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Published: 4 June 2021
Last updated: 19 February 2023

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1

Hsu, Tai-Wen, Jian-Wu Lai, and Yuan-Jyh Lan. "EXPERIMENTAL AND NUMERICAL STUDIES ON WAVE PROPAGATION OVER COARSE GRAINED SLOPING BEACH." Coastal Engineering Proceedings 1, no. 32 (January 25, 2011): 26. http://dx.doi.org/10.9753/icce.v32.waves.26.

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In this paper, the hydrodynamics and turbulence on wave propagation over coarse grained sloping beach is investigated by both experimental and numerical methods. The coarse grained sloping beach was conducted over a 1:5 smooth inclined bottom with two layers of spherical balls. A set of newly and rarely experimental data for the distribution and evolution of the wave and velocity field over porous sloping beach were measured in this study. The particle image velocimetry (PIV) and digital image process (DIP) techniques are employed to measure the flow field and free surface both inside and outside regions for a coarse grain porous sloping bed. Eleven fields of views (FOVs) were integrated to represent the global results converting the entire propagating waves from the outer to the inner surf zones and swash zones. In addition, a high-resolution CCD Camera was constructed to capture wave propagating images continuously. Subsequent digital image processing (DIP) techniques that including image enhancement, coordinate transformation, edge detection and sub-pixel concept for resolution advancement were developed to analysis the image and get the information of wave motions. In this experimental study, the PIV and DIP techniques offer a possibility for measuring full scale spatio-temporal information of the wave motions and velocity field within / without the porous sloping bed without instructive instrument. Furthermore, the FLOW-3D which based on the Navier-Stokes equations was adopted for CFD computations. The direct three-dimensional simulations were employed for simulating wave profile and velocity field for the sloping beach. Numerical results were favorably compared with experiments to examine the validity of the model. According to the comparison of the wave and velocity data of hydraulic physical model with computational results, the direct three-dimensional simulations method can offer results much agreement with the experimental data in the global regions. The results showed that direct three-dimensional simulations can resolve the wave and velocity profile more complete and reasonable descriptions from outer to the inner porous layer and it is true no matter in the surf zone, swash zone and within the porous layer. Moreover, according to the experimental analysis, the process of the turbulence characteristics of the maximum turbulent kinetic energy, turbulent kinetic energy dissipation rate and turbulence intensity occurred between the toe of breaker and surface of porous layer. In addition, general discussion of hydrodynamics and turbulence on wave propagation over coarse grained sloping beach and impermeable sloping bed were investigated with the results of direct three-dimensional simulations in this study. The results showed that wave propagation over coarse grained sloping beach effects the breaker types in the shallow water, i.e. the steepening and overturning of the front face due to plunging breaker over impermeable sloping beach becomes indistinctively and the breaker type transform into the collapsing type. Besides, the dissipation of wave energy due to the role of infiltration and friction are significant differences from surf zone to swash zone between the coarse grained and impermeable sloping beach.
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2

Constantin, Adrian. "Edge waves along a sloping beach." Journal of Physics A: Mathematical and General 34, no. 45 (November 6, 2001): 9723–31. http://dx.doi.org/10.1088/0305-4470/34/45/311.

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3

EVANS, D. V. "EDGE WAVES OVER A SLOPING BEACH." Quarterly Journal of Mechanics and Applied Mathematics 42, no. 1 (1989): 131–42. http://dx.doi.org/10.1093/qjmam/42.1.131.

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4

Raubenheimer, B., R. T. Guza, Steve Elgar, and N. Kobayashi. "Swash on a gently sloping beach." Journal of Geophysical Research 100, no. C5 (1995): 8751. http://dx.doi.org/10.1029/95jc00232.

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5

Ton, Bui An. "Water waves over a sloping beach." Journal of Mathematical Analysis and Applications 122, no. 2 (March 1987): 555–81. http://dx.doi.org/10.1016/0022-247x(87)90284-8.

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6

Izumiya, Takashi, and Masahiko Isobe. "BREAKING CRITERION ON NON-UNIFORMLY SLOPING BEACH." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 25. http://dx.doi.org/10.9753/icce.v20.25.

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This paper deals with the breaker height on non-uniformly sloping beaches. A large number of experiments were carried out to obtain a breaking criterion on bar and step-type beaches. Based on the experimental data, a relationship among the breaker height, water depth, and wave period is investigated for various bottom configurations. As a result, the breaker height on non-uniformly sloping beaches is found to be well predicted by substituting an equivalent bottom slope in Goda's breaker index which has been obtained for uniformly sloping beaches. The equivalent bottom slope is defined as the mean slope in the distance of 5hg offshoreward from a breaking point, where hg denotes the water depth at the breaking point. The method for calculating the breaker height on natural beaches is also presented.
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7

Billson, Oliver, Paul Russell, and Mark Davidson. "Storm Waves at the Shoreline: When and Where Are Infragravity Waves Important?" Journal of Marine Science and Engineering 7, no. 5 (May 11, 2019): 139. http://dx.doi.org/10.3390/jmse7050139.

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Infragravity waves (frequency, f = 0.005–0.05 Hz) are known to dominate hydrodynamic and sediment transport processes close to the shoreline on low-sloping sandy beaches, especially when incident waves are large. However, in storm wave conditions, how their importance varies on different beach types, and with different mixes of swell and wind-waves is largely unknown. Here, a new dataset, comprising shoreline video observations from five contrasting sites (one low-sloping sandy beach, two steep gravel beaches, and two compound/mixed sand and gravel beaches), under storm wave conditions (deep water wave height, H0 up to 6.6 m, and peak period, Tp up to 18.2 s), was used to assess: how the importance and dominance of infragravity waves varies at the shoreline? In this previously unstudied combination of wave and morphological conditions, significant infragravity swash heights (Sig) at the shoreline in excess of 0.5 m were consistently observed on all five contrasting beaches. The largest infragravity swash heights were observed on a steep gravel beach, followed by the low-sloping sandy beach, and lowest on the compound/mixed sites. Due to contrasting short wave breaking and dissipation processes, infragravity frequencies were observed to be most dominant over gravity frequencies on the low-sloping sandy beach, occasionally dominant on the gravel beaches, and rarely dominant on the compound/mixed beaches. Existing empirical predictive relationships were shown to parameterize Sig skillfully on the sand and gravel beaches separately. Deep water wave power was found to accurately predict Sig on both the sand and gravel beaches, demonstrating that, under storm wave conditions, the wave heights and periods are the main drivers of infragravity oscillations at the shoreline, with the beach morphology playing a secondary role. The exception to this was the compound/mixed beach sites where shoreline infragravity energy remained low.
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8

IFUKU, MAKOTO. "Propagation of long wave on sloping beach." PROCEEDINGS OF COASTAL ENGINEERING, JSCE 36 (1989): 99–103. http://dx.doi.org/10.2208/proce1989.36.99.

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9

Miles, John. "Edge waves on a gently sloping beach." Journal of Fluid Mechanics 199 (February 1989): 125–31. http://dx.doi.org/10.1017/s0022112089000315.

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Edge waves of frequency ω and longshore wavenumber k in water of depth h(y) = h1H(σy/h1), 0 [les ] y < ∞, are calculated through an asymptotic expansion in σ/kh1 on the assumptions that σ [Lt ] 1 and kh1 = O(1). Approximations to the free-surface displacement in an inner domain that includes the singular point at h = 0 and the turning point near gh ≈ ω2/K2 and to the eigenvalue λ ≡ ω2/σgh are obtained for the complete set of modes on the assumption that h(y) is analytic. A uniformly valid approximation for the free-surface displacement and a variational approximation to Λ are obtained for the dominant mode. The results are compared with the shallow-water approximations of Ball (1967) for a slope that decays exponentially from σ to 0 as h increases from 0 to h1 and of Minzoni (1976) for a uniform slope that joins h = 0 to a flat bottom at h = h1 and with the geometrical-optics approximation of Shen, Meyer & Keller (1968).
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10

Miles, John. "Wave reflection from a gently sloping beach." Journal of Fluid Mechanics 214, no. -1 (May 1990): 59. http://dx.doi.org/10.1017/s0022112090000040.

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11

Evans, D. V. "Mechanisms for the generation of edge waves over a sloping beach." Journal of Fluid Mechanics 186 (January 1988): 379–91. http://dx.doi.org/10.1017/s0022112088000199.

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Two mechanisms for the generation of standing edge waves over a sloping beach are described using classical linear water-wave theory. The first is an extension of the result of Yih (1984) to a class of localized bottom protrusions on a sloping beach in the presence of a longshore current. The second is a class of longshore surface-pressure distributions over a beach. In both cases it is shown that Ursell-type standing edge-wave modes can be generated in an appropriate frame of reference. Typical curves of the mode shapes are presented and it is shown how in certain circumstances the dominant mode is not the lowest.
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12

Faraci, Carla, Carmelo Petrotta, Pietro Scandura, Enrico Foti, and Paolo Blondeaux. "THE FLOW OVER ASYMMETRICAL RIPPLES: EXPERIMENTAL INVESTIGATION ON THE MORPHODYNAMIC BEHAVIOR." Coastal Engineering Proceedings, no. 35 (June 23, 2017): 35. http://dx.doi.org/10.9753/icce.v35.sediment.35.

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This paper reports on an experimental campaign focused on the generation and evolution of small scale bedforms over a sloping sandy beach. The wave propagation over a sloping bed triggers a flow asymmetry that reflects on the bedform characteristics. Morphodynamic analyses on ripple evolution and migration led to observe that at the equilibrium the ripples have larger offshore flanks and are leant toward the beach. However migration velocity may be onshore or offshore directed. The equilibrium ripple characteristics seem to be well described by Nielsen (1981) ripple predictor.
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13

Islam, Mohammad Shaiful, Naoki Akita, Tomoaki Nakamura, Yong-Hwan Cho, and Norimi Mizutani. "Experimental Investigation on the Mechanism of Longshore Sediment Transport Using a Circular Wave Basin." Journal of Marine Science and Engineering 10, no. 9 (August 25, 2022): 1189. http://dx.doi.org/10.3390/jmse10091189.

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In this paper, a hydraulic model experiment was conducted to investigate the mechanism of longshore sediment transport on a sloping beach of 1:7 using a circular wave tank equipped with a spiral wave maker. The experimental results revealed that cross-shore sediment transport was predominant up to the formation of equilibrium cross-section. Then the longshore sediment transport was actively dominant near the bar after the development of equilibrium topography. The wave-breaking positions and the characteristics of sand displacement in the vicinity of the wave-breaking zone were observed throughout the installation of fluorescent sands in different cross-sections under several wave conditions on the same terrain to presume the coastal erosion. From the outcomes, it was confirmed that the gradient of the average water level due to the obliquely incident waves breaking and the differences in breaking positions along the shoreline accelerated the generation of longshore currents and longshore sediment transport in the sloping beach profile. Moreover, the actively longshore sediment transport tendency throughout the breaking waves and the longshore current had been confirmed in this study where the gradually increasing wave heights influenced the stronger degree of wave breaking on the sloping beach, which enhanced the sediment transport procedure to deform the beach profile.
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14

Fuentes, Mauricio A., Javier A. Ruiz, and Sebastián Riquelme. "The runup on a multilinear sloping beach model." Geophysical Journal International 201, no. 2 (March 16, 2015): 915–28. http://dx.doi.org/10.1093/gji/ggv056.

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15

Sun, S. M., and M. C. Shen. "Linear water waves over a gently sloping beach." Quarterly of Applied Mathematics 52, no. 2 (June 1, 1994): 243–59. http://dx.doi.org/10.1090/qam/1276236.

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16

Kurkin, Andrey, and Efim Pelinovsky. "Focusing of edge waves above a sloping beach." European Journal of Mechanics - B/Fluids 21, no. 5 (September 2002): 561–77. http://dx.doi.org/10.1016/s0997-7546(02)01201-3.

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17

Ionescu-Kruse, Delia. "Instability of edge waves along a sloping beach." Journal of Differential Equations 256, no. 12 (June 2014): 3999–4012. http://dx.doi.org/10.1016/j.jde.2014.03.009.

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18

Muzylev, Sergey V., Sergey N. Bulgakov, and Matias Duran-Matute. "Edge capillary-gravity waves on a sloping beach." Physics of Fluids 17, no. 4 (April 2005): 048103. http://dx.doi.org/10.1063/1.1879052.

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19

Gelb, Anne, David Gottlieb, and Nathan Paldor. "Wind Set-down Relaxation on a Sloping Beach." Journal of Computational Physics 138, no. 2 (December 1997): 644–64. http://dx.doi.org/10.1006/jcph.1997.5837.

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20

Jeffrey, Alan, and Armando Majorana. "Finite amplitude water waves above a sloping beach." Wave Motion 7, no. 3 (May 1985): 229–33. http://dx.doi.org/10.1016/0165-2125(85)90008-3.

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21

Budaev, B. V. "Scattering of acoustic waves on a sloping beach." Journal of Mathematical Sciences 83, no. 2 (January 1997): 198–203. http://dx.doi.org/10.1007/bf02405813.

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22

Chang, Y. C., D. S. Jeng, and H. D. Yeh. "Tidal propagation in an oceanic island with sloping beaches." Hydrology and Earth System Sciences Discussions 7, no. 1 (February 22, 2010): 1407–30. http://dx.doi.org/10.5194/hessd-7-1407-2010.

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Abstract. In this study, a new analytical solution for describing the tide-induced groundwater fluctuations in oceanic islands with finite length and different slopes of the beaches is developed. Unlike previous solutions, the present solution is not only applicable for a semi-infinite coastal aquifer, but also for an oceanic island with finite length and different sloping beaches. The solution can be used to investigate the effect of higher-order components and beach slopes on the water table fluctuations. The results demonstrate the effect of higher-order components increases with the shallow water parameter or amplitude parameter and the water table level increases as beach slopes decrease.
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23

Chang, Y. C., D. S. Jeng, and H. D. Yeh. "Tidal propagation in an oceanic island with sloping beaches." Hydrology and Earth System Sciences 14, no. 7 (July 26, 2010): 1341–51. http://dx.doi.org/10.5194/hess-14-1341-2010.

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Abstract. In this study, a new analytical solution for describing the tide-induced groundwater fluctuations in oceanic islands with finite length and different slopes of the beaches is developed. Unlike previous solutions, the present solution is not only applicable for a semi-infinite coastal aquifer, but also for an oceanic island with finite length and different sloping beaches. The solution can be used to investigate the effect of higher-order components and beach slopes on the water table fluctuations. The results demonstrate the effect of higher-order components increases with the shallow water parameter or amplitude parameter and the water table level increases as beach slopes decrease.
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24

Ghazali, A., and Harry H. Yeh. "NEARSHORE BEHAVIOR OF BORE ON A UNIFORMLY SLOPING BEACH." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 66. http://dx.doi.org/10.9753/icce.v20.66.

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Using the laser-induced fluorescent method, the detailed transition process from bore to run-up mode is clarified experimentally. The transition process is found to be different from the previous predictions, and might provide an explanation for the discrepancies of the run-up height between the theory and laboratory measurements. Turbulence generated in a bore appears to be highly three-dimensional and sporadic. Turbulence generated close to the shore is advected with the bore-front motion and violent turbulent actions result during the transition from bore to run-up mode.
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25

Pramanik, A. K., and S. R. Majumdar. "Transient Development of Gravity Waves on a Sloping Beach." SIAM Journal on Applied Mathematics 45, no. 6 (December 1985): 928–42. http://dx.doi.org/10.1137/0145056.

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26

Zhevandrov, Peter. "Edge waves on a gently sloping beach: uniform asymptotics." Journal of Fluid Mechanics 233 (December 1991): 483–93. http://dx.doi.org/10.1017/s0022112091000563.

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Edge waves on a beach of gentle slope ε [Lt ] 1 are considered. For constant slope, Ursell (1952) has obtained a complete set of trapped modes and shown that there exists only a finite number n of such modes, (2n + 1)β < ½π, β = tan−1ε. For non-uniform slope the formulae for the trapped-mode frequencies were heuristically derived by Shen, Meyer & Keller (1968). For small n ∼ O(1) Miles (1989) has obtained formulae which coincide with Shen et al.'s (1968) with accuracy to O(ε) and differ from them by O(ε2). However, Miles’ formulae fail at n ∼ 1/ε. In this paper it is proved that Shen et al.'s (1968) formulae are valid for all n (including n ∼ 1/ε) with accuracy to O(ε) and corrections of any order in ε are given. Uniform asymptotic expansions are obtained for the corresponding eigenfunctions. These expansions give Miles’ (1989) result for small n. The formulae for the frequencies and the eigenfunctions have the same structure for both the full dispersion system and the shallow-water equation. For small n the frequencies for both models coincide with accuracy to O(ε2), but for n ∼ 1/ε they differ by O(1). In the last section the effect of rotation following Evans (1989) is taken into account. All the asymptotics have formal character, i.e. they satisfy the corresponding equations with accuracy to O(εN), N being arbitrarily large. The rigorous justification of these asymptotics is under way.
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27

Blondeaux, Paolo, Maurizio Brocchini, and Giovanna Vittori. "Sea waves and mass transport on a sloping beach." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, no. 2025 (September 8, 2002): 2053–82. http://dx.doi.org/10.1098/rspa.2001.0958.

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28

Purnama, Anton. "Effluent Discharges from Two Outfalls on a Sloping Beach." Applied Mathematics 05, no. 19 (2014): 3117–26. http://dx.doi.org/10.4236/am.2014.519295.

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29

Scandura, Pietro, Enrico Foti, and Carla Faraci. "Mass transport under standing waves over a sloping beach." Journal of Fluid Mechanics 701 (May 14, 2012): 460–72. http://dx.doi.org/10.1017/jfm.2012.181.

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AbstractThis paper deals with the mass transport induced by sea waves propagating over a sloping beach and fully reflected from a wall. It is shown that for moderate slopes the classical recirculation cell structure holds for small Reynolds numbers only. When the Reynolds number is large, the cells interact among themselves giving rise to the merging of the negative cells and the confinement of the positive ones near the bottom. Under such circumstances the fluid moves onshore near the bottom and offshore near the free surface. The seaward decrease of the vorticity produced at the bottom appears to be the reason for the merging phenomenon.
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30

García‐Medina, Gabriel, H. Tuba Özkan‐Haller, Rob A. Holman, and Peter Ruggiero. "Large runup controls on a gently sloping dissipative beach." Journal of Geophysical Research: Oceans 122, no. 7 (July 2017): 5998–6010. http://dx.doi.org/10.1002/2017jc012862.

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31

Vousdoukas, Michalis I., Luis Pedro M. Almeida, and Óscar Ferreira. "Beach erosion and recovery during consecutive storms at a steep-sloping, meso-tidal beach." Earth Surface Processes and Landforms 37, no. 6 (December 7, 2011): 583–93. http://dx.doi.org/10.1002/esp.2264.

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32

Putra, Aprizon, and Try Al Tanto. "The Suitability Ecotourism Beach Based Geopasial in Padang City, Indonesia." Sumatra Journal of Disaster, Geography and Geography Education 1, no. 1 (June 6, 2017): 83. http://dx.doi.org/10.24036/sjdgge.v1i1.40.

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Padang city has a coastline 80.24 km with a water area 72,000 ha, and 19 small islands. Overall, coastal in Padang consists of beach sloping 41.52 km, cliff 22.08 km, muddy 8.19 km, and type of artificial beach in form of building coastal protection. Research aims for identify suitability for ecotourism beach (category of recreation beach and mangrove). Methodology used ie with matrix of suitability ecotourism beach using geospatial approach. Research results for suitability category recreation beach in 24 locations in beach Padang 18 locations are in category of very suitable with a value 82.28 % and only beach in Bung Hatta University are in category conditional with a value 27 %. Suitability category ecotourism mangrove in 19 locations in beach Padang 6 location is in a category is in accordance with a value 92.11 % and 4 location is in a category conditional/not suitable to value 50.88 %.
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33

Faraci, Carla, Pietro Scandura, Carmelo Petrotta, and Enrico Foti. "Wave-Induced Oscillatory Flow Over a Sloping Rippled Bed." Water 11, no. 8 (August 5, 2019): 1618. http://dx.doi.org/10.3390/w11081618.

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In this paper, the findings of an experimental analysis aimed at investigating the flow generated by waves propagating over a fixed rippled bed within a wave flume are reported. The bottom of the wave flume was constituted by horizontal part followed by a 1:10 sloping beach. Bedforms were generated in a previous campaign performed with loose sand, and then hardened by means of thin layers of concrete. The flow was acquired through a Vectrino Profiler along two different ripples, one located in the horizontal part of the bed and the second over the sloping beach. It was observed that, on the horizontal bed, near the bottom, ripple lee side triggered the appearance of an onshore directed steady streaming, whereas ripple stoss side gave rise to an offshore directed steady streaming. On the sloping bed, a strong return current appears at all positions, interacting with the rippled bottom. The turbulence is non-negligible within the investigated water depth, particularly when velocities were onshore directed, due to flow asymmetry. Turbulence caused a considerable flow stirring which, above a non-cohesive bed, could lift the sediment up in the water column and give rise to a strong sediment transport.
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34

Vousdoukas, M. I. "Erosion/accretion patterns and multiple beach cusp systems on a meso-tidal, steeply-sloping beach." Geomorphology 141-142 (March 2012): 34–46. http://dx.doi.org/10.1016/j.geomorph.2011.12.003.

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35

Salauddin, M., and J. M. Pearson. "Experimental Study on Toe Scouring at Sloping Walls with Gravel Foreshores." Journal of Marine Science and Engineering 7, no. 7 (June 27, 2019): 198. http://dx.doi.org/10.3390/jmse7070198.

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Sea defences, such as urban seawalls can fail due to the development of a scour hole at the toe of the structure. The scour depth or the information on ground levels at the structure toe is required for the sustainable management of coastal defences, due to its influence on the structural performance. This research reports and summarises the main findings of a new laboratory study on toe scouring at a smooth sloping wall with permeable gravel foreshore. A set of small-scale laboratory experiments of wave-induced scouring at sloping seawalls were conducted. Two gravel sediments of prototype d50 values of 13 mm and 24 mm were used to simulate the permeable 1:20 (V:H) gravel beach configurations in the front of a smooth 1 in 2 sloping wall. Each experiment comprised of a sequence of around 1000 random waves of a JONSWAP energy spectrum with a peak enhancement factor of 3.3. The relationship of the scour depth with toe water depth, Iribarren number, and wall slope were investigated from the test results of this work and through a comparison with available datasets in the literature. The results of this study showed that the relative toe water depth and Iribarren number influence the relative toe scour depth at a sloping structure on a shingle beach. Within the experimental limitations, the maximum toe scour depths were observed for the experiments under spilling and plunging wave attack.
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36

Islam, Mohammad Shaiful, Tomoaki Nakamura, Yong-Hwan Cho, and Norimi Mizutani. "Investigation of the Spiral Wave Generation and Propagation on a Numerical Circular Wave Tank Model." Journal of Marine Science and Engineering 11, no. 2 (February 9, 2023): 388. http://dx.doi.org/10.3390/jmse11020388.

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A two-phase incompressible flow model in three-dimensional cylindrical coordinates is applied for oblique wave generation in a numerical circular wave tank. The governing equations are discretized by a finite volume method, and a mass source function is added to reproduce oblique waves through a spiral wave generator positioned at the center of the tank. The volume of fluid method is implemented to track the free surfaces between the air and fluid, and the zonal embedded grid system is adopted to obtain a grid-independent solution in the cylindrical coordinates. A permeable, circumferentially sloping topography (1:7), similar to a natural beach profile, is set up for investigating wave propagation and other characteristics. The simulation and physical experimental results are compared, which show a good agreement in randomly selected water surface elevation profiles and wave heights under the same wave and sloping conditions. The spiral waves are reproduced and propagated in a phenomenon similar to that observed in the physical experiment. The results also show that the wave-breaking positions differ in different wave conditions and suggest a relationship with cross-shore and longshore velocity distribution in terms of incident wave heights and wave-breaking positions in different wave periods on the same sloping topography. Furthermore, this model can be used to investigate the mechanism of longshore current generation and the influences of beach slope on the generated wave propagation in a sloping topography.
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37

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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38

Al-Barwani, H. H., and Anton Purnama. "Analytical solutions for brine discharge plumes on a sloping beach." Desalination and Water Treatment 11, no. 1-3 (November 2009): 2–6. http://dx.doi.org/10.5004/dwt.2009.835.

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39

STUHLMEIER, RAPHAEL. "ON EDGE WAVES IN STRATIFIED WATER ALONG A SLOPING BEACH." Journal of Nonlinear Mathematical Physics 18, no. 1 (January 2011): 127–37. http://dx.doi.org/10.1142/s1402925111001210.

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40

Matsutomi, Hideo. "On the Propagation of a Bore Over a Sloping Beach." Coastal Engineering in Japan 28, no. 1 (December 1985): 45–58. http://dx.doi.org/10.1080/05785634.1985.11924404.

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41

LIU, PHILIP L. F., PATRICK LYNETT, and COSTAS E. SYNOLAKIS. "Analytical solutions for forced long waves on a sloping beach." Journal of Fluid Mechanics 478 (March 10, 2003): 101–9. http://dx.doi.org/10.1017/s0022112002003385.

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We derive analytic solutions for the forced linear shallow water equation of the following form:<?TeX \partial^2 Y \over \partial t^2}-b{\partial \over \partial x}\left(x {\partial Y \over \partial x}\right)={\partial^2 f\over \partial t^2 ?>for x>0, in which Y(x,t) denotes an unknown variable, f(x,t) a prescribed forcing function and b a positive constant. This equation has been used to describe landslide-generated tsunamis and also long waves induced by moving atmospheric pressure distributions. We discuss particular and general solutions. We then compare our results with numerical solutions of the same equation and with the corresponding solutions of the nonlinear depth-integrated equations and discuss them in terms of landslide-generated tsunamis.
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42

PACKHAM, B. A. "A NOTE ON GENERALIZED EDGE WAVES ON A SLOPING BEACH." Quarterly Journal of Mechanics and Applied Mathematics 42, no. 3 (1989): 441–46. http://dx.doi.org/10.1093/qjmam/42.3.441.

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43

de Bakker, A. T. M., T. H. C. Herbers, P. B. Smit, M. F. S. Tissier, and B. G. Ruessink. "Nonlinear Infragravity–Wave Interactions on a Gently Sloping Laboratory Beach." Journal of Physical Oceanography 45, no. 2 (February 2015): 589–605. http://dx.doi.org/10.1175/jpo-d-14-0186.1.

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AbstractA high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy transfers to investigate energy flows within the spectra. Energy flows are identified by dividing transfers into four types of triad interactions, with triads including one, two, or three infragravity–frequency components, and triad interactions solely between short-wave frequencies. In the shoaling zone, the energy transfers are generally from the spectral peak to its higher harmonics and to infragravity frequencies. While receiving net energy, infragravity waves participate in interactions that spread energy of the short-wave peaks to adjacent frequencies, thereby creating a broader energy spectrum. In the short-wave surf zone, infragravity–infragravity interactions develop, and close to shore, they dominate the interactions. Nonlinear energy fluxes are compared to gradients in total energy flux and are observed to balance nearly completely. Overall, energy losses at both infragravity and short-wave frequencies can largely be explained by a cascade of nonlinear energy transfers to high frequencies (say, f > 1.5 Hz) where the energy is presumably dissipated. Infragravity–infragravity interactions seem to induce higher harmonics that allow for shape transformation of the infragravity wave to asymmetric. The largest decrease in infragravity wave height occurs close to the shore, where infragravity–infragravity interactions dominate and where the infragravity wave is asymmetric, suggesting wave breaking to be the dominant mechanism of infragravity wave dissipation.
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44

Akyildiz, Yilmaz. "Conservation laws for shallow water waves on a sloping beach." International Journal of Mathematics and Mathematical Sciences 9, no. 2 (1986): 387–96. http://dx.doi.org/10.1155/s0161171286000480.

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Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane.
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45

Akylas, T. R., and S. Knopping. "The evolution of subharmonic edge wavepackets on a sloping beach." Wave Motion 8, no. 5 (September 1986): 399–405. http://dx.doi.org/10.1016/0165-2125(86)90026-0.

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46

Seo, Seung-Nam, and Philip L. F. Liu. "Edge waves generated by the landslide on a sloping beach." Coastal Engineering 73 (March 2013): 133–50. http://dx.doi.org/10.1016/j.coastaleng.2012.10.008.

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47

Zhang, Mingliang, Yongpeng Ji, Yini Wang, Hongxing Zhang, and Tianping Xu. "Numerical investigation on tsunami wave mitigation on forest sloping beach." Acta Oceanologica Sinica 39, no. 1 (January 2020): 130–40. http://dx.doi.org/10.1007/s13131-019-1527-y.

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48

Sapsuha, Isman, Royke M. Rampengan, Esry T. Opa, Hermanto K. Manengkey, Wilmy K. Pelle, and Ferdinand F. Tilaar. "KEMIRINGAN LERENG DAN GRANULOMETRI SEDIMEN GISIK TANJUNG MERAH, BITUNG SULAWESI UTARA." JURNAL PESISIR DAN LAUT TROPIS 7, no. 2 (July 17, 2019): 90. http://dx.doi.org/10.35800/jplt.7.2.2019.24197.

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Beach slope and sediment granulometry is one of the importat aspect in coastal management. Beach offers a variety of functions and potential to be utilized. In the interests of phisical use in the beach, coastal structure in the form of groynes has been built. Actually, the groin has been used as a dock. This research was conducted with the aim of revealing the slope and granulometry sediment in Tanjung Merah beach. The results obtained, the beach slope is considered sloping and very sloping, the composition of the sediment consists mainly of medium sand, fine sand and very fine sand. Sediment distribution analysis obtained results, the main grain size was mainly in the form of medium sand, sorting was mainly classified as poor, skewness was mostly asymmetrie strong to large size, most curtosis was mesokurtic. The results of the study indicate the occurrence of the process of erosion and deposition ia certain spaces on the beach studied.Keywords: Tanjung Merah, beach slope, sediment granulometryKemiringan lereng dan granulometri sedimen gisik merupakan salah satu aspek penting dalam pengelolaan pantai. Gisik menawarkan beragam fungsi dan potensi untuk dimanfaatkan. Dalam kepentingan pemanfaatan lahan gisik, berbagai modifikasi dilakukan oleh manusia. Pada gisik di Tanjung Merah, telah dibangun struktur pantai berupa groin. Secara aktual, groin tersebut telah difunsikan sebagai dermaga. Penelitian ini dilakukan dengan tujuan mengungkapkan kemiringan dan granulometri sedimen di gisik Tanjung Merah. Hasil penelitian yang diperoleh, lereng gisik terkriteria miring dan sangat miring, komposisi sedimen terutama terdiri dari pasir sedang, pasir halus, dan pasir sangat halus. Analisis distribusi memperoleh hasil, rataan empirik terutama berupa pasir sedang, penyortiran terutama terklasifikasi buruk, kemencengan terbanyak berupa asimetris kuat ke ukuran besar, peruncingan terbanyak berupa mesokurtik. Hasil studi mengindikasikan terjadi proses erosi dan deposisi pada ruang-ruang tertentu di gisik yang ditelaah.Kata kunci : Tanjung Merah, kemiringan lereng, granulometri sedimen
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49

Ginting, M. A., S. R. Pudjaprasetya, and D. Adytia. "Two-Layer Non-Hydrostatic Scheme for Simulations of Wave Runup." Journal of Earthquake and Tsunami 13, no. 05n06 (September 26, 2019): 1941004. http://dx.doi.org/10.1142/s1793431119410045.

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There are indisputable research supporting scientific argument that propagation of (tsunami) wave from intermediate depth towards shallower coastal area needs dispersive wave model. For tsunami wave simulation, efficiency of the numerical scheme is an important issue. In this paper, the two-layer non-hydrostatic model as developed previously in Pudjaprasetya et al. [2017] “A non-hydrostatic two-layer staggered scheme for transient waves due to anti-symmetric seabed thrust,” J. Earthquake Tsunami 11, 1–17, to study tsunami generation and propagation, is adopted. Restricting to 1+1 dimension, here, we focus on the performance of the scheme in simulating wave propagation in coastal areas, in particular predicting the run-up height. First, we conducted a simulation of harmonic wave over a sloping beach to conform the analytical shoreline motion by Carrier and Greenspan [1958] “Water waves of finite amplitude on a sloping beach,” J. Fluid Mech. 4, 97–109. The ability of the scheme in accommodating dispersion and non-linearity were shown via simulation of a solitary wave that propagates over a flat bottom. This solitary wave simulation provides an evaluation of the convergence aspect of the model. Further, several benchmark tests were conducted; a solitary wave over a sloping beach to mimic the experimental data by Synolakis [1986] “The run-up of solitary waves,” J. Fluid Mech. 185, 523–545, as well as solitary wave over a composite beach. Good agreement with laboratory data was obtained in terms of wave signal, whereas for relatively low amplitude, the solitary run-up height conforms the analytical formula. Moreover, the scheme is tested for simulating the Beji–Battjes experiment Beji, S. and Battjes, J. A. [1993] “Experimental investigation of wave propagation over a bar,” Coast. Eng. 19, 151–162. As well as wave focusing experiment by Kurnia et al. [2015] “Simulations for design and reconstruction of breaking waves in a wavetank,” Proc. ASME 2015 34th Int. Conf. Ocean, Offshore and Arctic Engineering, Newfoundland, Canada, 31 May–5 June 2015, pp. 2–7.
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50

Ostrovsky, Lev A., and Karl R. Helfrich. "Some New Aspects of the Joint Effect of Rotation and Topography on Internal Solitary Waves." Journal of Physical Oceanography 49, no. 6 (June 2019): 1639–49. http://dx.doi.org/10.1175/jpo-d-18-0154.1.

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AbstractUsing a recently developed asymptotic theory of internal solitary wave propagation over a sloping bottom in a rotating ocean, some new qualitative and quantitative features of this process are analyzed for internal waves in a two-layer ocean. The interplay between different singularities—terminal damping due to radiation and disappearing quadratic nonlinearity, and reaching an “internal beach” (e.g., zero lower-layer depth)—is discussed. Examples of the adiabatic evolution of a single solitary wave over a uniformly sloping bottom under realistic conditions are considered in more detail and compared with numerical solutions of the variable-coefficient, rotation-modified Korteweg–de Vries (rKdV) equation.
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