Application of wavelet transform analysis to landslide generated waves

The aim of this paper is to illustrate the results of a preliminary study on aerial landslide-generated waves, which has been mainly intended to establish a method for analyzing water surface records. Some simple physical experiments, reproducing the Scott Russell's wave generator, were carried out in a small two-dimensional wave flume; the Wavelet Transform (WT) is applied to analyze wave measurements and it is shown that useful information can be obtained by means of this technique. The celerity of impulsively generated waves, reflection by an overflow structure and seiching phenomena of the flume are studied. A discussion of the results along with some remarks about ongoing research is also given.     

Resonance Induced by Edge Waves in Hua-Lien Harbor

This article first reviews previous numerical studies on the resonance problem of Hua-Lien Harbor. All the research leads to the conclusion that resonance can be stimulated by 2-D infragravity waves. However, a literature survey suggests that outside the harbor these plane infragravity waves are too small to excite violent water-body movement inside. On the other hand, 3-D infragravity waves trapped along the coastline, also known as edge waves, are more likely to exist outside the harbor and their effect needs to be thoroughly discussed. Based on previous measurements, the response of Hua-Lien Harbor is best simulated using edge waves of 160 and 140 second periods and their resonance mechanisms are analyzed. The former case has a longitudinal resonant mode and hence the amplitude in the inner harbor is large. The latter case has a transverse mode in the outer basin and hence only berths in the outer basin are influenced. These features are both consistent with field measurement. Therefore, it is very likely that edge waves are responsible for the resonance of Hua-Lien Harbor. Finally, based on observation after the construction of the present offshore breakwaters, a theory is proposed to explain the trapping of incident edge waves, and a measure to further reduce the resonance is discussed.     

深水波中进动共振的数值模拟研究

进动(precession)共振是一种非线性共振相互作用,2016年才有学者对这一现象进行研究。采用非静压二维自由表面流模型模拟了深水条件下重力波的进动共振现象。通过边界造波的方法产生双色波,分析了触发进动共振的初始条件;探讨了进动共振在小振幅前提条件下发生的简化初始条件。数值模拟分析两组对称测点,对不同测点的波面、能量谱进行对比分析。数值结果表明:非静压二维自由表面流模型可以模拟进动共振现象,并且可以采用双色波作为条件来研究深水五波进动共振现象,进动共振需要一定的能量转化时间,进动共振发生的条件是三波组合的进动频率等于一个系统存在的非线性频率。     

Observation of edge waves trapped on the continental shelf in the vicinity of Makurazaki Harbor, Kyushu, Japan

Sea-bottom pressure gauges were used to measure sea levels at two points on the shelf off the southern coast of Satsuma Peninsula, Kyushu, Japan. Spectral analysis of the observed records and the tide-gauge record of Makurazaki Harbor revealed several predominant common peaks. At the same time, the eigenmodes for the trapped waves on the shelf and inside Makurazaki Bay were obtained numerically using a two-dimensional model, and the periods and the spatial distribution of amplitudes of the proper modes were obtained. A comparison of the calculated modes with the periods and phase patterns of the observed peaks clarified that peaks with periods of 19.5, 16, 13.3, and 12.2 minutes in the shelf region were the modes of standing-edge waves, and the peak with the period of 16 minutes in Makurazaki Harbor was the fundamental mode of the harbor. Among the modes of standing-edge waves, the mode of the period 16 minutes on the shelf had nearly the same period as that of the fundamental mode of Makurazaki Harbor. An analysis of changes of spectral densities of these two modes confirmed that the fundamental mode of the Makurazaki Harbor was induced by this standing-wave mode.     

Prediction of impact pressure induced by breaking waves on vertical cylinders in random seas

This paper presents a method to statistically predict the magnitude of impact pressure (including extreme values) produced by deep water waves breaking on a circular cylinder representing a column of an ocean structure. Breaking waves defined here are not those whose tops are blown off by the wind but those whose breaking is associated with steepness. The probability density function of wave period associated with breaking waves is derived for a specified wave spectrum, and then converted to the probability density function of impact pressure. Impacts caused by two different breaking conditions are considered; one is the impact associated with waves breaking in close proximity to the column, the other is an impact caused by waves approaching the column after they have broken. As an example of the application of the present method, numerical computations are carried out for a wave spectrum obtained from measured data in the North Atlantic.     

Displacements induced by breaking waves on axially loaded cylindrical shells

Forced vibrations of the walls of a vertical cylindrical shell under the impact of a breaking wave are studied theoretically. The wave action is modelled as a pressure distribution which varies in time and space. A linear dynamic analysis of the transient response is carried out by means of the modal superposition technique, in which the static stresses are considered. The results show that in thin shells, the transient displacements could be of the order of the thickness of the shell. It is suggested that these large displacements could play an important role in eroding the buckling capacity of the structural component. The problem of limiting the dynamic displacements is discussed by interaction diagrams for static axial load-dynamic lateral pressure, and by examination of the confluence of shell and wave parameters for which the transient displacements do not exceed a given value.     

Numerical investigation of oscillations induced by submerged sliding masses within a harbor of constant slope

Oscillations within a rectangular harbor of constant slope induced by submerged sliding masses are investigated numerically based on Boussinesq-type equations and results are used to reveal the characteristics of the generated oscillations. The numerical result of each transverse eigenfrequency is very close to the theoretical prediction and the spatial structure of each mode of the oscillations may also be well captured by the existing analytical solutions based on shallow water equations. The investigation shows that relatively small-scale sliding masses whose width is small compared with the harbor width may induce obvious transverse oscillations. The predominant transverse components are those with small mode numbers when the solid slides start moving from the backwall. In comparing the oscillations induced by the slides of constant velocity and those accelerated by gravity force with bottom friction, it is observed that the movements accelerated by gravity force may facilitate the development of very low transverse oscillation modes while those with constant velocity may also be in favor of the higher ones. The augmentation of the sliding velocity along the constant slope may shift the amplitudes of the oscillation components to smaller values, which corresponds to the physical understandings of the waves generated by underwater sliding masses or landslides. While the sliding masses may not act on an isolated point of the bottom but follow a certain trajectory along the harbor, the transverse oscillations induced by them are sensitive to their position of departure in both the cross-harbor direction and the offshore direction. Longitudinal oscillations may be induced by relatively large sliding masses of harbor width on a constant slope within the harbor. Although the longitudinal oscillations may not reach a steady state without forcing terms at the entrance of the harbor, some patterns of several low-mode ones occur and wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions. It is revealed that the longitudinal oscillations are also sensitive to the moving velocity and initial location of the sliding masses.     

Transient response of harbours to long waves under resonance conditions

This paper presents the results of a study aimed at quantifying the time–response of harbour basins to long waves under resonance conditions. On the basis of numerical simulations reproducing long waves in the yacht harbour of Rome (Ostia, Italy), it shows that the results valid for periodic forcing waves, acting for an infinitely long time, as those provided by models based on elliptic equations like the Helmoltz and the mild-slope equations, can be misleading with respect to the more realistic ones that can be obtained using time-varying wave equations. Taking advantage of the similarity between the processes studied here and a simple one-dimensional resonator, a method is also proposed to roughly estimate a time–response parameter of each mode of the harbour, using results from steady-state numerical model results, commonly applied for studying harbour resonance in engineering practice. On the basis of further numerical simulations, aimed at reproducing schematic harbour layouts, the effect on resonance of the position of the entrance and of an outer harbour is studied. The results indicate that the effects of design solutions to reduce resonance, by placing the entrance at the middle of the harbour, or using the outer harbour as a resonator, can be correctly evaluated only when considering the time needed for the oscillations to fully develop.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Penetration depth of the dynamic response of seabed induced by internal solitary waves

We use flume experiments and numerical modeling to examine the penetration depth of internal solitary waves (ISWs) on partially saturated porous sandy silt and clayey silt seabed. The results of the experiment and model showed that the instantaneous excess pore water pressure in both the sandy silt and clayey silt seabed followed the same trend of decreasing with the seabed depth. In general, the excess pore water pressure generated by the sandy silt was bigger than that by clayey silt at the same depth. The ISW-induced excess pore water pressure greatly influenced the surface seabed and showed a linear relationship. The penetration depth was approximately one order of magnitude smaller than the half-wavelength of the ISWs, which might be larger than the penetration depth induced by surface waves. Our study results are helpful for understanding the damage that ISWs inflict upon the seabed and for informing future field experiments designed to directly measure the interaction between ISWs and seabed sediments.     

海浪产生磁场的能量分布计算

结合前人在海浪功率谱研究以及海浪产生磁场两方面的研究,求出了海浪-磁场系统的传递函数,计算了传递函数的峰值、对应的峰值频率,分析了这些指标随高度的变化.根据理论分析,给出了感应磁场总功率的表达式和峰值频率满足的方程,指出海浪感应磁场是一个窄带随机过程.最后选择几种典型的海浪谱,计算了它们感应的磁场功率谱以及总功率、功率谱峰值、峰值频率以及等效噪声带宽.     

长周期波浪激发矩形港池多模态共振研究

长和宽接近的矩形港池存在横向、纵向及横纵向混合共振模态。采用基于混合有限元的椭圆型缓坡方程数值模型模拟不同波浪入射角的低频波浪激发矩形港池的多模态共振,并分析不同平面布置形式的矩形港池模态响应特性。结果表明,斜向波浪会激发港池的横向共振模态,其放大因子受入射角度影响较大,而纵向共振模态的放大因子受入射角度影响较小。口门宽度对港池的共振模态个数与放大因子均有影响,具体为:随着口门宽度增加,各阶模态放大因子减小。口门位置对纯横向以及纯纵向共振的振荡模式有显著影响,而对横向纵向混合模态影响较小。各阶模态放大因子的大小和波节线与波腹线与口门的相对位置密切相关。     

两层流体中内波作用下Spar平台运动响应

研究两层流体中Spar平台在内波作用下的运动响应问题。在线性势流理论框架,提出在内波作用下Spar平台运动响应及分段式悬链线系泊张力特性的计算方法。数值分析两层流体内界面位置、入射内波的波长以及系泊索初始预张力对Spar平台运动响应及其系泊索张力特性的影响规律,结果表明内波对Spar平台纵摇运动响应的影响是小的,但对Spar平台纵荡与垂荡运动响应及其系泊索张力的影响是不可忽视的。因此,在Spar平台的设计中,考虑内波的影响是重要的。     

Modelling linear wave transformation induced by dissipative structures—Random waves

The relevant theory is presented and numerical results are compared with the analytical solution for the interaction of non-breaking waves with an array of vertical porous circular cylinders on a horizontal bed. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. The influence of the mechanical properties of porous structures and wave irregularity on wave transformation is analysed. Results for unidirectional and multidirectional wave spectra are compared to those obtained for regular waves. The model presented reproduces well the analytical results and provides a tool for analysing several engineering problems.     

Effect of different span heights on the pipeline impact forces induced by deep-sea landslides

With the development of marine energy in full swing, an increasing number of pipelines are being installed in deep-sea areas, which inevitably pass through extremely complex topographic conditions, to form natural sections of suspension over submarine canyons. The seabed is easily eroded and shaped by active deep-sea bottom currents and watercourses, resulting in different span heights for pipelines originally laid on the seabed. In particularly, deep-sea geological hazards frequently occur, and submarine landslides seriously threaten the safe operation of the pipelines. To address these problems, an improved numerical analysis method combined with low-temperature rheological models of landslides and the optimization design method of the geometric model, is developed to simulate the landslides’ impacts on pipelines. Based on these, the effect of the span heights on the pipelines’ impact forces induced by deep-sea landslides is systematically investigated, and three modes of the forces on pipelines under the impact of landslides and related mechanism are proposed. Further, the span height ratio is put forward, and four formulas for evaluating the forces on pipeline are established. Through the analysis of calculation results, the lift force coefficient even increases nearly 20 times considering different span heights. This research provides a theoretical basis for the design and protection of deep-sea pipelines.     

Large-scale experiments on beach profile evolution and surf and swash zone sediment transport induced by long waves,wave groups and random waves

New large-scale laboratory data are presented on the influence of long waves, bichromatic wave groups and random waves on sediment transport in the surf and swash zones. Physical model testing was performed in the large-scale CIEM wave flume at UPC, Barcelona, as part of the SUSCO (swash zone response under grouping storm conditions) experiment in the Hydralab III program (Vicinanza et al., 2010). Fourteen different wave conditions were used, encompassing monochromatic waves, bichromatic wave groups and random waves. The experiments were designed specifically to compare variations in beach profile evolution between monochromatic waves and unsteady waves with the same mean energy flux. Each test commenced with approximately the same initial profile. The monochromatic conditions were perturbed with free long waves, and then subsequently substituted with bichromatic wave groups with different bandwidth and with random waves with varying groupiness. Beach profile measurements were made at half-hourly and hourly intervals, from which net cross-shore transport rates were calculated for the different wave conditions. Pairs of experiments with slightly different bandwidth or wave grouping show very similar net cross-shore sediment transport patterns, giving high confidence to the data set. Consistent with recent small-scale experiments, the data clearly show that in comparison to monochromatic conditions the bichromatic wave groups reduce onshore transport during accretive conditions and increase offshore transport during erosive conditions. The random waves have a similar influence to the bichromatic wave groups, promoting offshore transport, in comparison to the monochromatic conditions. The data also indicate that the free long waves promote onshore transport, but the conclusions are more tentative as a result of a few errors in the test schedule and modifications to the setup which reduced testing time. The experiments suggest that the inclusion of long wave and wave group sediment transport is important for improved near-shore morphological modeling of cross-shore beach profile evolution, and they provide a very comprehensive and controlled series of tests for evaluating numerical models. It is suggested that the large change in the beach response between monochromatic conditions and wave group conditions is a result of the increased significant and maximum wave heights in the wave groups, as much as the presence of the forced and free long waves induced by the groupiness. The equilibrium state model concept can provide a heuristic explanation of the influence of the wave groups on the bulk beach profile response if their effective relative fall velocity is larger than that of monochromatic waves with the same incident energy flux.     

浅水中浮体在波浪作用下运动的三维时域计算模型

港口中系泊船在波浪作用下运动问题的本质是浅水波浪与浮体的相互作用。与深水情况不同,浅水问题应当考虑水底、水域边界的影响及浅水波浪自身的特性,单一模型很难实现该模拟过程。为此,建立了Boussinesq方程计算入射波和Laplace方程计算散射波的全时域组合计算模型。有限元法求解的Boussinesq方程能使入射波充分考虑到水底、水域边界的影响和浅水波浪的特性;散射波被线性化,采用边界元法求解,并以浮体运动时的物面条件为入射波和散射波求解的匹配条件。该方法为完全的时域方法,计算网格不随时间变动,计算过程较为方便。通过与实验及其他数值方法的结果进行比较,验证了本模型对非线性波面、浮体的运动都有比较理想的计算结果,显示了本模型对非线性问题具有较好的计算能力。     

Viscosity and nonlinearity effects on the forces and waves generated by a floating twin hull under heave oscillation

Nonlinear hydrodynamics of a twin rectangular hull under heave oscillation is analyzed using numerical methods. Two-dimensional nonlinear time-domain solutions to both inviscid and viscous problems are obtained and the results are compared with linear, inviscid frequency-domain results obtained in [26] to quantify nonlinear and viscous effects. Finite-difference methods based on boundary-fitted coordinates are used for solving the governing equations in the time domain [2]. A primitive-variables based projection method [6] is used for the viscous analysis and a mixed Eulerian–Lagrangian formulation [11] for inviscid analysis. The algorithms are validated and the order of accuracy determined by comparing the results obtained from the present algorithm with the experimental results of Vugt [22] for a heaving rectangle in the free surface. The present study on the twin-hull hydrodynamics shows that at large and non-resonant regular frequencies, and small amplitude of body oscillation, the fluid viscosity does not significantly affect the wave motion and the radiation forces. At low frequencies however the viscosity effect is found to be significant even for small amplitude of body oscillation. In particular, the hydrodynamic force obtained from the nonlinear viscous analysis is found to be closer to the linear inviscid force than the nonlinear inviscid force to the linear inviscid force, the reason for which is attributed to the wave dampening effect of viscosity. Since the wave lengths generated at smaller frequencies of oscillation are longer and therefore the waves could have a more significant effect on the dynamic pressure on the bottom of the hulls which contribute to the heave force, the correlation between the heave force and the wave elevation is found to be larger at smaller frequencies. Because of nonlinearity, the wave radiation and wave damping force remained nonzero even at and around the resonant frequencies – with the resonant frequencies as determined in [26] using linear potential flow theory. As to be expected, the nonlinear effect on the wave force is found to be significant at all frequencies for large amplitude of oscillation compared to the hull draft. The effect of viscosity on the force, by flow separation, is also found to be significant for large amplitude of body oscillation.     

波浪与带窄缝方箱作用共振现象的数值模拟

By introducing a source term into the Laplace equation, a two-dimensional fully nonlinear time-domain numerical wave flume (NWF) is developed to investigate the resonance induced by the interaction bet...