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Journal articles on the topic 'Wave slope'
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1
Shen, Y., R. Lindenbergh, B. Hofland, and R. Kramer. "CHANGE ANALYSIS OF LASER SCANS OF LABORATORY ROCK SLOPES SUBJECT TO WAVE ATTACK TESTING." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2/W4 (September 13, 2017): 139–47. http://dx.doi.org/10.5194/isprs-annals-iv-2-w4-139-2017.
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For better understanding how coastal structures with gentle slopes behave during high energy events, a wave attack experiment representing a storm of 3000 waves was performed in a flume facility. Two setups with different steepness of slope were compared under the same conditions. In order to quantify changes in the rock slopes after the wave attack, a terrestrial laser scanner was used to obtain 3D coordinates of the rock surface before and after each experiment. Next, through a series of processing steps, the point clouds were converted to a suitable 2D raster for change analysis. This allowed to estimate detailed and quantitative change information. The results indicate that the area around the artificial coast line, defined as the intersection between sloped surface and wave surface, is most strongly affected by wave attacks. As the distances from the sloped surface to the waves are shorter, changes for the mildly sloped surface, slope 1 (1 : 10), are distributed over a larger area compared to the changes for the more steeply sloped surface, slope 2 (1 : 5). The results of this experiment show that terrestrial laser scanning is an effective and feasible method for change analysis of rock slopes in a laboratory setting. Most striking results from a process point of view is that the transport direction of the rocks change between the two different slopes: from seaward transport for the steeper slope to landward transport for the milder slope.
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Nian, Ting Kai, Bo Liu, and Ping Yin. "Seafloor Slope Stability under Adverse Conditions Using Energy Approach." Applied Mechanics and Materials 405-408 (September 2013): 1445–48. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.1445.
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The effects of ocean waves on the stability of seafloor slopes are of great importance in marine environment. The stability of a seafloor slope considering wave-induced pressure is analyzed using the kinematic approach of limit analysis combined with a strength reduction technique. A seafloor slope without waves is considered first. Furthermore, waved-induced pressure is considered to act on the surface of slope as an external load to analyze the effects on the stability of slope by waves. The results show that the adverse effect of waves on slope stability increases with an increase of the wave height as well as a decrease of the water depth.
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K G, Parvathy, and Prasad K. Bhaskaran. "Wave attenuation in presence of mangroves: A sensitivity study for varying bottom slopes." International Journal of Ocean and Climate Systems 8, no. 3 (April 24, 2017): 126–34. http://dx.doi.org/10.1177/1759313117702919.
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Mangroves thrive in the intertidal areas (interface between land and sea) of tropical and sub-tropical belt and play an important role in overall attenuation of nearshore waves. Multiple interactions of waves with mangrove trunks and roots and bottom friction are the two primary mechanisms responsible for wave attenuation in mangrove forests. Earlier studies, comprising both analytical and experimental, reported an exponential decay in wave height for waves propagating over vegetation with idealized bottom topography and a few on sloping bottom. But hardly studies have attempted to characterize the wave attenuation by vegetation over varying seabed slopes since mangroves generally grow luxuriantly on gradual topography having large tidal amplitudes. Nowadays, several studies are being carried out on development of artificial mangroves to reduce the coastal hazard risks; thenceforth, there is an imperative requirement to study the wave damping characteristics of mangroves on varying seabed slopes. Consequently, this study performs sensitivity experiments to analyze the wave attenuation over mangroves with different sea-bottom slopes using a third-generation wave model. The study exposes sensitivity of wave attenuation characteristics to different beach slopes in the presence of mangroves and aims at understanding how the wave attenuation characteristics by mangroves differ with varying bottom slopes. The total percentage energy reduction for waves reaching the shoreline after propagating through mangroves on mild slope (1:80, 1:40) is observed to be 93%–98%, nearly 84% for 1:20 slope, and 67% for steep slope (1:10). The study reveals that the wave height decays exponentially for the mild slope and found to be consistent with the earlier studies, but as the degree of bottom steepness increases, the wave height reduction becomes gradual, and this can be attributed to the water depth variation, shoaling, breaking, and reflection characteristics associated with different slopes, in the presence of mangroves.
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Carr, Magda, Marek Stastna, Peter A. Davies, and Koen J. van de Wal. "Shoaling mode-2 internal solitary-like waves." Journal of Fluid Mechanics 879 (October 2, 2019): 604–32. http://dx.doi.org/10.1017/jfm.2019.671.
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The propagation of a train of mode-2 internal solitary-like waves (ISWs) over a uniformly sloping, solid topographic boundary, has been studied by means of a combined laboratory and numerical investigation. The waves are generated by a lock-release method. Features of their shoaling include (i) formation of an oscillatory tail, (ii) degeneration of the wave form, (iii) wave run up, (iv) boundary layer separation, (v) vortex formation and re-suspension at the bed and (vi) a reflected wave signal. Slope steepness, $s$, is defined to be the height of the slope divided by the slope base length. In shallow slope cases ($s\leqslant 0.07$), the wave form is destroyed by the shoaling process; the leading mode-2 ISW degenerates into a train of mode-1 waves of elevation and little boundary layer activity is seen. For steeper slopes ($s\geqslant 0.13$), boundary layer separation, vortex formation and re-suspension at the bed are observed. The boundary layer dynamics is shown (numerically) to be dependent on the Reynolds number of the flow. A reflected mode-2 wave signal and wave run up are seen for slopes of steepness $s\geqslant 0.20$. The wave run up distance is shown to be proportional to the length scale $ac^{2}/g^{\prime }h_{2}\sin \unicode[STIX]{x1D703}$ where $a,c,g^{\prime },h_{2}$ and $\unicode[STIX]{x1D703}$ are wave amplitude, wave speed, reduced gravity, pycnocline thickness and slope angle respectively.
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Yamashita, Kei, Taro Kakinuma, and Keisuke Nakayama. "SHOALING OF NONLINEAR INTERNAL WAVES ON A UNIFORMLY SLOPING BEACH." Coastal Engineering Proceedings 1, no. 33 (December 15, 2012): 72. http://dx.doi.org/10.9753/icce.v33.waves.72.
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The internal waves in the two-layer systems have been numerically simulated by solving the set of nonlinear equations in consideration of both strong nonlinearity and strong dispersion of waves. After the comparison between the numerical results and the BO solitons, as well as the experimental data, the internal waves propagating over the uniformly sloping beach are simulated including the cases of the mild and long slopes. The internal waves show remarkable shoaling after the interface touches the critical level. In the lower layer, the horizontal velocity becomes larger than the local linear celerity of internal waves in shallow water just before the crest peak and the position is defined as the wave-breaking point when the ratio of nonlinear parameter to beach slope is large. The ratio of initial wave height to wave-breaking depth becomes larger as the slope is milder and the wave nonlinearity is stronger. The wave height does not increase so much before wave-breaking on the mildest slope.
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Kantarzhi, Izmail, Sergii Kivva, and Natalia V. Shunko. "NUMERICAL STUDY OF WAVE RUN-UP AT PERMEABLE FIXED REVETMENT SLOPE." Coastal Engineering Proceedings, no. 35 (June 23, 2017): 32. http://dx.doi.org/10.9753/icce.v35.structures.32.
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The numerical model of wave surface elevation and water filtration in the saturated-unsaturated porous medium is developed. The model uses to define the parameters of the wave run-up at the slope protected by the permeable fixed layer. The model shows the wave surface in the different times, including the wave run-up height at the slope and wave run-down. Also, the velocities in the upper protected layer as well in the soil body of the slope are defined. Model is verified with using of the published large-scale tests with the slopes protected by Elastocoast technology layers. The tests were carried out in the wave flume of Technical University Braunschweig. The numerical model may be applied to calculate the maximal waves run-up at the protected engineering and beach slopes in natural conditions.
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Legg, Sonya. "Scattering of Low-Mode Internal Waves at Finite Isolated Topography." Journal of Physical Oceanography 44, no. 1 (January 1, 2014): 359–83. http://dx.doi.org/10.1175/jpo-d-12-0241.1.
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Abstract A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h0/H0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h0/H0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h0/H0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefore increases as both incoming wave Froude number and topographic height increase. At critical slopes, the dissipation is enhanced along the slope facing the incoming wave. In contrast, at subcritical slopes, dissipation is small until the wave amplitude is sufficiently enhanced by the shoaling topography to exceed the critical Froude number; then large dissipation extends all the way to the surface. The results are shown to generalize to variable stratification and different topographies, including axisymmetric seamounts. The regimes for low-mode internal wave breaking at isolated critical and subcritical topography identified by these simulations provide guidance for the parameterization of the mixing due to radiated internal tides.
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Chen, Weiyun, Dan Wang, Lingyu Xu, Zhenyu Lv, Zhihua Wang, and Hongmei Gao. "On the Slope Stability of the Submerged Trench of the Immersed Tunnel Subjected to Solitary Wave." Journal of Marine Science and Engineering 9, no. 5 (May 13, 2021): 526. http://dx.doi.org/10.3390/jmse9050526.
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Wave is a common environmental load that often causes serious damages to offshore structures. In addition, the stability for the submarine artificial slope is also affected by the wave loading. Although the landslide of submarine slopes induced by the waves received wide attention, the research on the influence of solitary wave is rare. In this study, a 2-D integrated numerical model was developed to investigate the stability of the foundation trench under the solitary wave loading. The Reynolds-averaged Stokes (RANS) equations were used to simulate the propagation of a solitary wave, while the current was realized by setting boundary inlet/outlet velocity. The pore pressure induced by the solitary wave was calculated by Darcy’s law, and the seabed was characterized by Mohr–Coulomb constitutive model. Firstly, the wave model was validated through the comparison between analytical solution and experimental data. The initial consolidation state of slope under hydrostatic pressure was achieved as the initial state. Then, the factor of stability (FOS) for the slope corresponding to different distances between wave crest and slope top was calculated with the strength reduction method. The minimum of FOS was defined as the stability index for the slope with specific slope ratio during the process of dynamic wave loading. The parametric study was conducted to examine the effects of soil strength parameters, slope ratio, and current direction. At last, the influence of upper slope ratio in a two-stage slope was also discussed.
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Wu, Honggang, Zhixin Wu, Hao Lei, and Tianwen Lai. "Application of BRFP New-Type Anchor Cable Material in High Slopes against Earthquakes." Advances in Civil Engineering 2021 (February 13, 2021): 1–19. http://dx.doi.org/10.1155/2021/6689718.
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To clarify the feasibility of BFRP (basalt fiber reinforced plastics) anchors instead of steel anchors in the seismic application of slopes under different vibration strengths, a series of shaking table tests were carried out to strengthen the slope using BFRP anchors and steel anchors, respectively. By studying the dynamic response recorded in the slope model and the observed experimental phenomena, the acceleration dynamic response and displacement spectrum dynamic response of the two slope models were analyzed. The test results show that the deformation stage of the slope reinforced by the two types of anchors is basically the same during the test, that is, elastic, plastic (potential sliding surface and plastic strengthening), and failure stages, respectively. The slope is in the elastic stage before the 0.2 g seismic wave, and it gradually enters the plastic stage after the 0.4 g seismic wave. However, the peak acceleration and displacement of the slope reinforced by steel anchors are greater than those of the slope reinforced by BFRP anchors under the same working conditions of seismic waves. In addition, we found that the acceleration response spectrum distribution curve of each measuring point in the short period has an obvious amplification effect along the elevation, and its predominant period has a forward migration phenomenon with the increase of the height of the measuring point, which also indicates that the higher frequency seismic wave has a greater impact on the top of the slope. The BFRP anchors, as a kind of flexible structure supporting slope, can effectively reduce the impact of seismic waves on the slope and attenuate seismic waves to a certain extent compared with steel anchors. Furthermore, the BFRP anchors can be deformed in coordination with the slope, which can improve the overall working performance of the slope, especially limit the dynamic response of the middle and lower slopes. These results can provide a theoretical guide for the seismic design of BFRP anchors for high slopes.
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Shen, Yueqian, Jinguo Wang, Roderik Lindenbergh, Bas Hofland, and Vagner G. Ferreira. "Range Image Technique for Change Analysis of Rock Slopes Using Dense Point Cloud Data." Remote Sensing 10, no. 11 (November 12, 2018): 1792. http://dx.doi.org/10.3390/rs10111792.
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The use of a terrestrial laser scanner is examined to measure the changes of rock slopes subject to a wave attack test. Real scenarios are simulated in a water flume facility using a wave attack experiment representing a storm of 3000 waves. The stability of two rock slopes of different steepness was evaluated under the set conditions. For quantification of the changes of the slopes after the wave attack test, terrestrial laser scanning was used to acquire dense 3D point cloud data sampling for slope geometries before and after the wave attack experiment. After registration of the two scans, representing situations before and after the wave attack, the cloud-to-cloud distance was determined to identify areas in the slopes that were affected. Then, a range image technique was introduced to generate a raster image to facilitate a change analysis. Using these raster images, volume change was estimated as well. The results indicate that the area around the artificial coast line is most strongly affected by wave attacks. Another interesting phenomenon considers the change in transport direction of the rocks between the two slopes: from seaward transport for the steeper slope to landward transport for the milder slope. Using the range image technique, the work in this article shows that terrestrial laser scanning is an effective and feasible method for change analysis of long and narrow rock slopes.
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Saville, Jr., Thorndike. "WAVE RUN-UP ON COMPOSITE SLOPES." Coastal Engineering Proceedings 1, no. 6 (January 29, 2011): 41. http://dx.doi.org/10.9753/icce.v6.41.
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A method is presented for determining wave run-up on composite slopes from laboratory- derived curves for single slopes. The method is one of successive approximations and involves replacement of the actual composite slope with a hypothetical single slope obtained from the breaking depth and an estimated run-up value. Comparison of predicted values is made with actual laboratory data.
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Xiaoli, Guo, Yan Jiancheng, Li Xueliang, Wen Xin, and Li Xingli. "Study on shaping slope stability of dump in eastern grassland open-pit mine." E3S Web of Conferences 194 (2020): 04043. http://dx.doi.org/10.1051/e3sconf/202019404043.
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The dumps in the open-pit mining area in the eastern grassland are prone to landslides due to the fragile ecological environment, so it is inevitable to reshape the dump slopes. In order to explore a more scientific method for slope shaping of open-pit mine dump, slope stability analysis were used to compare effect of three types of slope-type (wave-shaped, slope-shaped and step-shaped slope shaping method)in outside dumping site of Baori Hiller open-pit mine. The results show that the slope stability is negatively correlated with the slope angle, and the stability of different shaping slopes is realized as wave-shaped slope (F=2.711)> Slope-shaped slope(F=2.513)>Step-shaped slope(F=1.047), in which the wave type and slope type are all within the safe range, but the step type slope is unstable; in consideration of cost, stability and erosion resistance, it is better to set the slope angle of the dump to 15°.The wave-shaped shaping method of the natural dumping of the excavation field outside the Baori Hiller open-pit mine has the best effect and is worth promoting.
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Wang, Gang, and Jin-Hai Zheng. "SUBHARMONIC GENERATION OF TRANSVERSE OSCILLATIONS INDUCED BY INCIDENT REGULAR WAVES." Coastal Engineering Proceedings 1, no. 33 (September 27, 2012): 11. http://dx.doi.org/10.9753/icce.v33.waves.11.
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It is generally accepted that there are transverse oscillation, which are concentrated and confined to the backwall and decay asymptotically offshore, existed in the harbor of constant slope, however, whether these oscillations can be induced by the normally incident waves is not clear. This numerical investigation aims at providing the subharmonic generations of transverse oscillations within the harbor of a plane slope by waves normally impacting on. For the harbor of perfectly plane slopes, the subharmonic transverse oscillations are small on the mild and moderate slopes but evident on the steep slope. This instability can take place only if the incident wave amplitude exceeds a threshold value, and transverse oscillations can even grow up to a larger value than that of longitudinal oscillations. The magnitudes of transverse oscillations are approximately the same, only their growth rates are affected by the incident wave amplitude.
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Popov, I. J. "EXPERIMENTAL RESEARCH IN FORMATION BY WAVES OF STABLE PROFILES OF UPSTREAM FACES OF EARTH DAMS AND RESERVOIR SHORES." Coastal Engineering Proceedings 1, no. 7 (January 29, 2011): 16. http://dx.doi.org/10.9753/icce.v7.16.
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Within the last few years the Soviet hydraulic engineers have been making continuous efforts to avoid use of concrete slabs and blocks and stone riprap as protective cover of upstream slopes of earth dams and reservoir shores against the disrupting effects of waves generated by the action of wind upon the water surface. Their efforts have been aimed at finding the cheaper procedure. Of all the possible ways of slope and shore protection, an engineering measure, the idea of which consists in distributing the wave energy dissipation over a considerably large portion of a sufficiently gentle slope, should be given a special attention. This measure makes it possible to substantially relieve the protective cover and in some cases to leave the slope uncovered. The possibility of unlined slopes, stable enough agains wave action is proved out by the experience of reservoir operation. Shores and underwater slopes of artificial lakes composed of non-cohesive soils are usually subject to considerable disintegration due to wave action. The process of disintegration which goes on rather fast at the initial stage of lake existence, slowff down with the formation of a flat lake-side shallow, whereon dissipation of wave energy takes place. At a certain stage of development the underwater slope assumes such dimensions and outlines which enable it to dissipate the whole of the wave energy and practically to protect shores from further destruction. The profile of the slope at which it will permanently stand underwater is referred to as the "profile of equilibrium" or "dynamically stable profile". The term "equilibrium" in this case doesn't imply absolute immovability of the material acted on by waves, but stands for such a movable state at which particles of the soil are making oscillatory movements round some middle position without the resultant movement neither towards nor off shore.
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Chen, Zhonghuan, Sergey Fomel, and Wenkai Lu. "Accelerated plane-wave destruction." GEOPHYSICS 78, no. 1 (January 1, 2013): V1—V9. http://dx.doi.org/10.1190/geo2012-0142.1.
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When plane-wave destruction (PWD) is implemented by implicit finite differences, the local slope is estimated by an iterative algorithm. We propose an analytical estimator of the local slope that is based on convergence analysis of the iterative algorithm. Using the analytical estimator, we design a noniterative method to estimate slopes by a three-point PWD filter. Compared with the iterative estimation, the proposed method needs only one regularization step, which reduces computation time significantly. With directional decoupling of the plane-wave filter, the proposed algorithm is also applicable to 3D slope estimation. We present synthetic and field experiments to demonstrate that the proposed algorithm can yield a correct estimation result with shorter computational time.
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van Dam, Marcos A., and Richard G. Lane. "Wave-front slope estimation." Journal of the Optical Society of America A 17, no. 7 (July 1, 2000): 1319. http://dx.doi.org/10.1364/josaa.17.001319.
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Schoonees, Talia B., Nils B. Kerpen, Sven Liebisch, and Torsten Schlurmann. "WAVE OVERTOPPING PREDICTION OF A GENTLE SLOPED STEPPED REVETMENT." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 99. http://dx.doi.org/10.9753/icce.v36.papers.99.
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Stepped revetments are multi-functional coastal structures o ering protection against flooding. Despite the fact that these structures have been implemented for more than 60 years, comprehensive design guidance is lacking. Previous research studied overtopping of stepped revetments with slopes ranging between 1:1 to 1:4. To address the knowledge gap of predicting overtopping of stepped revetments with gentler slopes, this paper presents results of physical model tests for a 1:6 sloped stepped revetment with step heights of 0.05 m. The tests were conducted in a 110 m long, 2.2 m wide and 2.0 m deep wave flume. A fit through the overtopping results is compared with the reference curve for a smooth slope of EurOtop (2016), which allows the determination of the influence factor for roughness ( gamma_f ) of the stepped revetment. A value of gamma_f = 0.74 (r^2 of 0.94) is proposed to be used in combination with the overtopping prediction formula of EurOtop (2016) for slopes under breaking wave conditions. The results of the study indicate a high slope dependency for gamma_f .
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Lara, Javier L., Andrea Ruju, and Inigo J. Losada. "Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2129 (November 10, 2010): 1215–42. http://dx.doi.org/10.1098/rspa.2010.0331.
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This paper presents the numerical modelling of the cross shore propagation of infragravity waves induced by a transient focused short wave group over a sloping bottom. A dataset obtained through new laboratory experiments in the wave flume of the University of Cantabria is used to validate the Reynolds averaged Navier–Stokes type model IH-2VOF. A new boundary condition based on the wave maker movement used in the experiments is implemented in the model. Shoaling and breaking of short waves as well as the enhancement of long waves and the energy transfer to low-frequency motion are well addressed by the model, proving the high accuracy in the reproduction of surf zone hydrodynamics. Under the steep slope regime, a long wave trough is radiated offshore from the breakpoint. Numerical simulations conducted for different bottom slopes and short wave steepness suggest that this low-frequency breakpoint generated wave is controlled by both the bed slope parameter and the Iribarren number. Moreover, the numerical model is used to investigate the influence that a large flat bottom induces on the propagation pattern of long waves.
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Jingbo, Su, Zhu Feng, Geng Ying, and Ni Xingye. "Numerical Study of Wave Overtopping Based on Local Method of Approximate Particular Solution Method." Advances in Mechanical Engineering 6 (January 1, 2014): 541717. http://dx.doi.org/10.1155/2014/541717.
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In order to study the wave overtopping process, this paper establishes a two-dimensional numerical wave flume based on a meshless algorithm, local method of approximate particular solution (the LMAPS method), and the technology of momentum source wave. It calculates the climbing and overtopping process under regular waves on a typical slope, results of which are more consistent with the physical model test results. Finally, wave action simulation is carried out on six different structural forms of wave walls (vertical wave wall, 1/4 arc wave wall, reversed-arc wave wall, smooth surface wave wall with 1: 3 slope ratio, smooth surface wave wall with 1: 1.5 slope ratio and stepped surface wave wall with 1: 1.5 slope ratio). Numerical results of the simulation accurately describe the wave morphological changes in the interaction of waves and different structural forms of wave walls, in which, average error of wave overtopping is roughly 6.2% compared with the experimental values.
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Scott, Nicholas, Tetsu Hara, Edward J. Walsh, and Paul A. Hwang. "Observations of Steep Wave Statistics in Open Ocean Waters." Journal of Atmospheric and Oceanic Technology 22, no. 3 (March 1, 2005): 258–71. http://dx.doi.org/10.1175/jtech1702.1.
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Abstract A new wavelet analysis methodology is proposed to estimate the statistics of steep waves. The method is applied to open ocean wave height data from the Southern Ocean Waves Experiment (1992) and from a field experiment conducted at Duck, North Carolina (1997). Results show that high wave slope crests appear over a wide range of wavenumbers, with a large amount being much shorter than the dominant wave. At low wave slope thresholds, all wave fields have roughly the same amount of wave crests regardless of wind forcing. The steep wave statistic decays exponentially with the square of the wave slope threshold, with a decay rate that is larger for the low wind cases than the high wind cases. Comparison of the steep wave statistic with independent measurements of the breaking wave statistic suggests a breaking wave slope threshold of about 0.12. The steep wave statistic does not scale with the cube of the wind speed, suggesting that other factors besides the wind speed also affect its level. Comparison of the steep wave statistic to the saturation spectrum reveals a reasonable correlation at moderate wave slope thresholds.
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Kimmoun, Olivier, H. C. Hsu, and Amin Chabchoub. "EVOLUTION OF UNSTABLE WAVE PACKETS OVER VARIABLE BATHYMETRY." Coastal Engineering Proceedings, no. 36v (December 28, 2020): 8. http://dx.doi.org/10.9753/icce.v36v.waves.8.
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Several field observations have reported the formation of rogue waves in coastal zones, see Chien et al. (2002) for an example in Taiwanese sea. The mechanisms that lead to the occurrence of rogue waves in finite water depth to shallow water are not well understood yet under the conjecture of modulation instability. Indeed, this theory for uni-directional waves shows that when kh is lower than a threshold of 1.363 in homogeneous water depth conditions, the wave train becomes stable to side-band perturbations. Then if the wave train is stable, the appearance of rogue waves is not possible within this linear stability framework. One explanation may come from the complex wave transformation mechanisms in variable bathymetry, especially, for cases of steep slopes or near the edge between a steep slope and a gentle slope as it is the case of the continental shelf. Very few laboratory experiments have been so far addressing the influence of the bathymetry on extreme wave occurrence (Baldock and Swan (1996), Kashima et al. (2012), Ma et al. (2015)).Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a5M4PS-Lo4Q
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Thaha, Muhammad Arsyad, P. H. Mukhsan, A. M. Subhan, and A. Ildha Dwipuspita. "Single Slope Shore Protection as a Wave Energy Catcher." MATEC Web of Conferences 203 (2018): 01008. http://dx.doi.org/10.1051/matecconf/201820301008.
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Wave energy is being increasingly regarded in many countries as a major, promising and renewable resource. This paper presents the development of slope coastal protection as a wave energy converter by capturing sea water into the reservoir through overtopping process. Physical models simulation were conducted at The Laboratory of Coastal Engineering, Hasanuddin University. A model of 30 cm x 90 cm in the 30° degree of slope made from acrylic material equipped with a reservoir at the top surface of the structures to catch seawater through run up and overtopping. Models were simulated with various wave high and periods as well as high of freeboard. The results showed that the overtopping discharge (Q) much influenced by relative freeboard height (Fb/d), wave steepness (Hi/L), reflected waves (Kr) and the number of standing waves (Nsw). The increasing Fb, the decreasing Q; the increasing wave steepness, the increasing overtopping discharge. It was found that the larger the reflection coefficient, the greater the discharge overtopping. Standing waves in front of the structure due to the superposition of the incident wave and reflection waves also contribute to enlarge the overtopping discharge.
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HENN, DOUGLAS S., and R. IAN SYKES. "Large-eddy simulation of flow over wavy surfaces." Journal of Fluid Mechanics 383 (March 25, 1999): 75–112. http://dx.doi.org/10.1017/s0022112098003723.
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Large-eddy simulation is used to investigate fully developed turbulent flow in a neutral channel wherein the lower wall is sinusoidal. The numerical results are compared with experimental observations for wave slopes ranging from 0 to 0.628. Particular emphasis is placed on the separated flow induced by a large-amplitude wave. A detailed comparison with the data of Buckles, Hanratty & Adrian (1984) shows generally good agreement. Large-eddy simulation surface pressures are integrated to calculate form drag as a function of wave slope. Drag is found to increase quadratically with slope for small-amplitude waves, with a somewhat slower increase for larger amplitudes. However, comparison with experimental measurements is confounded by uncertainties with the values reported in the literature. An interesting feature characteristic of all wavy-surface simulations is an increase in transverse velocity fluctuations on the wave upslope. Although the precise mechanism responsible is not known, analysis shows it to be associated with temporally persistent vortex-like structures localized near the surface. The magnitude of the fluctuation increase appears to scale quadratically with slope for small-amplitude waves, in contrast to the streamwise fluctuations, which increase linearly.
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Cho, Yong Jun. "On the Effects of Non-Gaussian Wave-Slope Distribution on the Failure Probability of an Armour block of Rubble Mound Breakwater." Korea Society of Coastal Disaster Prevention 8, no. 3 (July 30, 2021): 165–79. http://dx.doi.org/10.20481/kscdp.2021.8.3.165.
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This study examined the effect of non-Gaussian wave slope distribution on the failure probability of an armoring rock of rubble mound breakwater using numerical simulation. Numerical simulation was carried out using the Van der Meer equation and Level III reliability design method based on the Monte Carlo simulation. In doing so, modified Glukhovskiy wave height distribution and situ wave height data collected at Ulleungdo from January 1, 1979-December 31, 2019 were used. Tri-modal Gaissuian wave slope distribution was also used, which showed good agreements with situ wave data collected at Mangbang from April 26, 2017, to April 20, 2018. The probability coefficients of tri-modal Gaussian distribution were estimated using Matlab-based statistics and machine learning toolbox, MLE [Maximum Likelihood Estimates]. In the numerical simulation, the intrinsic limitations of Gaussian distribution were revealed, such as imposing a non-negligible probability mass even in the negative wave slope, under-shooting in longer and shorter waves, and over-shooting in mid-scale waves. In the case of failure probability of an armoring rock, Gaussian distribution was shown to give underestimated failure probability. The extent of underestimation was more considerable at Mangbang, where a tidal terrace of lower depth and gently varying slope was developed than at Ulleungdo. These differences were triggered by the presence of probability plateau formed in wave slope distribution whenever infra-gravity waves appear in random wave packet due to the resonant wave-wave interaction. Therefore, it can be easily conceivable that probability plateau has a significant effect on the armoring rock failure probability. Therefore, PIANC's recommendation that wave slope follows Gaussian distribution needs to be amended. Moreover, the reliability-based design of breakwater should be implemented based on tri-modal Gaussian wave slope distribution, which can accurately reproduce probability plateau.
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AGHSAEE, PAYAM, LEON BOEGMAN, and KEVIN G. LAMB. "Breaking of shoaling internal solitary waves." Journal of Fluid Mechanics 659 (July 15, 2010): 289–317. http://dx.doi.org/10.1017/s002211201000248x.
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The breaking of fully nonlinear internal solitary waves of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. Our simulations were limited to narrow-crested waves, which are more common than broad-crested waves in geophysical flows. The simulations were performed for a wide range of boundary slopes S ∈ [0.01, 0.3] and wave slopes extending the parameter range to weaker slopes than considered in previous laboratory and numerical studies. Over steep slopes (S ≥ 0.1), three distinct breaking processes were observed: surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary-layer separation, respectively. Over mild slopes (S ≤ 0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation as it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental time scale. The breaking location was modelled as a function of wave amplitude (a), characteristic wave length and the isopycnal length along the slope. The breaker type was characterized in wave slope (Sw = a/Lw, where Lw is a measure of half of the wavelength) versus S space, and the reflection coefficient (R), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and wave Reynolds number (Rew) on R, boundary-layer separation and the evolution of global instability were studied. High Reynolds numbers (Rew ~ 104) were found to trigger a global instability, which modifies the breaking process relative to the lower Rew case, but not necessarily the breaking location, and results in a ~ 10 % increase in R, relative to the Rew ~ 103 case.
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Eslami A., Sepehr, and Marcel R. A. Van Gent. "WAVE OVERTOPPING AND RUBBLE MOUND STABILITY UNDER COMBINED LOADING OF WAVES AND CURRENT." Coastal Engineering Proceedings 1, no. 32 (January 29, 2011): 12. http://dx.doi.org/10.9753/icce.v32.structures.12.
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Coastal structures such as breakwaters are usually studied under wave loading only. However, at several locations also a current is present. For instance, breakwaters along intake and outfall channels of power plants and desalination plants, or structures in regions with important tidal currents, experience wave loading that can be affected by currents. Nevertheless, wave overtopping and rubble mound stability are usually studied under wave loading only; the effects of waves on wave overtopping and rock slope stability have been summarised in many empirical design formulae. None of the existing empirical relations account for the effects of currents on the wave loading and consequently on wave overtopping and rock slope stability. The effects of wave-current interaction on wave overtopping and rubble mound stability has not been quantified, other than that for mild currents these processes are dominated by waves. Therefore, the present study is focussed on wave loading in combination with a strong current. This study is based on physical model tests in a wave-current basin. The results show to what extent wave overtopping and rubble mound stability are affected by wave loading in combination with a current. Wave overtopping and the damage to rock slopes generally reduce due to the presence of a current compared to the situation without a current.
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Lien, Ren-Chieh, Eric A. D’Asaro, Frank Henyey, Ming-Huei Chang, Tswen-Yung Tang, and Yiing-Jang Yang. "Trapped Core Formation within a Shoaling Nonlinear Internal Wave." Journal of Physical Oceanography 42, no. 4 (April 1, 2012): 511–25. http://dx.doi.org/10.1175/2011jpo4578.1.
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Abstract Large-amplitude (100–200 m) nonlinear internal waves (NLIWs) were observed on the continental slope in the northern South China Sea nearly diurnally during the spring tide. The evolution of one NLIW as it propagated up the continental slope is described. The NLIW arrived at the slope as a nearly steady-state solitary depression wave. As it propagated up the slope, the wave propagation speed C decreased dramatically from 2 to 1.3 m s−1, while the maximum along-wave current speed Umax remained constant at 2 m s−1. As Umax exceeded C, the NLIW reached its breaking limit and formed a subsurface trapped core with closed streamlines in the coordinate frame of the propagating wave. The trapped core consisted of two counter-rotating vortices feeding a jet within the core. It was highly turbulent with 10–50-m density overturnings caused by the vortices acting on the background stratification, with an estimated turbulent kinetic energy dissipation rate of O(10−4) W kg−1 and an eddy diffusivity of O(10−1) m2 s−1. The core mixed continually with the surrounding water and created a wake of mixed water, observed as an isopycnal salinity anomaly. As the trapped core formed, the NLIW became unsteady and dissipative and broke into a large primary wave and a smaller wave. Although shoaling alone can lead to wave fission, the authors hypothesize that the wave breaking and the trapped core evolution may further trigger the fission process. These processes of wave fission and dissipation continued so that the NLIW evolved from a single deep-water solitary wave as it approached the continental slope into a train of smaller waves on the Dongsha Plateau. Observed properties, including wave width, amplitude, and propagation speed, are reasonably predicted by a fully nonlinear steady-state internal wave model, with better agreement in the deeper water. The agreement of observed and modeled propagation speed is improved when a reasonable vertical profile of background current is included in the model.
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Melville, W. Kendall, and Alexey V. Fedorov. "The equilibrium dynamics and statistics of gravity–capillary waves." Journal of Fluid Mechanics 767 (February 18, 2015): 449–66. http://dx.doi.org/10.1017/jfm.2014.740.
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AbstractRecent field observations and modelling of breaking surface gravity waves suggest that air-entraining breaking is not sufficiently dissipative of surface gravity waves to balance the dynamics of wind-wave growth and nonlinear interactions with dissipation for the shorter gravity waves of $O(10)$ cm wavelength. Theories of parasitic capillary waves that form at the crest and forward face of shorter steep gravity waves have shown that the dissipative effects of these waves may be one to two orders of magnitude greater than the viscous dissipation of the underlying gravity waves. Thus the parasitic capillaries may provide the required dissipation of the short wind-generated gravity waves. This has been the subject of speculation and conjecture in the literature. Using the nonlinear theory of Fedorov & Melville (J. Fluid Mech., vol. 354, 1998, pp. 1–42), we show that the dissipation due to the parasitic capillaries is sufficient to balance the wind input to the short gravity waves over some range of wave ages and wave slopes. The range of gravity wave lengths on which these parasitic capillary waves are dynamically significant approximately corresponds to the range of short gravity waves that Cox & Munk (J. Mar. Res., vol. 13, 1954, pp. 198–227) found contributed significantly to the mean square slope of the ocean surface, which they measured to be proportional to the wind speed. Here we show that the mean square slope predicted by the theory is proportional to the square of the friction velocity of the wind, ${u_{\ast }}^{2}$, for small wave slopes, and approximately $u_{\ast }$ for larger slopes.
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Peng, Ningbo, Yun Dong, Ye Zhu, and Jie Hong. "Influence of Ground Motion Parameters on the Seismic Response of an Anchored Rock Slope." Advances in Civil Engineering 2020 (December 23, 2020): 1–10. http://dx.doi.org/10.1155/2020/8825697.
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The seismic response of rock slopes is closely related to the dynamic characteristics of earthquakes. In this study, based on a numerical model of rock slopes with bolt support, the seismic responses of both anchored and unanchored rock slopes under different seismic waves are calculated. The results show that a “cumulative effect” of the relative permanent displacement of the slope is generated during seismic action, and it is found that the permanent displacement of the slope is caused by larger earthquake accelerations. The dynamic responses of an anchored slope are analyzed in terms of the wave type, frequency, amplitude, and duration and are compared with those of an unanchored rock slope. This comparison suggests that the nominal shear strain increases with the amplitude and duration, which decreases as frequency increases. The axial force is directly related to the surrounding rock strain. The maximum axial force of the bolt is near the rock interface, which shows that the structural plane of the slope plays a dominant role in the seismic response. The seismic waves are random, whereas the structural plane of the rock slope is certain. The seismic response characteristics of the slope under different earthquake conditions are similar, and the dynamic stability of the slope can be attributed to the structural analysis of the rock slope.
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McFall, Brian C., and Hermann M. Fritz. "Physical modelling of tsunamis generated by three-dimensional deformable granular landslides on planar and conical island slopes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2188 (April 2016): 20160052. http://dx.doi.org/10.1098/rspa.2016.0052.
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Tsunamis generated by landslides and volcanic island collapses account for some of the most catastrophic events recorded, yet critically important field data related to the landslide motion and tsunami evolution remain lacking. Landslide-generated tsunami source and propagation scenarios are physically modelled in a three-dimensional tsunami wave basin. A unique pneumatic landslide tsunami generator was deployed to simulate landslides with varying geometry and kinematics. The landslides were generated on a planar hill slope and divergent convex conical hill slope to study lateral hill slope effects on the wave characteristics. The leading wave crest amplitude generated on a planar hill slope is larger on average than the leading wave crest generated on a convex conical hill slope, whereas the leading wave trough and second wave crest amplitudes are smaller. Between 1% and 24% of the landslide kinetic energy is transferred into the wave train. Cobble landslides transfer on average 43% more kinetic energy into the wave train than corresponding gravel landslides. Predictive equations for the offshore propagating wave amplitudes, periods, celerities and lengths generated by landslides on planar and divergent convex conical hill slopes are derived, which allow an initial rapid tsunami hazard assessment.
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Van der Meer, Jentsje, Yvo Provoost, and Gosse Jan Steendam. "THE WAVE RUN-UP SIMULATOR, THEORY AND FIRST PILOT TEST." Coastal Engineering Proceedings 1, no. 33 (December 14, 2012): 65. http://dx.doi.org/10.9753/icce.v33.structures.65.
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The idea of the Wave Run-up Simulator is based on the experiences with the Wave Overtopping Simulator. It is possible to simulate wave tongues overtopping a dike crest in reality. It must also be possible to simulate waves in the run-up and run-down zone of the seaward slope. This is the zone after waves have broken and when they rush-up the slope. The present paper describes this new idea of the Wave Run-up Simulator, why it is useful to develop the machine, to perform research with it and to develop a prediction method for slope strength. In fact, a prediction method can already be developed from the Cumulative Overload Method, which was developed on the basis of results with the Wave Overtopping Simulator, see Van der Meer et al. (2010). It also means that tests on the seaward slope will be done for validation purposes only. The paper describes in detail what is known about the movement of waves in this run-up zone and what actually the Wave Run-up Simulator has to simulate. Not a lot of research has been performed to describe the wave run-up process in detail, physically nor statistically. Finally, the pilot test has been described including hydraulic measurements on the slope.
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Kerpen, Nils B., Talia Schoonees, and Torsten Schlurmann. "Wave Overtopping of Stepped Revetments." Water 11, no. 5 (May 17, 2019): 1035. http://dx.doi.org/10.3390/w11051035.
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Wave overtopping—i.e., excess of water over the crest of a coastal protection infrastructure due to wave run-up—of a smooth slope can be reduced by introducing slope roughness. A stepped revetment ideally constitutes a slope with uniform roughness and can reduce overtopping volumes of breaking waves up to 60% compared to a smooth slope. The effectiveness of the overtopping reduction decreases with increasing Iribarren number. However, to date a unique approach applicable for a wide range of boundary conditions is still missing. The present paper: (i) critically reviews and analyzes previous findings; (ii) contributes new results from extensive model tests addressing present knowledge gaps; and (iii) proposes a novel empirical formulation for robust prediction of wave overtopping of stepped revetments for breaking and non-breaking waves. The developed approach contrasts a critical assessment based on parameter ranges disclosed beforehand between a smooth slope on the one hand and a plain vertical wall on the other. The derived roughness reduction coefficient is developed and adjusted for a direct incorporation into the present design guidelines. Underlying uncertainties due to scatter of the results are addressed and quantified. Scale effects are highlighted.
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Cho, Yong Jun. "Level III Reliability Design of an Armor Block of Rubble Mound Breakwater Using Probabilistic Model of Wave Height Optimized for the Korean Sea Wave Conditions and Non-Gaussian Wave Slope Distribution." Journal of Marine Science and Engineering 9, no. 2 (February 19, 2021): 223. http://dx.doi.org/10.3390/jmse9020223.
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In this study, a Level III reliability design of an armor block of rubble mound breakwater was developed using the optimized probabilistic wave height model for the Korean marine environment and Van der Meer equation. To demonstrate what distinguishes this study from the others, numerical simulation was first carried out, assuming that wave slope follows Gaussian distribution recommended by PIANC. Numerical results showed that Gaussian wave slope distribution overpredicted the failure probability of armor block, longer and shorter waves, and on the contrary, underpredicted waves of the medium period. After noting the limitations of Gaussian distribution, some efforts were made to develop an alternative for Gaussian distribution. As a result, non-Gaussian wave slope distribution was analytically derived from the joint distribution of wave amplitude and period by Longuet–Higgins using the random variables transformation technique. Numerical results showed that non-Gaussian distribution could effectively address the limitations of Gaussian distribution due to its capability to account for the nonlinear resonant wave–wave interaction and its effects on the wave slope distribution that significantly influences the armor block’s stability. Therefore, the non-Gaussian wave slope distribution presented in this study could play an indispensable role in addressing controversial issues such as whether or not enormous armor blocks like a Tetrapod of 100 t frequently mentioned in developing countermeasures against rough seas due to climate change is too conservatively designed.
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Yan, Zi Tong, Liang Qiu Cheng, Feng Yi, Tai Zhong Chen, Han Sun, and Chun Ling Wang. "Study Based on FLUENT of Broken Internal Waves in Different Slope Angles." Applied Mechanics and Materials 638-640 (September 2014): 1769–77. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1769.
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Internal waves will break in the process of communication, the broken will make water in upper and lower mixing, which has significant influence on the hydrodynamic and layered characteristics of density stratification of the water. In order to reveal the propagation of internal solitary waves, a 3d numerical wave flume was built. The research of the propagation of internal solitary waves in the regular topography and broken on slopes was based on FLUENT. Comparing the fragmentation degree of different slope angle and researching the energy dissipation of the wave propagation process , which are supposed to successfully match the results with the experiment results, can provide new methods and means for the further study of internal wave breaking characteristics and the improvement of ecological environment of water bodies.
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ASAKAWA, Yosuke, Hiroshi OKAMOTO, Katsumi SEKI, and Masaru MIZUGUCHI. "Wave Reflection from Compound Slope." PROCEEDINGS OF COASTAL ENGINEERING, JSCE 55 (2008): 806–10. http://dx.doi.org/10.2208/proce1989.55.806.
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Guérin, Thomas, Anouk de Bakker, and Xavier Bertin. "On the Bound Wave Phase Lag." Fluids 4, no. 3 (August 9, 2019): 152. http://dx.doi.org/10.3390/fluids4030152.
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More than three decades ago, it was noted that the ocean infragravity bound wave increasingly lags behind the forcing short-wave groups when propagating towards the shore. To date, the most recent theoretical prediction of this so-called phase lag remained a first-order approximation in terms of depth variations. Here, a new semi-analytical solution is proposed which does not rely on this approximation. Strong agreement is obtained when the new solution is compared with high-resolution laboratory data involving both bichromatic and random wave conditions. This newly proposed theoretical phase lag is then extensively compared with the former one, highlighting an increasing discrepancy between the two solutions as the relative bottom slope increases. The four influencing parameters, namely the bottom slope, the water depth, the incident short-wave peak period and the incident group period, are shown to impact, each in a specific way, the bound wave phase lag. While the latter is seen to increase with lower water depths and/or with higher short-wave peak periods, both the bottom slope and the group period can affect the phase lag in a different manner. Indeed, steeper bed slopes induce lower phase lags in shallow water but higher ones in deep water, while higher group periods induce higher phase lags for gentle slopes but lower ones for steep slopes.
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Mares-Nasarre, Patricia, M. Esther Gómez-Martín, and Josep R. Medina. "Influence of Mild Bottom Slopes on the Overtopping Flow over Mound Breakwaters under Depth-Limited Breaking Wave Conditions." Journal of Marine Science and Engineering 8, no. 1 (December 19, 2019): 3. http://dx.doi.org/10.3390/jmse8010003.
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The crest elevation of mound breakwaters is usually designed considering a tolerable mean wave overtopping discharge. However, pedestrian safety, characterized by the overtopping layer thickness (OLT) and the overtopping flow velocity (OFV), is becoming more relevant due to the reduction of the crest freeboards of coastal structures. Studies in the literature focusing on OLT and OFV do not consider the bottom slope effect, even if it has a remarkable impact on mound breakwater design under depth-limited breaking wave conditions. Therefore, this research focuses on the influence of the bottom slope on OLT and OFV exceeded by 2% of incoming waves, hc,2% and uc,2%. A total of 235 2D physical tests were conducted on conventional mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors with 2% and 4% bottom slopes. Neural networks were used to determine the optimum point to estimate wave characteristics for hc,2% and uc,2% calculation; that point was located at a distance from the model toe of three times the water depth at the toe (hs) of the structure. The influence of the bottom slope is studied using trained neural networks with fixed wave conditions in the wave generation zone; hc,2% slightly decreases and uc,2% increases as the gradient of the bottom slope increases.
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Simpson, Alexandra, Merrick Haller, David Walker, Patrick Lynett, and David Honegger. "Wave-by-Wave Forecasting via Assimilation of Marine Radar Data." Journal of Atmospheric and Oceanic Technology 37, no. 7 (July 1, 2020): 1269–88. http://dx.doi.org/10.1175/jtech-d-19-0127.1.
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AbstractThis work describes a phase-resolving wave-forecasting algorithm that is based on the assimilation of marine radar image time series. The algorithm is tested against synthetic data and field observations. The algorithm couples X-band marine radar observations with a phase-resolving wave model that uses the linear mild slope equations for reconstruction of water surface elevations over a large domain of O(km) and a prescribed time window of O(min). The reconstruction also enables wave-by-wave forecasting through forward propagation in space and time. Marine radar image time series provide the input wave observations through a previously given relationship between backscatter intensity and the radial component of the sea surface slope. The algorithm assimilates the wave slope information into the model via a best-fit wave source function at the boundary that minimizes the slope reconstruction error over an annular region at the outer ranges of the radar images. The wave model is then able to propagate the waves across a polar domain to a location of interest at nearer ranges. The constraints on the method for achieving real-time forecasting are identified, and the algorithm is verified against synthetic data and tested using field observations.
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Schaffer, Hemming A., and Ib A. Svendsen. "SURF BEAT GENERATION ON A MILD-SLOPE BEACH." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 79. http://dx.doi.org/10.9753/icce.v21.79.
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Two dimensional generation of surf beats by incident wave groups is examined theoretically. An inhomogeneous wave equation describes the amplitude of the surf beat wave. The forcing function is the modulation of the radiation stress. The short waves are amplitude modulated both outside and inside the surf zone causing the long wave generation to continue right to the shore line. Resonant generation as shallow water is approached is included. The analytical solution is evaluated numerically and shows a highly complicated amplitude variation of the surf beat depending on the parameters of the problem.
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Dong, Jie, Leiping Xue, Kaiyu Cheng, Jian Shi, and Chi Zhang. "An Experimental Investigation of Wave Forces on a Submerged Horizontal Plate over a Simple Slope." Journal of Marine Science and Engineering 8, no. 7 (July 9, 2020): 507. http://dx.doi.org/10.3390/jmse8070507.
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We experimentally investigated the forces induced by monochromatic and solitary waves on a submerged horizontal plate in a wave flume. The experimental results of two-dimensional wave forces on the plate over a 1:10 simple slope and a flat bottom are presented. The effects of the uneven bottom on wave loads are discussed by comparing the results with those in a constant water depth. The measured nonlinear wave forces exhibited considerable discrepancies with the theoretical results from the linear wave theory. The wave forces on the plate induced by monochromatic waves over the simple slope in intermediate water showed no appreciable difference with the flat-bottom results. The solitary wave forces in terms of the downward vertical force and overturning moment significantly decreased in the existence of the simple slope. Furthermore, the dependency of the wave length, wave height and the submergence depth on the wave loads is also discussed.
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Drijfhout, Sybren, and Leo R. M. Maas. "Impact of Channel Geometry and Rotation on the Trapping of Internal Tides." Journal of Physical Oceanography 37, no. 11 (November 1, 2007): 2740–63. http://dx.doi.org/10.1175/2007jpo3586.1.
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Abstract The generation and propagation of internal tides has been studied with an isopycnic three-dimensional ocean model. The response of a uniformly stratified sea in a channel, which is forced by a barotropic tide on its open boundary, is considered. The tide progresses into the channel and forces internal tides over a continental slope at the other end. The channel has a length of 1200 km and a width of 191.25 km. The bottom profile has been varied. In a series of four experiments it is shown how the cross-channel geometry affects the propagation and trapping of internal tides, and the penetration scale of wave energy, away from the continental slope, is discussed. In particular it is found that a cross-channel bottom slope constrains the penetration of the internal tidal energy. Most internal waves refract toward a cross-channel plane where they are trapped. The exception is formed by edge waves that carry part of the energy away from the continental slope. In the case of rotation near the continental slope, the Poincaré waves that arise in the absence of a cross-channel slope no longer bear the characteristics of the wave attractor predicted by 2D theory, but are almost completely arrested, while the right-bound Kelvin wave preserves the 2D attractor in the cross-channel plane, which is present in the nonrotating case. The reflected, barotropic right-bound Kelvin wave acts as a secondary internal wave generator along the cross-channel slope.
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De, Gopa S., Donald F. Winterstein, and Mark A. Meadows. "Comparison of P‐ and S‐wave velocities and Q’S from VSP and sonic log data." GEOPHYSICS 59, no. 10 (October 1994): 1512–29. http://dx.doi.org/10.1190/1.1443541.
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We compared P‐ and S‐wave velocities and quality factors (Q’S) from vertical seismic profiling (VSP) and sonic log measurements in five wells, three from the southwest San Joaquin Basin of California, one from near Laredo, Texas, and one from northern Alberta. Our purpose was to investigate the bias between sonic log and VSP velocities and to examine to what degree this bias might be a consequence of dispersion. VSPs and sonic logs were recorded in the same well in every case. Subsurface formations were predominantly clastic. The bias found was that VSP transit times were greater than sonic log times, consistent with normal dispersion. For the San Joaquin wells, differences in S‐wave transit times averaged 1–2 percent, while differences in P‐wave transit times averaged 6–7 percent. For the Alberta well, the situation was reversed, with differences in S‐wave transit times being about 6 percent, while those for P‐waves were 2.5 percent. For the Texas well, the differences averaged about 4 percent for both P‐ and S‐waves. Drift‐curve slopes for S‐waves tended to be low where the P‐wave slopes were high and vice versa. S‐wave drift‐curve slopes in the shallow California wells were 5–10 μs/ft (16–33 μs/m) and the P‐wave slopes were 15–30 μs/ft (49–98 μs/m). The S‐wave slope in sandstones in the northern Alberta well was up to 50 μs/ft (164 μs/m), while the P‐wave slope was about 5 μs/ft (16 μs/m). In the northern Alberta well the slopes for both P‐ and S‐waves flattened in the carbonate. In the Texas well, both P‐ and S‐wave drifts were comparable. We calculated (Q’s) from a velocity dispersion formula and from spectral ratios. When the two Q’s agreed, we concluded that velocity dispersion resulted solely from absorption. These Q estimation methods were reliable only for Q values smaller than 20. We found that, even with data of generally outstanding quality, Q values determined by standard methods can have large uncertainties, and negative Q’s may be common.
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Meng, Yanqiu, Guoping Chen, and Shichang Yan. "WAVE INTERACTION WITH DECK OF JETTY ON A SLOPE." Coastal Engineering Proceedings 1, no. 32 (January 17, 2011): 21. http://dx.doi.org/10.9753/icce.v32.posters.21.
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Experimental investigations were carried out on wave-induced uplift loads on deck of shore-connecting high pile jetty on a slope in regular waves. A study on effect of gap (between deck end and shore line) on wave impact was also performed. It is found that the maximum uplift loads generally lag behind the maximum impact pressure and are associated with the pressure uniformly distributed along deck. Analysis of the measured data confirms that the distribution length for the uniform pressure is equivalent to wave contact length x. When x is larger than the width of deck B, it is taken as B. The non-dimensional uplift load increases with the increased relative deck clearance Δh/η. The increasing tendency continues up to Δh/η=0.2 and at that location the wave uplift load reaches a peak. After that, the load decreases until at certain deck level the above trend of load start to repeat once more. Generally, two peaks of wave uplift load occur in the range of deck clearance tested. The magnitude of the second wave load peak is larger than the first one. The non-dimensional wave force is observed to increase when the ratio of the wave length to the deck width increase up to a certain ratio. Beyond that ratio the force is less sensitive to the variation of the deck width. It is also found that the force reduces with increase in gap width. This decreasing trend of force is favorable for the design. From the investigation with wide range of input wave and structure parameters, simple predictive equation for wave uplift load was proposed for regular waves.
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Ebrahimi, Ali, Mahdi Behdarvandi Askar, Sadeq Haqiqi Pour, and Vahid Chegini. "Investigation of Various Random Wave Run-up Amounts under the Influence of Different Slopes and Roughnesses." Environment Conservation Journal 16, SE (December 5, 2015): 301–8. http://dx.doi.org/10.36953/ecj.2015.se1635.
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The aim of this study was to investigate the effect of an upstream slope and its roughness on the run-up level of waves. In this study, it was attempted to propose an appropriate and effective solution regarding the issue of wave run-up on seawalls through using a sloping seawall and examining the roughness on these slopes.
The intended slopes for seawalls were 22, 27, 32, 39 degrees, respectively and had the roughness heights on wall surface were 15 cm, 20 cm and 30 cm. Moreover, four types of roughness layouts on the wall surface were investigated. The results, obtained from investigating the effect of slope and roughness on the run-up level of waves, were analyzed after drawing tables and figures. The results show that by increasing slope gradient of the structure, the run-up level also increases, thus, it can be concluded that the run-up level is directly correlated to the structure gradient. The highest run-up level is related to a diagram with a slope of 39 degrees and its lowest level is related to a slope of 22 degrees. Furthermore, the layout type 3 was recognized to be the best layout having the lowest run-up level. The results also revealed that the best and most efficient height for roughness is equal to 30 cm which has the lowest run-up level in all the slopes and layouts. Moreover, the impact of run-up was investigated according to the geometric shapes of layouts on the seawall surface and the results were presented.
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Le, Hai Trung, Jentsje Van der Meer, Gerrit Jan Schiereck, Vu Minh Cat, and Gerben Van der Meer. "WAVE OVERTOPPING SIMULATOR TESTS IN VIET NAM." Coastal Engineering Proceedings 1, no. 32 (January 30, 2011): 2. http://dx.doi.org/10.9753/icce.v32.structures.2.
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Sea dikes in Viet Nam have been built up during a long history. Every year, about 4 to 6 storms attack the coast and cause severe damages of the sea dikes. Till now, little is known about strength and stability of the inner slope covered with grass under impacts of wave overtopping during storm surges. Destructive tests have been performed with the Wave Overtopping Simulator in Viet Nam revealing that grass slopes are able to withstand a certain amount of wave overtopping. In Hai Phong, a slope section covered by Vetiver grass could suffer a maximum wave overtopping discharge of up to 120 l/s per m. In Nam Dinh, three tested locations within a short dike section of 50 m show a large variation in erosion resistance of the Bermuda grass slope with maximum discharge of 20, 40 and 70 l/s per m.
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Liu, Chuanzheng, Gang Wang, and Wei Han. "Effect of Slip Surface’s Continuity on Slope Dynamic Stability Based on Infinite Slope Model." Mathematics 7, no. 1 (January 8, 2019): 58. http://dx.doi.org/10.3390/math7010058.
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The slip surface is an important control structure surface existing in the landslide. It not only directly affects the stability of the slope through the strength, but also affects the stress field by affecting the propagation of the stress wave. Many research results have been made on the influence of non-continuous stress wave propagation in rock and soil mass and the dynamic response to seismic slopes. However, the effect of the continuity of the slip surface on the slope dynamic stability needs further researches. Therefore, in this paper, the effect of slip surface on the slope’s instantaneous safety factor is analyzed by the theoretical method with the infinite slope model. Firstly, three types of slip surface model were established, to realize the change of sliding surface continuity in the infinite slope. Then, based on wave field analysis, the instantaneous safety factor was used to analyze the effect of continuity of slip surface. The results show that with the decreasing of slip surface continuity, the safety factor does not simply increase or decrease, and is related to slope features, incident wave and continuity of slip surface. The safety factor does not decrease monotonically with the increasing of slope angle and thickness of slope body. Moreover, the reflection of slope surface has a great influence on the instantaneous safety factor of the slope. Research results in this paper can provide some references to evaluate the stability of seismic slope, and have an initial understanding of the influence of structural surface continuity on seismic slope engineering.
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Yang, Jia Xuan, Xun Qiang Li, Li Jun Yu, Lei Wang, and Hong Wang. "Surf Shoaling and Breaking on Two-Slope Flume Experiments." Advanced Materials Research 971-973 (June 2014): 760–63. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.760.
Full textAbstract:
A flume experiment is carried out to explore regular waves shoaling and breaking in surf zone. The topography is two-slope model, which is composed of a steep slope 1:5 and a gentle slope 1:40. The incidence waves have heights of 0.05, 0.06, 0.07, 0.08, 0.09 and 0.10 m, and periods of 1.0 sec. In order to describe the wave propagation in surf zone, wave height is collected by wave gauges and wave breaking is recorded by high-speed camera. The results show that, when incidence height is increased, the breaking height increases, while the location of breaking point moves forward. When the incidence height is larger enough, the trend slow down. Besides, secondary breakup is observed in case 0.08, 0.09 and 0.10m. The transient period from primary breakup to secondary breakup is a very important phase. Computing and forecasting methods of surf with complicated topography need further study.
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Sullivan, Peter P., Michael L. Banner, Russel P. Morison, and William L. Peirson. "Turbulent Flow over Steep Steady and Unsteady Waves under Strong Wind Forcing." Journal of Physical Oceanography 48, no. 1 (January 2018): 3–27. http://dx.doi.org/10.1175/jpo-d-17-0118.1.
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AbstractTurbulent flow over strongly forced steep steady and unsteady waves is simulated using large-eddy simulation (LES) with time t and space x varying wave height h(x, t) imposed as a lower boundary condition. With steady waves, h(x, t) is based on measurements of incipient and active breaking waves collected in a wind-wave flume, while a numerical wave code is used to generate an unsteady evolving wave packet (group). Highly intermittent airflow separation is found in the simulations, and the results suggest separation near a wave crest occurs prior to the onset of wave breaking. The form (pressure) drag is most sensitive to the wave slope, and the form drag can contribute as much as 74% to the total stress. Wind and scalar profiles from the LES display log-linear variations above the wave surface; the LES wind profiles are in good agreement with the measurements. The momentum roughness increases as the water surface changes from wind ripples to incipient breaking to active breaking. However, the scalar roughness decreases as the wave surface becomes rougher. This highlights major differences in momentum and scalar transport over a rough wavy surface. For a rapidly evolving, strongly forced wave group, the form drag is highly correlated with the wave slope, and intermittent separation is found early in the packet evolution when the local wave slope −∂h/∂x(x, t) ≥ 0.22. The packet root-mean-square wave slope is 0.084, but the form drag fraction is 2.4 times larger than a comparably forced steady wave. Thus, a passing wave group can induce unsteadiness in the wind stress.
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Hwang, Paul A., Yalin Fan, Francisco J. Ocampo-Torres, and Héctor García-Nava. "Ocean Surface Wave Spectra inside Tropical Cyclones." Journal of Physical Oceanography 47, no. 10 (October 2017): 2393–417. http://dx.doi.org/10.1175/jpo-d-17-0066.1.
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AbstractDirectional wave spectra acquired in hurricane reconnaissance missions are compared with wind-wave spectral models. The comparison result is quantified with two indices of model–measurement spectral agreement. In the main region of hurricane coverage, the indices vary sinusoidally with the azimuth angle referenced to the hurricane heading while showing a weak dependence on the radial distance from the hurricane center. The measured spectra agree well with three models evaluated in the back and right quarters, and they are underdeveloped in the front and left quarters. The local wind and wave directions also show a weak radial dependence and sinusoidal variation along the azimuth. The wind and wave vectors are almost collinear in the back and right quarters; they diverge azimuthally and become almost perpendicular in the left quarter. The azimuthally cyclical correlation between the indices of spectral agreement and the wind-wave directional difference is well described by the sinusoidal variations. Also discussed is the wide range of the spectral slopes observed in both hurricane and nonhurricane field data. It is unlikely that the observed spectral slope variation is caused by Doppler frequency shift from background currents. No clear correlation is found between spectral slope and various wind and wave parameters. The result suggests that the spectral slope needs to be treated as a stochastic random variable. Complementing the existing wind-wave spectral models that prescribe a fixed spectral slope of either −4 or −5, a general spectral model with its spectral parameters accommodating a variable spectral slope is introduced.
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Paroka, Daeng, Andi Haris Muhammad, and Sabaruddin Rahman. "Estimation of Effective Wave Slope Coefficient of Ships with Large Breadth and Draught Ratio." Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan 17, no. 1 (February 26, 2020): 40–49. http://dx.doi.org/10.14710/kapal.v17i1.28399.
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One of parameters to estimate heel angle of a ship in beam seas is effective wave slope coefficient. In the weather criterion of IMO, the effective wave slope coefficient is determined as function of ratio between distance of center of gravity from the sea surface and the ship draught. The others methods could be used to estimate the effective wave slope coefficient are simplified strip theory and model experiment. A ship with shallow draught and large vertical center of gravity can have an effective wave slope coefficient larger than 1.0 if the coefficient is calculated by using the formulae of weather criterion. Therefore, an alternative method to estimate the coefficient is necessary when it is applied to ships with geometry characteristics different with those used to develop the formulae. This research conducts to estimate the effective wave slope coefficient using three different methods, namely the formulae of weather criterion, the simplified strip theory and model experiment. Results of the three methods may provide enough evidence about suitable method to estimate the effective wave slope coefficient of ships with breadth and draught ratio larger than 3.5 like the Indonesian ro-ro ferries. Results and discussion show that the effective wave slope coefficient obtained by using the formulae of weather criterion is larger compared to that obtained by using the simplified strip theory and the model experiment. Here, the result of simplified strip theory for wave frequency the same as the roll natural frequency of subject ship is similar with the result of model experiment. This results show that the simplified strip theory can be used as an alternative method to determine the effective wave slope of a ship with breadth and draught ratio larger than 3.5 if the result of model experiment does not available.