{"title":"Wave attenuation by cultivated seaweeds: A linearized analytical model","authors":"Zhilong Wei , Morgane Weiss , Trygve Kristiansen , David Kristiansen , Yanlin Shao","doi":"10.1016/j.coastaleng.2024.104642","DOIUrl":"10.1016/j.coastaleng.2024.104642","url":null,"abstract":"<div><div>An analytical framework is presented to describe the attenuation of regular and irregular waves propagating over floating seaweed farms. Kelp blades suspended on longlines are modelled, as a first approximation, as rigid bars rotating around their upper ends. Assuming small-amplitude blade motions under low to moderate sea conditions, the frequency-dependent transfer function of the rotations can be obtained, with quadratic drag loads linearized. Subsequently, the hydrodynamic problem with regular waves propagating over suspended seaweed canopies is formulated using the continuity equation and linearized momentum equations with additional source terms in the vegetation region. Analytical solutions are obtained for attenuated regular waves with their heights decaying exponentially as they propagate over the canopy. These solutions are utilized as the basis for predicting wave attenuation of irregular waves while stochastic linearization of the quadratic drag loads is employed. In contrast to energy-conservation-based models, which assume the velocity profile follows linear wave theory, the present solution can predict the reduced velocity inside the canopy. The analytical solutions are validated against experimental data and verified against a numerical flow solver. The model is capable of resolving the wave attenuation, along with velocity profiles and phase lag. Drag and inertial force exhibit cancellation effects on wave decay and both affect phase lag.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104642"},"PeriodicalIF":4.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-26DOI: 10.1016/j.coastaleng.2024.104646
Thomas A.G. Smyth , Thomas Pagon , Ian J. Walker
{"title":"Exploring wind flow dynamics in foredune notches using Computational Fluid Dynamics (CFD)","authors":"Thomas A.G. Smyth , Thomas Pagon , Ian J. Walker","doi":"10.1016/j.coastaleng.2024.104646","DOIUrl":"10.1016/j.coastaleng.2024.104646","url":null,"abstract":"<div><div>Coastal dunes offer a wide range of valuable ecosystem services such as protection from erosion, flooding, sea-level rise, and provision of specialised habitat for endangered, endemic, or migratory species. Foredune blowouts and landward migrating parabolic dunes play an important role in many coastal dune settings creating ecological heterogeneity associated with inland sand transport, nutrient supply, and geomorphic disturbance processes. However, as coastal dunes globally are being increasingly stabilised by vegetation and declining in their ecological resilience and functionality, anthropogenic interventions, such as the removal of invasive species and excavation of foredune notches, have emerged to simulate and restore critical aeolian processes required to maintain dune morphodynamics and onshore sediment transport between the beach and inland dunes. This study employed computational fluid dynamics (CFD) modelling to investigate key controls on the wind flow dynamics and sand transport potential within idealised foredune notches of varying widths, slopes, and planform shape (rectangular vs. trapezoidal) for perpendicular and oblique incident wind directions. Compared with empirical findings from similarly engineered notches, our results show that notch width significantly influences shear velocity in the excavated notch ‘slot’, with narrower notches (25 m wide) enhancing wind flow acceleration and inland sediment transport potential. Spatial patterns of shear velocity throughout notches were also sensitive to incident wind direction, with maximum shear velocities, and consequent inland sand transport potential, occurring when winds were parallel to the orientation of the notch. On the lobes of the notches, shear velocity and sand transport potential were greatest during oblique winds. Our results suggest that a relatively narrow notch (e.g. 25 m as opposed to 50 m or 100 m), aligned with the prevailing wind direction, creates the most favourable conditions for transporting sediment from the beach to the dune behind. These findings underscore the importance of notch design in coastal dune restoration, offering critical insights for optimising interventions aimed at sustaining aeolian sediment transport from the beach to the hinterdune.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104646"},"PeriodicalIF":4.2,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-25DOI: 10.1016/j.coastaleng.2024.104648
Filipe Miranda , Diogo Mendes , José Miguel Castro , Paulo Rosa-Santos , Francisco Taveira-Pinto , Tiago Fazeres-Ferradosa
{"title":"Physical modelling study on wave damping induced by an idealized floating kelp farm","authors":"Filipe Miranda , Diogo Mendes , José Miguel Castro , Paulo Rosa-Santos , Francisco Taveira-Pinto , Tiago Fazeres-Ferradosa","doi":"10.1016/j.coastaleng.2024.104648","DOIUrl":"10.1016/j.coastaleng.2024.104648","url":null,"abstract":"<div><div>A physical modelling study was carried out to investigate random wave damping promoted by an idealized floating kelp farm. The experimental conditions spanned intermediate water depths and both linear and nonlinear water waves. Unlike previous studies of wave damping promoted by vegetation, the floating kelp farm was placed close to the water surface with a ratio between vegetation height and water depth close to 0.25. The wave transmission coefficient induced by the floating kelp farm ranged between 0.56 and 0.96. This coefficient decreased for longer floating kelp farms and it was a function of the ratio between kelp farm length and incident wavelength and of the relative wave depth. Spectral analysis showed that wave damping was not frequency-dependent for wave frequencies close to the peak frequency. The wave transmission coefficients of a floating kelp farm with about 100 culture lines and with an extension of approximately 200 m were similar to those of submerged detached breakwaters with a relative crest freeboard smaller than −0.4. Furthermore, the bulk drag coefficient of near-surface idealized floating kelp farms can be modelled as a function of the Keulegan-Carpenter number. This study highlights the potential viability of nature-based solutions such as floating kelp farms for coastal protection.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104648"},"PeriodicalIF":4.2,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-24DOI: 10.1016/j.coastaleng.2024.104647
Wen Deng , Tania Kenyon , Karen Eigeland , David P. Callaghan , Tom E. Baldock
{"title":"Structural and hydrodynamic modelling of the probability of breakage of branching and plate coral colonies","authors":"Wen Deng , Tania Kenyon , Karen Eigeland , David P. Callaghan , Tom E. Baldock","doi":"10.1016/j.coastaleng.2024.104647","DOIUrl":"10.1016/j.coastaleng.2024.104647","url":null,"abstract":"<div><div>Climate change is amplifying the intensity of severe weather events, with coastal regions such as coral reefs facing heightened vulnerability to cyclonic wave forces. Structural models to predict bending stress and breakage of corals have been developed for coral colonies to enhance comprehension and prediction of the effects of hydrodynamic disturbances on coral reefs. However, there is scope for improving these predictions by evolving the methodology for quantifying complicated and variable coral morphologies. This study aims to predict breakage thresholds for two of the most prevalent coral morphologies: branching and plate corals (using <em>Acropora muricata</em> and <em>Acropora hyacinthus</em> as study species). Laboratory and field measurements were taken to assess coral morphologies and material characteristics. Morphological features of 47 branching colonies and 100 plate colonies were surveyed at the study site (Heron Reef, southern GBR) and the tensile strength of 80 coral samples was obtained by <em>in situ</em> and laboratory testing. Three-dimensional structural models of branching and plate coral colonies were developed, encompassing multiple coral colonies with varying morphological patterns from relatively shallow (5–7 m) to deep (9–12 m) zones. Model results were calibrated and verified with existing data, revealing that velocity thresholds of 1.7 m/s and 5.0 m/s would destroy 90% of the simulated branching coral structures growing in the deep and shallow parts of the forereef zone, respectively. In contrast, the plate corals have sufficient margins of safety even in extreme flow conditions (7 m/s). Additionally, skeletal strength and structural performance were adjusted based on varying degrees of bioerosion inside the coral skeleton. A higher probability of breakage was observed as the extent of bioerosion increased. The laboratory experiments of hydrodynamic loads on coral colony show that the sheltering effect due to one or two neighbouring colonies in the upwave direction is negligible. These models can be easily adjusted to provide predictions for other coral species, shapes, levels of bioerosion, and locations (e.g., sheltered or exposed areas). Comprehensive predictions about the level of expected damage and rubble generation in different areas can be used in reef management planning and restoration prioritization.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104647"},"PeriodicalIF":4.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-23DOI: 10.1016/j.coastaleng.2024.104644
S.P. Viaña-Borja , R. González-Villanueva , I. Alejo , R.P. Stumpf , G. Navarro , I. Caballero
{"title":"Satellite-derived bathymetry using Sentinel-2 in mesotidal coasts","authors":"S.P. Viaña-Borja , R. González-Villanueva , I. Alejo , R.P. Stumpf , G. Navarro , I. Caballero","doi":"10.1016/j.coastaleng.2024.104644","DOIUrl":"10.1016/j.coastaleng.2024.104644","url":null,"abstract":"<div><div>Coastal zones are strategic environments of high socioeconomic, political, and ecological value, with over half of the world's population residing within 200 km of the coast. This proximity highlights their vulnerability to extreme events, which are exacerbated by global changes, leading to significant coastal impacts such as erosion, flooding, and ecosystem services deterioration. Consequently, efficient and operational methodologies for continuous monitoring are urgently needed to face these challenges. Bathymetric data are essential for understanding coastal dynamics, yet traditional data collection methods are often constrained by logistical challenges and high costs. Spaceborne remote sensing techniques offer significant advantages over traditional ground-based methods, particularly in terms of cost-effectiveness and operational efficiency. Over the last half-century, different Satellite-derived bathymetry (SDB) methodologies have been developed; however, challenges still persist. In this research, we applied a robust SDB methodology to three different study sites: Cíes Islands, Baiona Bay, and Vao beach within the Ría de Vigo, Galicia (NW Spain). These areas offer diverse and complex mesotidal environments to test for the very first time the methodology's efficacy. SDB was retrieved with a median absolute error (MedAE) ranging from 0.35 m to 1.55 m for depths up to 14 m. Results with different data source were evaluated, obtaining MedAE for nautical charts ranging from 0.46 m to 1.55 m. The precision between the data sources were quite close. In addition, multi-image composite was generated using images coinciding with both low tide (LT) and high tide (HT) conditions across the three zones. The lowest MedAE values were consistently obtained in images classified as LT (0.46 m) corresponding to Vao area. The results highlight the potential of nautical charts as a reliable source of calibration data for SDB, confirm the effectiveness of multi-image and switching models to correct artifacts and turbidity, considering tidal effects, improving single image approaches, and leverage visible bands for precise depth retrieval under varying conditions.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104644"},"PeriodicalIF":4.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-23DOI: 10.1016/j.coastaleng.2024.104643
Shouqian Li , Shihuan Zhou , Yongjun Lu , Rui Hu , Wei Huang , J.A. Roelvink
{"title":"Experiment study on vortex evolution process and vorticity distribution in wave boundary layer flow over a rippled bed","authors":"Shouqian Li , Shihuan Zhou , Yongjun Lu , Rui Hu , Wei Huang , J.A. Roelvink","doi":"10.1016/j.coastaleng.2024.104643","DOIUrl":"10.1016/j.coastaleng.2024.104643","url":null,"abstract":"<div><div>Vortex over rippled bed acts as the main driving force for sediment transport under wave dynamics. Hydrodynamic experiments are carried out under matching conditions of wave dynamics and bed ripples, to reveal the vortex evolution process and vorticity distribution. The results indicate that the vortex body around the ripples experiences the evolution process of clockwise vortex formation, clockwise vortex detachment and dissipation, counterclockwise vortex formation, and counterclockwise vortex detachment and dissipation. Moreover, the vorticity at the ripple crest is proportional to <em>U</em><sub>w,rms</sub>/<em>λ</em> and <em>η</em>/<em>λ</em>, where <em>U</em><sub>w,rms</sub> represents the bottom velocity under wave action, <em>λ</em> represents the ripple length and <em>η</em> represents the ripple height. The vertical distribution of dimensionless vorticity depends on <em>η</em>. As <em>η</em> grows, the vorticity increases in the upper part and the vertical distribution of dimensionless vorticity becomes uniform. The circulation of the vortices is proportional to <em>U</em><sub>w,rms</sub> and <em>η</em>. The proposed expression for the vorticity at ripple crest, dimensionless vertical distribution of vorticity and circulation of the vortices all agrees well with the measured values. These findings lay the foundation for the study of the bottom sediment concentration.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104643"},"PeriodicalIF":4.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-11DOI: 10.1016/j.coastaleng.2024.104630
Bing Tai , Yuxiang Ma , Guohai Dong , Chan Ghee Koh , Tianning Tang , Marc Perlin
{"title":"An enhanced model for an extreme wave impacting a vertical cylinder","authors":"Bing Tai , Yuxiang Ma , Guohai Dong , Chan Ghee Koh , Tianning Tang , Marc Perlin","doi":"10.1016/j.coastaleng.2024.104630","DOIUrl":"10.1016/j.coastaleng.2024.104630","url":null,"abstract":"<div><div>The interaction between extreme waves and a vertical cylinder is a complex process due to the intricate impact physics, three-dimensional effects, and unique characteristics of breaking waves. To improve wave force predictions, an enhanced model based on a finite-water-extent slamming theory that incorporates wave profiles is proposed. In contrast to the infinite-water-extent assumption in typical wave slamming theories, a finite volume of water with dual free surfaces is used, which better captures the wave's boundary conditions. Strip theory and potential flow theory are adopted to calculate sectional wave forces on the cylinder by solving the governing and boundary equations. The wave profiles, which provide the boundary conditions, result in a more realistic distribution of sectional forces than the often-assumed uniform distribution. Comparison with experimental data shows that the proposed model indeed provides more accurate wave force predictions and exhibits a gradual rise in impact force instead of an abrupt change observed in commonly used models.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"194 ","pages":"Article 104630"},"PeriodicalIF":4.2,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-11DOI: 10.1016/j.coastaleng.2024.104628
Novan Tofany , Arnida L. Latifah
{"title":"Subaerial landslide-induced waves investigated with an adaptively mesh refined multiphase granular flow model","authors":"Novan Tofany , Arnida L. Latifah","doi":"10.1016/j.coastaleng.2024.104628","DOIUrl":"10.1016/j.coastaleng.2024.104628","url":null,"abstract":"<div><div>Impulsive waves generated by subaerial landslides pose a significant threat to coastal or enclosed basin environments. However, simulating the intricate mechanisms involved is challenging due to the multiphase nature of the process, involving air, water, and granular materials interactions. While multiphase computational fluid dynamics (CFD) models offer realistic physics for improved simulations of landslide-induced waves, their high computational cost restricts their use to small-scale laboratory cases or domains. This study presents a multi-variable adaptive mesh refinement (AMR) approach integrated into a multiphase-CFD granular flow model to simulate subaerial landslide-induced wave phenomena. The AMR integration achieves dynamically evolving mesh resolutions in key areas of interest, significantly reducing the total cell count and mitigating computational overhead. The model’s performance is assessed across three laboratory-scale scenarios varying in landslide masses, particle sizes, water depths, and domain sizes. Results demonstrate that AMR maintains static-mesh model accuracy while improving computational efficiency, particularly in high cell count scenarios. Key findings highlight the AMR-enhanced model’s ability to capture both landslide and wave dynamics, showing grid-independence behavior and substantial reduction in computational time. The study emphasizes selecting appropriate AMR parameters, such as the refinement interval, to balance model accuracy and computational efficiency. Additionally, the detailed analysis of landslide dynamics reveals critical influences on wave generation, emphasizing the role of landslide deformation and water penetration in the leading and secondary wave characteristics. Several limitations and computational issues arising from AMR implementation are identified, with recommendations for future improvements. Overall, this study provides valuable insights into the potential of AMR-enhanced multiphase-CFD models for accurately and efficiently simulating landslide-induced waves, offering significant implications for coastal engineering applications.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"195 ","pages":"Article 104628"},"PeriodicalIF":4.2,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-10-10DOI: 10.1016/j.coastaleng.2024.104629
Huiran Liu, Pengzhi Lin
{"title":"An adaptive internal mass source wave-maker for short wave generation","authors":"Huiran Liu, Pengzhi Lin","doi":"10.1016/j.coastaleng.2024.104629","DOIUrl":"10.1016/j.coastaleng.2024.104629","url":null,"abstract":"<div><div>The mass source wave-maker is commonly employed for generating water waves in numerical simulations, during which a correct amount of mass is introduced or subtracted from the internal flow region to produce target waves. The method has proven to be effective in producing waves in shallow and intermediate water depths, while its efficiency is declined for short wave generation. The main reason for this efficiency declination is that the internal mass source in deeper water region is not effective to generate short waves with their motions primarily on water surface. In order to overcome this shortcoming, many of the previous numerical treatments have introduced various enhancement factors into the source functions, which are empirically obtained and also violate the law of mass conservation. In this study, we develop a new adaptive internal wave-maker model that can be self-adjusted to suit different wave conditions. The line source starts from the bottom and extends to the computational cell right beneath free surface at each time step. The depth dependent weighting coefficient is introduced to the source function based on the linear wave theory for each wave component. No empirical coefficients are necessary, and the mass conservation is strictly and explicitly enforced. In principle, the method can be applied to all types of linear waves in the entire range of <em>kh</em>. The numerical experiments show that the present method can produce very good results for linear waves with <em>kh</em> up to 16.11, adequate for most of wave conditions in coastal engineering. For generation of fifth-order Stokes waves, the method can be extended straightforwardly for each of five wave components. For irregular waves composed of many linear wave components, different weighting coefficients can be readily calculated for each of them, respectively. As a result, the new model can generate irregular waves with overall better performance of reproducing wave spectrum, whose high-frequency part has been underestimated by previous methods. The numerical experiments also show that the new model can produce better results for focused waves where many linear waves of different frequencies start from the same point with specific phase angles, due to its capability of generating shorter wave components.</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"194 ","pages":"Article 104629"},"PeriodicalIF":4.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Coastal EngineeringPub Date : 2024-09-27DOI: 10.1016/j.coastaleng.2024.104626
Menno P. de Ridder , Dennis C.P. van Kester , Rick van Bentem , Djimin Y.Y. Teng , Marcel R.A. van Gent
{"title":"Wave overtopping discharges at rubble mound structures in shallow water","authors":"Menno P. de Ridder , Dennis C.P. van Kester , Rick van Bentem , Djimin Y.Y. Teng , Marcel R.A. van Gent","doi":"10.1016/j.coastaleng.2024.104626","DOIUrl":"10.1016/j.coastaleng.2024.104626","url":null,"abstract":"<div><div>Wave overtopping of coastal structures has been studied using physical model experiments with rubble mound breakwaters in shallow water. The mean overtopping discharge is determined for three different foreshore slopes and various hydrodynamic conditions. The hydrodynamic results confirm that energy is transferred to low-frequency waves in very shallow water and that the short waves are in phase with the lower-frequency waves in very shallow water. As a result, the extreme waves (e.g. 2% exceedance wave height) become relatively large in very shallow water due to the energy of the low-frequency waves affecting thereby the wave overtopping. To estimate the amount of energy at the low-frequency waves, an expression is derived which reasonably accurately predicts the low-frequency wave energy (RMSE of 0.06). Considering the non-dimensional overtopping discharge, the existing formulations for the non-dimensional mean wave overtopping discharge perform poorly to reasonably in shallow water with RMSLE ranging from 1.04 to 2.92. A parameter sensitivity study shows that the short-wave steepness, relative crest height and the low-frequency wave height are the most important parameters when predicting the mean overtopping discharge in shallow water. When including the short-wave steepness and relative crest height in an empirical formulation the RMSLE for the current dataset reduces to 0.69. A further increase in accuracy is found when the low-frequency wave height and 2% exceedance wave height are included (RMSLE 0.64).</div></div>","PeriodicalId":50996,"journal":{"name":"Coastal Engineering","volume":"194 ","pages":"Article 104626"},"PeriodicalIF":4.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}