Wave motions around different submerged structures

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Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters

Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described.     

没水倾斜板式防波堤消波性能分析

提出了一种将波浪中倾斜板问题等效化简为波浪中水平板单元组的方法,该方法建立在使用分离变量法求解水工结构边值问题的基础上,并使用伽辽金法精确求解连续边界条件,确定考虑衰减波态的速度势函数,从而求解没水倾斜板结构的消波性能。等效化简法计算精度于边界元法相当,且计算单元数量少、开销低。基于二维线性势波理论,对没水倾斜板式防波堤消波性能分析显示,没水板的倾斜角度、没水深度与板长是结构消波性能的控制因素:没水倾斜板防波堤的消波性能优于没水水平板防波堤的消波性能,随着没水板结构的倾斜角度增大,没水倾斜板结构的波浪透射系数显著减小,且长板优于短板,浅板优于深板;与前人的水槽实验对比显示,相对没水深度与波陡影响结构的消波性能,且波陡造成的波浪破碎贡献了显著的波能消耗。该结论对板式防波堤的结构配置、优化设计有重要意义。     

Wave decomposition phenomenon and spectrum evolution over submerged bars

Wave decomposition phenomenon and spectrum evolution over submerged bars are investigated by a previously developed numerical model. First, the computed free surface displacements of regular waves at various locations are compared with the available experimental data to confirm the validity of the numerical model, and satisfactory agreements are obtained. In addition, variations of decomposition characteristics with incident wave parameters and the change of energy spectrum for regular waves are also studied. Then the spectrum evolution of irregular waves over submerged bars, as well as the influence of incident peak wave period and the steepness of the front slope of the bar on spectrum evolution, is investigated. Wave decomposition and spectral shape are found to be significantly influenced by the incident wave conditions. When the upslope of the bar becomes 1:2, the length of the slope becomes shorter and will not benefit the generation of high frequency energy, so spectrum evolution is not significant.     

Wave height transformation and set-up between a submerged permeable breakwater and a seawall

In this study,we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall.Modified time-dependent mild-slope equations,which involve parameters of the porous medium,were used to calculate the wave height transformation and the mean water level change around a submerged breakwater.The numerical solution is verified with experimental data.The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall.In contrast to cases without a seawall,the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall.Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater.We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.     

Wave Forces on Submerged Semi-Circular Breakwater and Similar Structures

—The results of design and experiment of a submerged semi-circular breakwater at the Yangtzeestuary show that the submerged structure will be unsafe when the general empirical wave force formulafor semi-circular breakwater is used in design.Therefore,a new calculation method for the wave forces act-ing on a submerged semi-circular structure is given in this paper,in which the wave force acting on the in-side circumference of semi-circular arch is included,and the phase modification coefficient in the generalempirical formula is adjusted as well.The new wave force calculation method has been verified by the re-sults of seven related physical model tests and adopted in the design of the south esturary jetty of the firststage project of Deep Channel Improvement Project of the Yangtze River Estuary,the total jetty length be-ing 17.5km.     

Wave transmission and reflection at low-crested structures: Design formulae,oblique wave attack and spectral change

A part of the DELOS research focused on wave transformation at low-crested structures, called LCS. This paper gives a summary of all results. Wave transmission on rubble mound structures has been subject for more flume tests in the DELOS programme and simultaneously an existing database has been increased extensively by receiving data from other researchers in the world. This new database consists of more than 2300 tests and has been used to come up with the best 2D wave transmission formula for rubble mound LCS, although not necessarily new as existing ones have been evaluated. Oblique wave attack on LCS was a second objective within DELOS. Results were analysed leading to new empirical transmission formulae for smooth LCS and to conclusions on 3D effects for both rubble mound and smooth LCS. The spectral shape changes due to wave transmission and this change has been subject of analysis for all new test data described above. Although analysis has not been finished completely, former assumptions on spectral change were more or less confirmed. Finally, some analysis was performed on reflection at LCS and a first formula was derived to take into account the effect that wave overtopping or transmission reduces reflection and must be dependent on the crest height of the structure.     

近岸波浪折射-绕射-破波耗散联合模式的有限元数值研究

建立了近岸波浪折射-绕射-破波耗散的有限元数值模式。采用的有限元方法为改进的混合元法,其中外域开边界条件得到改进,内域有限元为伽廖金有限元。用理论解检验了所建立的数值模式,并将该模式应用到一个模型港湾。     

Static stability of submerged partial revetment structures under regular and irregular waves

Physical models of submerged partial revetment structures were built on natural beach sand with a diameter of 0.35 mm and specific gravity of 2.63. The armor units, the diameter and specific gravity of which varied in the range of 8.5–67.95 mm and 1.81–2.77 respectively, were placed only on wave breaking areas. A series of experiments has been conducted on the conditions of different armor units and different wave characteristics using regular waves and irregular waves. Based on the experimental data, the effects of wave height, wave period, diameter and specific gravity of armor units, water depth in the channel, and wave types on static damage of given structures are assessed. Some empirical formulas have been suggested through regression analysis to describe static stability and stability number of submerged partial revetment structures under pure regular waves, pure irregular waves, and regular–irregular waves. The suggested formulas compared with Van der Meer’s (1988) formulas and some differences have occurred because of differences among revetment types and test conditions; therefore, proposed formulas give reasonable results for the test conditions used.     

多个淹没水平圆柱诱发高阶谐波特性的数值与试验研究

基于势流理论采用时域高阶边界元方法建立了模拟非线性波浪与淹没水平双、三圆柱作用的数值水槽模型,其中采用混合欧拉-拉格朗日方法更新自由水面,四阶Runga-Kutta方法进行时间步进。利用两点法分离得到潜体下游高阶自由波,进而研究潜体间距、布置形式等对高倍频自由波的影响。同时在物理水槽内开展多潜体高阶谐波物理模型试验,并将试验结果与数值结果进行对比,吻合较好。研究发现:淹没双圆柱下游高阶谐波幅值随潜体间距呈现周期性振荡变化,其振荡的重现距离约为波长一半。而淹没三圆柱下游的高阶谐波随第一个间距呈周期性振荡变化,随第二个间距的增大而减小。     

Three-dimensional analysis of submerged, moored, horizontal, rigid cylinders used as breakwaters

Wave attenuation by moored cylinders is considered. The cylinders are submerged with their axes horizontal. Linear potential theory is applied. Three-dimensional motions of the cylinders subjected to normal and oblique monochromatic waves are determined using potential theory and a boundary integral method. Each cylinder has length 9.1 m (30 ft) and radius 1.5 m (5 ft), with its top 1.5 m (5 ft) below the still water line and its bottom 3.0 m (10 ft) above the seabed. Free-surface elevations are obtained for a single cylinder and for two cylinders in series. These configurations are effective wave barriers for a range of wave frequencies and incident angles.     

3-D Shear Wave Velocity Structure of the Crust and Upper Mantle in South China Sea and its Surrounding Regions by Surface Wave Dispersion Analysis

In this study, we construct a 3-D shear wave velocity structure of the crust and upper mantle in South China Sea and its surrounding regions by surface wave dispersion analysis. We use the multiple filter technique to calculate the group velocity dispersion curves of fundamental mode Rayleigh and Love waves with periods from 14 s to 120 s for earthquakes occurred around the Southeast Asia. We divide the study region (80° E–140° E, 16° S–32° N) into 3° × 3° blocks and use the constrained block inversion method to get the regionalized dispersion curve for each block. At some chosen periods, we put together laterally the regionalized group velocities from different blocks at the same period to get group velocity image maps. These maps show that there is significant heterogeneity in the group velocity of the study region. The dispersion curve of each block was then processed by surface wave inversion method to obtain the shear wave velocity structure. Finally, we put the shear wave velocity structures of all the blocks together to obtain the three-dimensional shear wave velocity structure of crust and upper mantle. The three-dimensional shear wave velocity structure shows that the shear wave velocity distribution in the crust and upper mantle of the South China Sea and its surrounding regions displays significant heterogeneity. There are significant differences among the crustal thickness, the lithospheric thickness and the shear wave velocity of the lid in upper mantle of different structure units. This study shows that the South China Sea Basin, southeast Sulu Sea Basin and Celebes Sea Basin have thinner crust. The thickness of crust in South China Sea Basin is 5–10 km; in Indochina is 25–40 km; in Peninsular Malaysia is 30–35 km; in Borneo is 30–35 km; in Palawan is 35 km; in the Philippine Islands is 30–35 km, in Sunda Shelf is 30–35 km, in Southeast China is 30–40 km, in West Philippine Basin is 5–10 km. The South China Sea Basin has a lithosphere with thickness of about 45–50 km, and the shear wave velocity of its lid is about 4.3–4.7 km/s; Indochina has a lithosphere with thickness of about 55–70 km, and the shear wave velocity of its lid is about 4.3–4.5 km/s; Borneo has a lithosphere with thickness of about 55–60 km, and the shear wave velocity of its lid is about 4.1–4.3 km/s; the Philippine Islands has a lithosphere with thickness of about 55–60 km, and the shear wave velocity of its lid is about 4.2–4.3 km/s, West Philippine Basin has a lithosphere with thickness of about 50–55 km, and the shear wave velocity of its lid is about 4.7–4.8 km/s, Sunda Self has a lithosphere with thickness of about 55–65 km, and the shear wave velocity of its lid is about 4.3 km/s. The Red-River Fault Zone probably penetrates to a depth of at least 200 km and is plausibly the boundary between the South China Block and the Indosinia Block.     

Approach to Calculating Methods of Wave Breaking Depth and Height

- Engineers in coastal engineering have been paying much attention to the research subject on wave breaking. In this paper, previous research results on the calculating methods of wave breaking depth and height are enumerated, the laws of wave transformation before and after wave breaking are investigated, an adequate supposition is made, and the effect of beach slope, bed friction and breaking turbulence on wave breaking is considered. By applying the theory of wave energy dissipation rate and combining with proper formulas of solitary waves, a new calculating formula of wave breaking depth and height on the movable bed is derived and examined with the data from experimental pools of different sizes, and it is proved to be of practicability.     

Modelling of Random Waves over Submerged Breakwaters and Its Application to Reflection Estimation

1.IntroductionGreat efforts have been devoted to the protection of coastal areas over many years by erectingdikes,seawalls,groin systems,and detached breakwaters.The sea walls,jetties,detached breakwa-ters,etc.are traditionally adopted as absorbingfacilit…     

Study on Wave Dissipation of the Structure Combined by Baffle and Submerged Breakwater

This paper proposes a structure combined by baffle and submerged breakwater (abbreviated to SCBSB in the following texts). Such a combined structure is conducive to the water exchange in the harbor, and has strong capability on wave dissipation. Our paper focuses on the discussion of two typical structures, i.e., the submerged baffle and rectangular breakwater combined with the upper baffle respectively, which are named as SCBSB1 and SCBSB2 for short. The eigenfunction method corrected by experimental results is used to investigate the wave dissipation characteristics. It shows that the calculated results agree well with the experimental data and the minimum value of the wave transmission coefficient can be obtained when the distance between the front and rear structures is from 1/4 to 1/2 of the incident wave length.     

Interaction mechanisms among waves,currents and a submerged plate

Wave-induced loads on a submerged plate, representative of submerged breakwater, coastal-bridge deck and a certain type of wave energy converter, in a uniform current are investigated in this study using fully nonlinear numerical wave tanks (NWTs) based on potential flow theory. The coupling effect of wave and current is explored, and the underlying interaction mechanisms of the hydrodynamic forces are described. The presence of a background current modifies the frequency dispersion. It produces changes of the water-surface elevation, and also has an effect on wave-induced loads. Depending on the nonlinearity, higher harmonic wave components are generated above the submerged plate. These contribute to the wave forces. It is found that the horizontal and the vertical force, hence the moment, are affected in the opposite way by the currents. The Doppler shifted effect dominates the vertical force and the moment on the plate. Whereas, the Doppler shifted effect and the generation of higher wave harmonics play opposite roles on the horizontal forces. The contribution of 2^nd order harmonics is found to be up to 30% of the linear component. The current-induced drag force, represented by the advection term ρU∂φ/∂x in the pressure equation, is found to lead to a decrease in the moment for the most range of wavelengths considered, and an increase in the moment for a small range of longer waves.     

A simple and effective model for Jones matrix to evaluate the transmission performance of Savart polariscope

Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an arbitrary incidence in the spatial domain. Analytical expressions of all the matrix components are determined with the consideration of all the main impact factors. This model needs only a few parameters hence it is convenient to be employed to evaluate the propagation performance of any birefringent optical system. The simulated results obtained with it demonstrate that this model gives a precise representation of the characteristic of light propagation in the Savart polariscope. This would provide useful suggestions for the design, calibration, and performance improvement of any other birefringent polarisation element and optical system.     

Forces and moment on a horizontal plate due to regular and irregular waves in the presence of current

This work presents an experimental study of a submerged plate used as a breakwater for coastal areas protection. Questions addressed concern the influence of current on the reflective power of the plate, and its influence on the hydrodynamic loads exerted on it. Results concern both monochromatic and irregular waves. Generally speaking, an influence of the current is found, changing the reflecting power of the structure up to 50%. A homogenized behavior of the loads and moments is found in the presence of currents, meaning that the load values become less sensitive to the frequency. Furthermore, the influence of waves reflected by the wave absorber, representing partially reflective conditions at the shore, is found to be of same order in the absence of current. In any case, the linear behavior of the breakwater is emphasized through the irregular waves approach.     

Assessment of SARAL/AltiKa Wave Height Measurements Relative to Buoy,Jason-2, and Cryosat-2 Data

SARAL/AltiKa GDR-T are analyzed to assess the quality of the significant wave height (SWH) measurements. SARAL along-track SWH plots reveal cases of erroneous data, more or less isolated, not detected by the quality flags. The anomalies are often correlated with strong attenuation of the Ka-band backscatter coefficient, sensitive to clouds and rain. A quality test based on the 1 Hz standard deviation is proposed to detect such anomalies. From buoy comparison, it is shown that SARAL SWH is more accurate than Jason-2, particularly at low SWH, and globally does not require any correction. Results are better with open ocean than with coastal buoys. The scatter and the number of outliers are much larger for coastal buoys. SARAL is then compared with Jason-2 and Cryosat-2. The altimeter data are extracted from the global altimeter SWH Ifremer data base, including specific corrections to calibrate the various altimeters. The comparison confirms the high quality of SARAL SWH. The 1 Hz standard deviation is much less than for Jason-2 and Cryosat-2, particularly at low SWH. Furthermore, results show that the corrections applied to Jason-2 and to Cryosat-2, in the data base, are efficient, improving the global agreement between the three altimeters.     

Combining rate-controlled porosimetry and NMR to probe full-range pore throat structures and their evolution features in tight sands: A case study in the Songliao Basin,China

To better understand reservoir quality and to produce accurate petrophysical interpretations, it is necessary to understand complex and heterogeneous pore throat structures in tight sands and to develop a technique to reveal the full range of pore and throat distributions. In this study, in order to characterize the features and evolutions of pore throat structures, nine samples from the Lower Cretaceous tight gas sandstone in the Songliao Basin of China are measured by nuclear magnetic resonance (NMR), rate-controlled porosimetry (RCP) and scanning electron microscopy (SEM). Throats with bifractal structures are found in these tight sands and can be divided into a backbone formation (BF) region and a percolation region using RCP data. Because (i) throats in the percolation region record treelike pore structures and are predominant in small pore spaces and (ii) a good correlation exists between NMR-derived T₂ relaxation times and the RCP-derived radius of throats, the throat distribution obtained via RCP can be used to calibrate the NMR PSD and then to partition the PSD into distributions of pore bodies and throats. These data indicate that (i) throats are more common than pore bodies in pore spaces of tight sands with lower permeability, (ii) pore bodies are connected to throats from both the BF and percolation regions, in which the fluid mobility in pore bodies is mainly controlled by the pore to throat ratio (PTR), which is related to the intersection throat of these two regions, and (iii) compaction, dissolution, clay cementation and sediment properties (e.g., rock compositions) have different impacts on the evolutions of pore bodies and throats, in which larger PTR values in tight sands are mainly produced by compaction and pore-bridging clay cementation, and lower contents of pore bodies are commonly related to abundant plastic compositions and pore-bridging clay cementation.