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1.
Cnoidal wave theory is appropriate to periodic wave progressing in water whose depth is less than 1/10 wavelength. However, the cnoidal wave theory has not been widely applied in practical engineering because the formula for wave profile involves Jacobian elliptic function. In this paper, a cnoidal wave-seabed system is modeled and discussed in detail. The seabed is treated as porous medium and characterized by Biot's partly dynamic equations (u–p model). A simple and useful calculating technique for Jacobian elliptic function is presented. Upon specification of water depth, wave height and wave period, Taylor's expression and precise integration method are used to estimate Jacobian elliptic function and cnoidal wave pressure. Based on the numerical results, the effects of cnoidal wave and seabed characteristics, such as water depth, wave height, wave period, permeability, elastic modulus, and degree of saturation, on the cnoidal wave-induced excess pore pressure and liquefaction phenomenon are studied. 相似文献
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1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et… 相似文献
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An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter. 相似文献
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This study investigates stem waves, propagating along a vertical wall, due to obliquely incident random waves through laboratory experiments and numerical simulations. Attention is paid to the difference or similarity between the stem waves due to periodic waves and random waves, the nonlinear and linear characteristics, and the effect of wave breaking on the evolution of stem waves. The following were found from this study: as the incident angle of waves become large or the nonlinearity of the incident waves become small, the significant stem wave height, normalized by the incident significant wave height, becomes large. This tendency is the same as that generated by the Stokes waves or cnoidal waves. However, regardless of the nonlinearity of incident waves, the width of stem waves is almost the same. This is a different point between the stem waves due to periodic and random waves. The wave breaking suppresses the growth of the stem waves. 相似文献
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The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress. 相似文献
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《Coastal Engineering》1999,37(2):123-148
The Navier–Stokes equations and the exact free surface boundary conditions are solved to simulate wave deformation and vortex generation in water waves propagating over a submerged dike. Incident waves are generated by a piston-type wavemaker set up in the computational domain. Numerical results are compared with experimental data in order to confirm the validity of the numerical model. The fast Fourier transform and a wave resolution technique are applied to decompose the transformed waves and the higher harmonics. Effects of different parameters on wave transformation and vortex generation are studied systematically. These parameters include the Ursell number, the Keulegan–Carpenter number, the water depth ratio, the Reynolds number, the length aspect ratio of the dike, and the type of dike. 相似文献
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通过波浪水槽实验,开展不同类型波浪作用下的沙质岸滩演化规律研究工作。本次实验研究不考虑比尺,采用1:10与1:20组成的复合沙质斜坡对岸滩进行概化,选取规则波和椭圆余弦波两种典型波浪作用,对波浪的传播、变形和破碎、上爬、回落过程以及波浪作用前后沙质岸滩床面地形进行了观测,探讨波浪作用下沙质岸滩剖面演化规律。本文实验工况中,规则波作用下,岸滩剖面呈现出沙坝剖面和滩肩剖面,椭圆余弦波作用下的岸滩剖面均呈滩肩形态,发现岸滩剖面形态不仅与波浪作用类型、强度、周期等因素相关,还与波浪破碎的强度等因素有关。通过对实验过程中现象的进行观察和分析,引入了卷破波水舌冲击角的概念。对波浪卷破破碎后形成的水流挟沙运动与岸滩剖面形态的关系进行定性分析,对水舌冲击角与Irribarren参数之间的关系进行定量分析,基于Irribarren参数与岸滩剖面形态的关系初步建立了波浪作用下沙质岸滩剖面形态判别关系式。通过本文实验结果和前人实验结果对趋势线进行拟合,求得其判别系数,判别式能够较好地划分淤积型岸滩、侵蚀型岸滩及过渡型岸滩三种岸滩形态。 相似文献
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D. L. Kriebel 《Ocean Engineering》1992,19(1)
Theoretical results for second-order wave run-up around a large diameter vertical circular cylinder are compared to results of 22 laboratory experiments conducted in regular nonlinear waves. In general, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around the cylinder. At the front of the cylinder, for example, measured maximum run-up exceeds linear theory by 44% on average but exceeds the nonlinear theory by only 11% on average. In some cases, both measured run-up and the second-order theory exceed the linear prediction by more than 50%. Similar results are found at the rear of the cylinder where the second-order theory predicts a large increase in wave amplitude for cases where the linear diffraction theory predicts little or no increase. Overall, the nonlinear diffraction theory is found to be valid for the same relative depth and wave steepness conditions applicable to Stokes second-order plane-wave theory. In the last section of the paper, design curves are presented for estimating the maximum second-order wave run-up for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness. 相似文献
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通过波浪水槽实验,对海平面变化造成的波浪动力因素改变引起的沙质岸滩形态响应开展机理性研究。实验采用1∶10单一沙质斜坡概化岸滩,利用3种不同实验水深模拟海平面变化,考虑椭圆余弦波、非规则波、规则波和孤立波4种类型波浪作用。实验对波浪在斜坡上的传播变形、破碎、上爬和回落过程的波高及波浪作用后的岸滩地形进行了测量。实验结果表明,椭圆余弦波、规则波和非规则波作用下,平衡岸滩呈现出滩肩形态,孤立波作用下则呈沙坝形态。海平面上升造成波浪动力增强,沙质岸滩平衡剖面形状基本保持不变向岸平移,槽谷、滩肩、沙坝位置以及岸线蚀退距离,均呈现出良好规律性。 相似文献
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Wave types of landslide generated impulse waves 总被引：2，自引：0，他引：2
Subaerial landslide generated impulse waves were investigated in a prismatic wave channel. Seven governing parameters, namely the still water depth, slide impact velocity, slide thickness, bulk slide volume, bulk slide density, slide impact angle, and grain diameter, were systematically varied. The generated impulse waves are nonlinear, intermediate- to shallow-water waves involving a small to considerable fluid mass transport. The Stokes wave, cnoidal wave, solitary wave, and bore theories were applied to describe the observed maximum waves. The theoretical and observed features of these four wave types are highlighted. A diagram allows to predict the wave type directly as a function of the slide parameters, the slide impact angle, and the still water depth. 相似文献
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Solitary waves have been commonly used as an initial condition in the experimental and numerical modelling of tsunamis for decades. However, the main component of a tsunami waves acts at completely different spatial and temporal scales than solitary waves. Thus, use of solitary waves as approximation of a tsunami wave may not yield realistic model results, especially in the coastal region where the shoaling effect restrains the development of the tsunami wave. Alternatively, N-shaped waves may be used to give a more realistic approximation of the tsunami wave profile. Based on the superposition of the sech2(*) waves, the observed tsunami wave profile could be approximated with the N-shaped wave method, and this paper presents numerical simulation results based on the tsunami-like wave generated based on the observed tsunami wave profile measured in the Tohoku tsunami. This tsunami-like wave was numerically generated with an internal wave source method based on the two-phase incompressible flow model with a Volume of Fluid (VOF) method to capture the free surface, and a finite volume scheme was used to solve all the governing equations. The model is first validated for the case of a solitary wave propagating within a straight channel, by comparing its analytical solutions to model results. Further, model comparisons between the solitary and tsunami-like wave are then made for (a) the simulation of wave run-up on shore and (b) wave transport over breakwater. Comparisons show that use of these largely different waveform shapes as inputs produces significant differences in overall wave evolution, hydrodynamic load characteristics as well as velocity and vortex fields. Further, it was found that the solitary wave uses underestimated the total energy and hence underestimated the run-up distance. 相似文献
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《Coastal Engineering》2005,52(3):257-283
Vortex generation and evolution due to flow separation around a submerged rectangular obstacle under incoming cnoidal waves is investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used in the measurement. Based on the PIV data, a characteristic velocity, phrased in terms of incoming wave height, phase speed, dimension of the obstacle, and a local Reynolds number are proposed to describe the intensity of vortex. The numerical model, which solves the two dimensional Reynolds Averaged Navier Stokes (RANS) equations, is used to further study the effects of wave period on the vortex intensity. Measurements for the mean and turbulent velocity fields further indicate that the time history of the intensity of fluid turbulence is closely related to that of the vortex intensity. 相似文献
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This paper presents the development of a generalized Boussinesq (gB) model for the periodic non-linear shallow-water waves. An incident cnoidal wave solution for the gB model is derived and applied to the wave simulation. A set of radiation boundary conditions is also established to transmit effectively the cnoidal waves out of the computational domain. The classical solutions of the second-order cnoidal waves are discussed within the content of the KdV equation and the generalized Boussinesq equations. An Euler's predictor-corrector finite-difference algorithm is used for numerical computation. The propagation of normally incident cnoidal waves in a channel is studied. The simulated wave profiles agree well with the analytical results. The temporal and spatial evolution of an obliquely incident cnoidal wave is also modelled. The phenomenon of Mach reflection is discussed. 相似文献
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The run-up and back-wash processes of single and double solitary waves on a slope were studied experimentally. Experiments were conducted in three different wave flumes with four different slopes. For single solitary wave, new experimental data were acquired and, based on the theoretical breaking criterion, a new surf parameter specifically for breaking solitary waves was proposed. An equation to estimate maximum fractional run-up height on a given slope was also proposed. For double solitary waves, new experiments were performed by using two successive solitary waves with equal wave heights; these waves were separated by various durations. The run-up heights of the second wave were found to vary with respect to the separation time. Particle image velocimetry measurements revealed that the intensity of the back-wash flow generated by the first wave strongly affected the run-up height of the second wave. Showing trends similar to that of the second wave run-up heights, both the back-wash breaking process of the first wave and the reflected waves were strongly affected by the wave–wave interaction. Empirical run-up formula for the second solitary wave was also introduced. 相似文献
17.
This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear (1961), confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7. 相似文献
18.
The purpose of this study is to investigate the characteristics of parameters for local scour depth around submarine pipes due to waves. Because it is impossible to consider all the factors that influence the scour, it is reasonable to investigate the correlations between parameters and scour. The experimental works about scour were performed for the conditions of 40, 60, 90 m pipe diameter, various wave periods, and wave height in the case of horizontal bed and 1/10 slope bed, respectively. Analyzing the results of experiments, the Reynolds number, Shields parameter, Keulegan-Carpenter number, Ursell number, and Modified Ursell number were estimated. The correlations between the relative scour depth, which is the maximum equilibrium local scour depth divided by the pipe diameter, and 5 parameters were analyzed. It was shown that there was hardly any correlation with the Reynolds number. In the case of a horizontal bed, the Keulegan-Carpent number had the highest correlation, but in the case of the slope bed the correlation was greatly reduced. The modified Ursell number showed a high correlation regardless of the type of bed. 相似文献
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A practical method for estimating the wave run-up height on a slender circular cylindrical foundation for wind turbines in nonlinear random waves is provided. The approach is based on the velocity stagnation head theory and Stokes second order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. Comparisons are made with measurements by De Vos et al. (2007), and some of the highest wave run-up events that were predicted agree with those measured. 相似文献
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This paper presents laboratory and numerical simulations of run-up induced by irregular waves breaking on a gentle-sloping planar beach. The experimental data are well reproduced by a numerical model based on the nonlinear shallow water equations. By extending the incoming wave conditions considered in the laboratory experiments, the model is applied to study the run-up variability under highly energetic incoming conditions. The numerical results support the idea that, for cases characterized by the same incident peak frequency, infragravity run-up increases almost linearly with the offshore significant wave height. Moreover, the most energetic conditions lead to an upper limit of the swash similarity parameter of about 1.8. 相似文献