related with various factors. A linear reduction of the mean force of obliquely incident waves is confirmed with an increase in the relative caisson length. Also the characteristics of reflection coefficient of diagonal waves are discussed.     

Wave Breaking Phenomena of Irregular Waves Combined with Opposing Current

- Experimental study and theoretical analysis show that the critical value of relative wave height (H/ d)b given by Goda and the critical wave steepness (H/ L)b given by Michell and Miche can be adopted as the spilling breaking indices of regular waves. According to the same principle, a systematic theoretical analysis and experiment of irregular waves have been done by the authors in order to solve the breaking problem of irregular waves. It is indicated that the authors' method for determining wave breaking of regular waves can also be used for irregular waves.     

Laboratory Study of the Nonlinear Transformation of Irregular Waves over A Mild Slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope (1?40). Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.     

A Model for Nonlinear Irregular Waves in Coastal Area

Based on the refraction-diffraction theory of irregular waves in the waters of slowly-varying cur-rents and depths,and the generation dissipation theory of wind wave,a model for nonlinear irregular wavesin coastal area is developed.In light of the specific conditions of coastal wave character and engineering ap-plication,a practical mathematical model for the nonlinear irregular waves is presented.with directional spec-trum in coastal area.Coast effect,refraction,whitecapping.bottom friction.current,wind and nonlinearaction are considered in this model.The numerical methods and schemes for wave refraction ray,energy con-servation of propagation,energy balance of the generation and dissipation of wind waves have been studied.Finally,the model is used for the directional wave spectrum computation in the Daya Bay.Compared withthe measured data with 956 wave bouys in the Daya Bay,the model results are in good agreement with themeasured results.     

Second-Oorder 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 constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be 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 were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. 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 second orders are derived. The boundary conditions for the determining 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.     

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.     

Action of Cnoidal Waves on Vertical Walls

Based on the 2nd order cnoidal wave theory, the characters of shallow water standing waves and their action on vertical walls are studied in this paper. The theoretical expressions of the wave surface elevation in front of and the wave pressure on the vertical wall are obtained. In order to verify the theoretical results, model tests were made in the State Key Laboratory of Coastal and Offshore Engineering at DUT. For the wave surface elevation in front of the wall and the wave forces on the wall at the moment when the wave surface at the wall surface goes down to the bottom of the wave trough, the calculated results coincide quite well with the experimental results. For the wave forces on the wall at the moment when the wave surface at the wall surface goes up to the top of the wave crest, the theoretical expressions are modified by the experimental results. For the convenience of practical use, calculations are made for the wave conditions which usually occur in enginering practice by use of the inves     

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity poten-tials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.     

Wave-Current Forces on Vertical Cylinders in Side-by-Side Arrangement for Irregular Waves Combined With Opposing Current

- The wave-current forces on vertical piles in side-by-side arrangement induced by irregular waves with opposing current are investigated experimentally in this paper. The characteristics in both time and frequency domain of in-line, lift and resultant forces are analyzed. The grouping effect coefficients of inline, lift and resultant forces on piles related to KC number and relative spacing parameters are given. These results are compared with those in the case of irregular waves combined with following currents. It is found that the results in these two cases are quite different. The range of KC number tested is 10- 60, the range of Reynolds number is (0.55-3.43) ×104.     

非线性相互作用对高频方向谱估计的影响

海浪组成波之间的三阶非线性相互作用产生的高次谐波,不仅改变了波面的外观形状,而且使得高频域不再满足通常的线性频散关系,当ｆ＞１．７ｆｐ时,频散关系应修改为ω２＝２ｇｋ。用最大似然法（ＭＬＭ）分析方向分布的结果表明：在二倍峰频附近,方向分布再次变窄,且能量在方向上的集中程度与海浪的成长状态有关,得到的高频方向分布跟Ｃａｕｄａｌ和Ｈａｕｓｅｒ（１９９６）的微波遥感结果定性一致。     

Experimental Study on Mean Overtopping of Sloping Seawall Under Oblique Irregular Waves

In this paper, domestic and abroad research progresses and related calculation formulae of the mean overtopping discharge are summarized. Through integral physical model experiments, the relation between the wave direction and the overtopping discharge on the top of the sloping dike is focused on and put into analysis and discussion; and a modified formula for mean overtopping discharges under oblique irregular waves is proposed. The study shows that the mean overtopping discharge generally goes down as the relative wave obliquity β increases for a fixed measurement point and the mean overtopping discharge generally increases as the wave steepness H/L decreases (the cycle increases) for a fixed relative wave obliquity.     

Theoretical and Experimental Study on the Acoustic Wave Energy After the Nonlinear Interaction of Acoustic Waves in Aqueous Media

Based on the Burgers equation and Manley?Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves’ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.     

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.     

Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect: Random Waves

New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is greatly saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.     

Soil-Structure Interaction Analysis of Jack-up Platforms Subjected to Monochrome and Irregular Waves

As jack-up platforms have recently been used in deeper and harsher waters, there has been an increasing demand to understand their behaviour more accurately to develop more sophisticated analysis techniques. One of the areas of significant development has been the modelling of spudcan performance, where the load-displacement behaviour of the foundation is required to be included in any numerical model of the structure. In this study, beam on nonlinear winkler foundation (BNWF) modeling—which is based on using nonlinear springs and dampers instead of a continuum soil media—is employed for this purpose. A regular monochrome design wave and an irregular wave representing a design sea state are applied to the platform as lateral loading. By using the BNWF model and assuming a granular soil under spudcans, properties such as soil nonlinear behaviour near the structure, contact phenomena at the interface of soil and spudcan (such as uplifting and rocking), and geometrical nonlinear behaviour of the structure are studied. Results of this study show that inelastic behaviour of the soil causes an increase in the lateral displacement at the hull elevation and permanent unequal settlement in soil below the spudcans, which are increased by decreasing the friction angle of the sandy soil. In fact, spudcans and the underlying soil cause a relative fixity at the platform support, which changes the dynamic response of the structure compared with the case where the structure is assumed to have a fixed support or pinned support. For simulating this behaviour without explicit modelling of soil-structure interaction (SSI), moment-rotation curves at the end of platform legs, which are dependent on foundation dimensions and soil characteristics, are obtained. These curves can be used in a simplified model of the platform for considering the relative fixity at the soil-foundation interface.     

Hydrodynamic Coefficients for Grouping Piles Under the Action of Irregular Waves

-The hydrodynamic coefficients for each of two piles and three piles in both side-by-side arrangement and tandem arrangement under the action of irregular waves are experimentally investigated. These coefficients vary with the KC number, the relative pile spacing, the number of piles and the pile location, and their relationships are presented in this paper. They can be used in Morison Equation and other equations to calculate directly the in-line wave forces and the transverse forces on each pile in array.     

非线性弱色散波内部流场的重构

基于势流理论和级数直接求逆方法,本文建立了基于Ｂｏｕｓｉｎｅｓｑ方程或Ｇｒｅｅｎ－Ｎａｇｈｄｉ方程给出的水深平均流速或某特征流速及波面信息重构非线性弱色散波内部流场的算法。以Ｂｏｕｓｉｎｅｓｑ方程的孤立波解为例,用本反演方法计算了孤立波的表面水平流速及底部水平流速。结果表明本算法是有效的。本反演算法可用于获取非线性弱色散波的内部流场的详细信息。