Non-breaking Conditions Research Articles

Numerical study of wave run-up on sea dikes with vegetated foreshores

Integrating coastal vegetation into sea dikes is a nature-based approach aimed at combining disaster prevention with ecological sustainability in coastal areas. This study investigates the impact of vegetation on the wave run-up on dikes through numerical analysis. The numerical model used in the study solves the Reynolds-averaged Navier–Stokes equations by adding a vegetation resistance force to account for momentum loss. A stabilized k–ω shear stress transport model considering the vegetation effect was adopted for turbulence closure. A series of numerical simulations was carried out on the wave run-up (Ru) on dikes, focusing on the effects of different vegetation heights, densities, zone lengths, and dike slopes under various wave conditions. The results indicate that vegetation can significantly decrease Ru and may cause the wave to change from breaking to nonbreaking on dikes. The Ru behaviors depend on whether waves break and can be well characterized by the Iribarren number and dimensionless wave momentum flux parameter under breaking and nonbreaking conditions, respectively. Finally, the multivariate non-linear regression (MNLR) and artificial neural network (ANN) methods were adopted to explore a prediction model for evaluating Ru. Comparisons showed that the prediction performance of the ANN model is superior to that of the MNLR model. The ANN model has the potential as a promising predictive tool for obtaining wave run-up on dikes with vegetated foreshores under breaking and nonbreaking conditions.

A comprehensive analysis of solitary wave run-up at sloping beaches using an extended experimental dataset

In this work, the phenomenon of wave run-up induced by solitary waves in breaking and nonbreaking conditions has been investigated. Despite several studies have been carried out to study this kind of physical process, a robust determination of solitary wave run-up on plane beaches over a wide range of wave conditions and beach slopes is still lacking. In this context, 99 laboratory tests were undertaken in the wave channel of the University of Calabria by adopting three beach slopes and three water depths. The experimental set-up was made up of four wave gauges, a pressure transducer, a velocimeter and an adjustable waterproof ramp to reproduce the plane sloping beach. Using graduated markers along the beach and a video camera, the run-up was deduced. The present experiments cover a range not extensively analyzed in literature, and specifically related to wave run-up comparable or greater than the water depth. The laboratory run-up, velocity and pressure data were validated using the IH-2VOF numerical model. Two different approaches, both for breaking and nonbreaking conditions, were used to obtain semi-analytical formulas for the wave run-up. The first approach is conventional, being based on wave non-linearity and beach slope, while the second is based on the wave energy.

Wave Attenuation by Vegetation: Model Implementation and Validation Study

Wave–vegetation interaction is implemented in the WAVEWATCH III (WW3) model. The vegetation sink term followed the early formulations of Dalrymple et al. (Journal of Waterway, Port, Coastal, and Ocean Engineering, 1984, 110, 67–79), which focused on monochromatic waves and vegetation approximated as an array of rigid, vertical cylinders, and was later expanded by Mendez and Losada (Coastal Engineering, 2004, 51, 103–118) for random wave transformations over mildly sloping vegetation fields under breaking and nonbreaking conditions assuming a Rayleigh distribution of wave heights. First, validation is carried out for 63 laboratory cases (Anderson and Smith, 2014) with homogeneous vegetation fields for single and double-peak wave spectra. Then, a field case application is conducted to assess the wave attenuation in a wetland environment with spatially variable vegetation fields during stormy conditions. The case study uses data collected at the Magothy Bay located in the Chesapeake Bay, United States, during Hurricanes Jose and Maria in 2017. The domain decomposition parallelization and the implicit scheme have been used for the simulations to efficiently resolve complex shorelines and high-gradient wave zones, incorporating dominant physics in the complicated coastal zone, including wave breaking, wave–current interaction, bottom friction and scattering, wave–vegetation interaction, and nonlinearity (Abdolali et al., 2020). The lab validation and field application demonstrate that WW3 is an effective tool for evaluating the capacity of wetland natural or nature-based features to attenuate wave energy to achieve coastal flood risk reduction.

Experimental Study for Downfall Pressure on the Floor behind Rubble-Mound Structure by Wave Overtopping: Non-Breaking Condition

The large uprush could be occurred when the waves hit the coastal structure and this uprush by wave could make the overtopping. The downfall of the wave overtopping water over the structure brought about the vertical impact loads. The vertical impact loads should be evaluated in order to design the pavement behind the crown wall however these loads were still unclear. In this study, the hydraulic model tests for the downfall impact loads by wave overtopping were performed and the various conditions were applied to the tests. The effect of the incident wave condition, the freeboard, the armour crest height and the height of the parapet were investigated. The test results showed that the parapet on the crown wall could reduce the wave overtopping however the inclusion of parapet could lead to the increased downfall wave pressures behind the crown wall. The empirical formulae were proposed for evaluating the maximum downfall pressures behind the crown wall of rubble mound structure.

Infragravity wave amplification by isolated topography: Field observations and semi-analytical modeling

Infragravity waves (IGWs) play a crucial role in nearshore hydrodynamics and are the primary drivers of coastal hazards such as harbor resonance and overtopping over seawalls. Field observations show that during five storm events in Fall 2013, the IGW heights at the landward side were significantly larger than those at the seaward side of an isolated shoal near Cape Canaveral, Florida, USA. The concurrent offshore incident waves were energetic with directions nearly perpendicular to the shoal. The maximum wave height-to-depth ratio was below 0.3, indicating no wave breaking. Here, we propose a semi-analytical model in combination with field observations to investigate the shoal-induced increase in the cross-shoal IGW energy flux. The model was proposed based on the theory of spatial evolution of nonlinear energy transfer from primary waves to IGWs over an idealized trapezoidal topography under nonbreaking conditions, and was calibrated using a numerical dataset of 21 test cases generated by the non-hydrostatic numerical wave model Simulating Waves till SHore (SWASH). The predicted increase in the cross-shoal IGW energy fluxes are in reasonable agreement with field observations, with 78% data variability explained by the model. Also, the IGW energy flux increase calculated from the observed IGW height increase was found to coincide with the observed IGW energy flux increase in the cross-shoal direction. The results strongly indicate that the observed amplification of IGWs near Cape Canaveral in Fall 2013 is largely attributed to the topography-induced nonlinear energy transfers from sea-swells to IGWs.

Horizontal Wave Pressures on the Crown Wall of Rubble Mound Breakwater under Non-Breaking Condition

The crown wall with parapet on top of the rubble mound breakwater represents a relatively economic and efficient solution to reduce the wave overtopping discharge. However, the inclusion of parapet leads to increased wave pressure on the crown wall. The wave pressure on the crown wall is investigated by physical model test. To design the crown wall the wave loads should be available, and the horizontal wave pressure is still unclear. Regarding to the horizontal wave pressure on the crown wall, a series of experiments were conducted by changing the rubble mound type structure and the wave conditions. Based on these results, pressure modification factors of Goda’s (1974, 2010) formula have been suggested, which can be applicable for the practical design of the crown wall of the rubble-mound breakwater covered by tetrapods.

An Analytical Spectral Model for Infragravity Waves over Topography in Intermediate and Shallow Water under Nonbreaking Conditions

AbstractThe theoretical model for group-forced infragravity (IG) waves in shallow water is not well established for nonbreaking conditions. In the present study, analytical solutions of the group-forced IG waves at O(β1) (β1 = hx/(Δkh), hx = bottom slope, Δk = group wavenumber, h = depth) in intermediate water and at in shallow water are derived separately. In case of off-resonance [β1μ−1 = O(β1), where is the resonant departure parameter, cg = group speed] in intermediate water, additional IG waves in quadrature with the wave group forcing (hereinafter, the nonequilibrium response or component) are induced at O(β1) relative to the equilibrium bound IG wave solution of Longuet–Higgins and Stewart (1962) in phase with the wave group. The present theory indicates that the nonequilibrium response is mainly attributed to the spatial variation of the equilibrium bound IG wave amplitude instead of group-forcing. In case of near-resonance [β1μ−1 = O(1)] in shallow water; however, both the equilibrium and nonequilibrium components are at the leading order. Based on the nearly-resonant solution, the shallow water limit of the local shoaling rate of bound IG waves over a plane sloping beach is derived to be ~h−1 for the first time. The theoretical predictions compare favorably with the laboratory experiment by Van Noorloos (2003) and the present numerical model results generated using SWASH. Based on the proposed solution, the group-forced IG waves over a symmetric shoal are investigated. In case of off-resonance, the solution predicts a roughly symmetric reversible spatial evolution of the IG wave amplitude, while in cases of near to full resonance the IG wave is significantly amplified over the shoal with asymmetric irreversible spatial evolution.

Ka-Band Radar Cross-Section of Breaking Wind Waves

The effective normalized radar cross section (NRCS) of breaking waves, σwb, is empirically derived based on joint synchronized Ka-band radar and video records of the sea surface from a research tower. The σwb is a key parameter that, along with the breaker footprint fraction, Q, defines the contribution of non-polarized backscattering, NP =σwbQ, to the total sea surface NRCS. Combined with the right representation of the regular Bragg and specular backscattering components, the NP component is fundamental to model and interpret sea surface radar measurements. As the first step, the difference between NRCS values for breaking and non-breaking conditions is scaled with the optically-observed Q and compared with the geometric optics model of breaker backscattering. Optically-derived Q might not be optimal to represent the effect of breaking waves on the radar measurements. Alternatively, we rely on the breaking crest length that is firmly detected by the video technique and the empirically estimated breaker decay (inverse wavelength) scale in the direction of breaking wave propagation. A simplified model of breaker NRCS is then proposed using the geometric optics approach. This semi-analytical model parameterizes the along-wave breaker decay from reported breaker roughness spectra, obtained in laboratory experiments with mechanically-generated breakers. These proposed empirical breaker NRCS estimates agree satisfactorily with observations.

Bound infragravity wave observations at the Nowshahr beaches, southern Caspian Sea

This paper presents the results of bound infragravity observation at the Nowshahr beach located in the southern part of the Caspian Sea. The water level data were measured at 6 stations along a transect perpendicular to the coastline. The bispectral method was utilized to show that the extreme values for the bound infragravity energy fraction (bii) were occurring when dimensionless values of wave height to depth ratio, relative depth, and wave steepness were in the range of 0.18‒0.22, 0.4‒0.5 and 0.015‒0.017, respectively. These detailed results could be equivalently summarized with the condition of having the Ursell number of peak waves within the range of 30‒40. The corresponding short wave groupiness factor (G.F.) values for waves with high values of bii were between 0.5 and 0.55. Also, it was revealed that the wave groupiness envelope had a positive correlation with infragravity wave energy level, but its correlation with the bound infragravity wave was negative when G.F. > 0.55. On the other hand, the low values of bii against the spectrum peakedness parameter for breaking waves followed an exponential relationship. The correlation of bound and free infragravity waves with wind waves was also studied. For non-breaking condition, the correlations of bound infragravity waves with swell and sea waves were considerable. The correlation of free waves with swells was also significant. In contrast, for breaking waves, a negligible correlation was observed between bound infragravity waves and wind waves.

Numerical Study of the Kinematic Motions of a Solitary Wave Hitting an Inclined Plate

In this study, we numerically investigated the vortex patterns and free-surface deformations of a solitary wave interacting with a bottom-mounted plate at various inclinations in shallow water. Assuming two-dimensional, incompressible, and non-breaking conditions, we considered a viscous fluid based on the streamfunction-vorticity algorithm used in Navier–Stokes equations. We solved the governing equations by finite analysis, and used an averaged two-time step method to consider nonlinear conditions on the free surface. To fit the irregular boundaries and reveal the fine details of the vortex phenomenon, we applied a transient boundary-fitted grid along with a local-grid-refinement technique and examined the vortex mechanics around the submerged barrier. We then compared the numerical solutions obtained for the flow patterns with existing experimental observations to ensure the efficiency and accuracy of the numerical model. In addition, we systematically simulated other cases using this model to explore kinematic phenomena such as streamlines, equi-vorticity lines, streak lines, timelines, and path lines.

A numerical study of sheet flow driven by velocity and acceleration skewed near-breaking waves on a sandbar using SedWaveFoam

A new methodology capable of concurrently resolving free surface wave field, bottom boundary layer, and sediment transport processes throughout the entire water column was recently developed in the OpenFOAM framework, called SedWaveFoam. In this study, SedWaveFoam is validated with large wave flume data for sheet flow driven by near-breaking waves. Good agreements are obtained for free surface elevation, flow velocity, turbulence kinetic energy, sediment concentration, and sheet flow sediment fluxes. Model results are used to investigate the joint effects of velocity skewness, acceleration skewness, and progressive wave streaming on sheet flow sediment transport. SedWaveFoam results are contrasted with rigid-lid one-dimensional-vertical model results to isolate the effect of the free surface. Onshore directed near-bed flow velocity and sediment flux are enhanced due to the presence of the free surface via progressive wave streaming. However, the enhancement of net onshore sediment transport for the near-breaking condition with both high velocity and acceleration skewness is several factors greater than that found in the nonbreaking condition with only high velocity skewness. Model results suggest that the large horizontal pressure gradient, which has a Sleath parameter exceeding 0.2, may play a key role. Momentary bed failure is identified via near-bed instability of the sheet flow layer, associated with a large bed shear stress and horizontal pressure gradient. Instantaneous near-bed vortices due to the near-bed instability correspond to the increase of horizontal pore pressure gradient during the wave crest, consistent with measured data. Model inter-comparison suggests that a two-dimensional model is crucial to capture the effect of momentary bed failure that increases sediment suspension during wave crest passage and net onshore sediment transport.

ROCK ARMOR DAMAGE IN DEPTH-LIMITED BREAKING WAVE CONDITIONS

The armor layer of a mound breakwaters is usually designed with a formula derived from physical tests in non-breaking wave conditions; however, most rubble mound breakwaters are placed in the wave breaking zone where the highest waves break before reaching the structure. The hydraulic stability formulas developed for rock-armored breakwaters in non-breaking conditions are not completely valid to characterize the hydraulic stability of these structures under depth-limited wave attack. In this study, five series of 2D physical tests were carried out on a bottom slope m=1/50 to analyze the hydraulic stability of double-layer rock armored breakwaters in depth-limited breaking wave conditions. Measurements taken by 12 wave gauges placed along the wave flume were compared with estimations of Hm0, H2% and H1/10 obtained from numerical model SwanOne. The significant wave height, Hm0, estimated or measured at a distance 3hs from the toe of the structure was the best characteristic wave to relate armor damage with stability number. The six-power relationship between dimensionless armor damage and stability number, found in this study, explained more than 94% of the variance in the damage observations. This relationship is valid for conventional non-overtopping double-layer rock-armored breakwaters on bottom slope m=1/50 and depth-limited breaking wave conditions.

Cubipod® Armor Design in Depth-Limited Regular Wave-Breaking Conditions

Armor stability formulas for mound breakwaters are commonly based on 2D small-scale physical tests conducted in non-overtopping and non-breaking conditions. However, most of the breakwaters built around the world are located in breaking or partially-breaking wave conditions, where they must withstand design storms having some percentage of large waves breaking before they reach the structure. In these cases, the design formulas for non-breaking wave conditions are not fully valid. This paper describes the specific 2D physical model tests carried out to analyze the trunk hydraulic stability of single- and double-layer Cubipod® armors in depth-limited regular wave breaking and non-overtopping conditions with horizontal foreshore (m = 0) and armor slope (α) with cotα = 1.5. An experimental methodology was established to ensure that 100 waves attacked the armor layer with the most damaging combination of wave height (H) and wave period (T) for the given water depth (hs). Finally, for a given water depth, empirical formulas were obtained to estimate the Cubipod® size which made the armor stable regardless of the deep-water wave storm.

Three-dimensional Variation of Wave Transmission around the Artificial Reefs: An Experimental Study

ABSTRACT Shin, S.; Bae, I., and Lee, J.-I., 2018. Three-dimensional variation of wave transmission around the artificial reefs: experimental and numerical studies. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1011–1015. Coconut Creek (Florida), ISSN 0749-0208. In this study, three-dimensional experiments were conducted to investigate the spatial variation of wave transmission characteristics under the different types and configurations of the artificial reefs. Partially permeable armored by tetrapods and impermeable structures were deployed with the different gaps. Incident wave conditions included both breaking and non-breaking conditions over the structures. Transmitted wave heights in cross-shore and alongshore directions were compared with the empirical formula. The results showed that the wave transmission phenomena were dependent of the structural typ...

3D Experimental Analysis of Turbulence Induced Scour in Front of the Ruble Mound Breakwater

ABSTRACT Cokgor, S. and Durmus, O., 2018. 3D experimental analysis of turbulence induced scour in front of the ruble mound breakwater. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1251–1255. Coconut Creek (Florida), ISSN 0749-0208. Laboratory data of velocity fields in front of a 45° angled side of a rubble-mound breakwater are presented and discussed for non-breaking wave condition. Velocity measurements were conducted near the breakwater by an acoustic Doppler velocimeter (Nortek Vectrino) regular wave. The raw data were analyzed by using a numerical-filtering scheme so that turbulent fluctuations are separated from the phase-dependent wave motions. Root mean square (RMS) values of the turbulent fluctuations in the vertical and horizontal directions were obtained. The spatial variations of the turbulent shear stress and of the turbulent kinetic energy (TK...

Hydraulic Experiments on Stable Armor Weight and Covering Range of Round Head of Rubble-Mound Breakwater Armored with Tetrapods: Non-breaking conditions

Hydraulic Experiments on Stable Armor Weight and Covering Range of Round Head of Rubble-Mound Breakwater Armored with Tetrapods: Non-breaking conditions

Calibration of overtopping roughness factors for concrete armor units in non-breaking conditions using the CLASH database

The roughness factor (γf) is a parameter used in overtopping estimators to account for the effects of armor unit geometry, the number of layers in the armor and other structural characteristics. Different values of γf for the same armors are given in the literature; however, in this study, the value of γf was calibrated for each overtopping estimator using the best available overtopping data. A methodology based on a bootstrapping technique is proposed to statistically characterize the roughness factors which best fit each formula. For each selected armor unit and overtopping formula, three percentiles (10%, 50% and 90%) of γf are given. Five sets of γf are given for five different overtopping estimators, calibrated using overtopping data from the CLASH database and additional tests with Cubipod armors in non-breaking conditions. The results indicate differences up to 20% in the optimum values of γf compared to those given in the literature. Optimum roughness factors are provided for the CLASH neural network (CLNN); the CLNN was found to be a better overtopping estimator than the other four overtopping formulas compared in this study. The γf is dependent on both the overtopping estimator and the dataset used. Armor porosity affects not only armor roughness and overtopping but also armor hydraulic stability; thus, recommended packing densities must be followed to avoid changes in porosity during lifetime. The sensitivity of the overtopping prediction to the roughness factor depends on the relative crest freeboard (Rc/Hm0); the greater the Rc/Hm0, the higher the sensitivity.

Streamwise velocity profiles in coastal currents

The ability to model marine currents can be a powerful device for many planning activities, for which the knowledge of the velocity field is of pivotal importance, such as the evaluation of current-induced loading on maritime structures or the diffusion and dispersion of polluted flow discharges. Observations of time-averaged velocity profiles, taken with a vessel mounted acoustic Doppler current profiler during a monitoring survey program in the seas of Southern Italy, are analysed in this paper. The measurements were taken under non-breaking conditions, offshore the surf zone, with the aim of reproducing the vertical trends of the streamwise velocity by means of standard theoretical laws. To evaluate also the possible influence of stratification on the current velocity profile shape, together with velocity measurements water temperature and salinity were also measured at the same time and locations, by means of a CTD recorder. The examined surveys referred to different time periods and sites, to guarantee a general validity of deductions. On the basis of the experiments, we verified the actual existence of a log-layer and concluded that the upper limit of the region in which the log law is applicable extends well beyond the inner region. Moreover, the deviations of the measured velocity from the logarithmic profiles above the height of the log layer is consistent with the effects of stratification. The parameters of the log law were estimated, depending on both flow dynamics and stratification in the target area. As a second step, in the most superficial and stratified layer, the velocity profiles were modelled by means of a power law, which fitted the measured data well. According to previous studies, the power law parameters result Reynolds number dependent by means of a new proposed formulation. Finally, the bottom stress and the bottom drag coefficient were investigated.

Hydraulic Experiments for Wave Transformation over a Submerged Elliptic Shoal

ABSTRACT Lee, J.-I.; Kim, Y.-T., and Cho, Y.-S., 2013. Hydraulic experiments for wave transformation over a submerged elliptic shoal. Hydraulic experiments were performed to investigate wave transformation by applying regular and unidirectional irregular waves to wave-propagation process over a submerged elliptic shoal. Under the condition that wave breaking did not occur at the center of the shoal, a wave caustic was observed at the lee side of the shoal and the wave heights of the regular waves were measured to be higher than those of the unidirectional irregular waves. Under the breaking condition, the wave heights measured at the center of the shoal were low, but were high at the lateral sides. For the breaking condition, unlike the nonbreaking condition, the wave heights of the unidirectional irregular waves were measured to be higher than those of the regular waves. It was verified that wave-breaking-induced currents affect the refraction and diffraction of waves in this study.

Laboratory study of solitary-wave transformation over bed-form roughness on fringing reefs

This paper presents the formulation and implementation of a series of two-dimensional flume experiments to investigate effects of bed-form roughness on coastal wave processes. The experiments were carried out on a fringing reef model in a 104-m long and 4.6-m high flume at Oregon State University. The reef model has a 1:12 face slope and a long flat section for examination of wave shoaling and breaking as well as bore formation and propagation. The model is 2.36m tall and the water depth ranges from 2.36 to 2.66m to produce dry and wet reef conditions. The bed-form roughness is modeled by timber beams placed across the flume in four configurations by varying the height from 0.038 to 0.076m and the spacing from 0.388 to 0.768m to provide a range of pitch ratios from 5 to 20. The incident solitary wave height varies from 10 to 50% of the water depth to cover a range of breaking and non-breaking conditions. A series of wire and sonic gauges measured the wave transformation along the flume and a digital camera recorded images of the breaking waves on a background grid painted on a flume wall. The bed forms decrease the effective depth for wave propagation and modify the structure of the free surface flow. In comparison to a control experiment with plain concrete surface, the solitary wave breaks earlier and dissipates more energy on the reef slope. The subsequent bore slows down with undulation over the shallow reef flat, but speeds up for more energetic flows in deeper water.