Dynamic pressures and forces exerted on impermeable and seaside perforated semicircular breakwaters due to regular waves

The semicircular breakwater (SBW) is a composite breakwater consisting of a semicircular caisson resting on a rubble mound. The SBW function as a barrier dissipates the incident wave energy and creates tranquillity on its leeside. The dynamic pressures due to regular waves exerted on seaside perforated SBWs with 7 and 11% of exposed surface area with perforations were measured. The measured pressures are compared with those exerted on impermeable SBWs. In addition, the forces exerted on the caisson alone are measured. The reflection coefficient, measured total forces on the caisson of the models, and the pressures are presented as functions of relative water depth. The effect of the water depth and the percentage of perforations on the above stated variables are examined, details of which are reported in this paper.     

Experimental study of long wave generation on sloping bottoms

Low-frequency waves generated on steep (1:10) and mild (1:40) slopes by six series of bichromatic wave groups are studied experimentally. The shorelines for both slopes are replaced by horizontal reaches of small depth. This reduces the reflection of long waves near the shoreline significantly, which for the first time makes possible the explicit observation of outgoing breakpoint forced long waves. The breakpoint and released bound long wave mechanisms on the different slopes are compared. Generally, the breakpoint forced long waves dominate the low-frequency wave field on the steep slope, while the released bound long waves are found to be more significant on the mild slope. Two parameters indexing the effectiveness of the breakpoint mechanism are compared and the normalized slope tends to give more realistic results. Shoaling of bound long waves is analyzed and the shallow-water equilibrium limit ~ h^−5/2 exhibits a good prediction of the variation of the bound long waves on both slopes.     

Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves

Two depth inversion algorithms (DIA) applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow (FNPF) theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values of wave celerity c and length L, and either wave height H or left–right asymmetry s₂/s₁, simultaneously measured at a number of locations in the direction of wave propagation, e.g., using video or radar remote sensing techniques. In these DIAs, an empirical relationship, calibrated for a series of computations in the numerical wave tank, is used to express c as a function of relative depth k_oh and deep water steepness k_oH_o. To carry out depth inversion, wave period is first predicted as the mean of observed L/c values, and H_o is then predicted, either based on observed H or s₂/s₁ values. The celerity relationship is finally inverted to predict depth h. The algorithms are validated by applying them to results of computations for cases with more complex bottom topography and different incident waves than in the original calibration computations. In all cases, root-mean-square (rms)-errors for the depth predictions are found to be less than a few percent, whereas depth predictions based on the linear dispersion relationship—which is still the basis for many state-of-the-art DIAs—have rms-errors 5 to 10 times larger.     

Prediction of geometrical properties of perfect breaking waves on composite breakwaters

Breaking wave loads on coastal structures depend primarily on the type of wave breaking at the instant of impact. When a wave breaks on a vertical wall with an almost vertical front face called the “perfect breaking”, the greatest impact forces are produced. The correct prediction of impact forces from perfect breaking of waves on seawalls and breakwaters is closely dependent on the accurate determination of their configurations at breaking. The present study is concerned with the determination of the geometrical properties of perfect breaking waves on composite-type breakwaters by employing artificial neural networks. Using a set of laboratory data, the breaker crest height, h_b, breaker height, H_b, and water depth in front of the wall, d_w, from perfect breaking of waves on composite breakwaters are predicted using the artificial neural network technique and the results are compared with those obtained from linear and multi-linear regression models. The comparisons of the predicted results from the present models with measured data show that the h_b, H_b and d_w values, which represent the geometry of waves breaking directly on composite breakwaters, can be predicted more accurately by artificial neural networks compared to linear and multi-linear regressions.     

Wave modelling in the vicinity of submerged breakwaters

This paper describes a simple method for modelling wave breaking over submerged structures, with the view of using such modelling approach in a coastal area morphodynamic modelling system.A dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking. Available models for energy dissipation due to wave breaking are developed for beaches (gentle slopes) and require further modifications to model wave breaking over submerged breakwaters.In this paper, wave breaking is split into two parts, namely: 1) depth-limited breaking modelled using Battjes and Janssen's (1978) theory [Battjes, J.A. and Jannsen, J.P.F.M. (1978). Energy loss and setup due to breaking of random waves. Proceedings of the 16th Int. Conf. Coast. Eng., Hamburg, Germany, pp. 569-587.] and 2) steepness limited breaking modelled using an integrated form of the Hasselmann's whitecapping dissipation term, commonly used in fully spectral wind–wave models. The parameter γ₂, governing the maximum wave height at incipient breaking (H_max = γ₂d) is used as calibration factor to tune numerical model results to selected laboratory measurements. It is found that γ₂ varies mainly with the relative submergence depth (ratio of submergence depth at breakwater crest to significant wave height), and a simple relationship is proposed. It is shown that the transmission coefficients obtained using this approach compare favourably with those calculated using published empirical expressions.     

Wave evolution over submerged sills: tests of a high-order Boussinesq model

A Boussinesq model accurate to O(μ)⁴, μ=k₀h₀ in dispersion and retaining all nonlinear effects is derived for the case of variable water depth. A numerical implementation of the model in one horizontal direction is described. An algorithm for wave generation using a grid-interior source function is derived. The model is tested in its complete form, in a weakly nonlinear form corresponding to the approximation δ=O(μ²), δ=a/h₀, and in a fully nonlinear form accurate to O(μ²) in dispersion [Wei, G., Kirby, J.T., Grilli, S.T., Subramanya R. (1995). A fully nonlinear Boussinesq model for surface waves: Part 1. Highly nonlinear unsteady waves. J. Fluid Mech., 294, 71–92]. Test cases are taken from the experiments described by Dingemans [Dingemans, M.W. (1994). Comparison of computations with Boussinesq-like models and laboratory measurements. Report H-1684.12, Delft Hydraulics, 32 pp.] and Ohyama et al. [Ohyama, T., Kiota, W., Tada, A. (1994). Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering, 24, 297–313.] and consider the shoaling and disintegration of monochromatic wave trains propagating over an elevated bar feature in an otherwise constant depth tank. Results clearly demonstrate the importance of the retention of fully-nonlinear effects in correct prediction of the evolved wave fields.     

Effects of longshore shelf variations on barotropic continental shelf waves,slope currents and ocean modes

Effects of continental shelf bends, converging depth contours and changing depth profiles are discussed. Some analysis is carried out for previously unstudied cases. Separate oceanic interior and shelf flow problems are formulated for a sufficiently narrow shelf. The ocean interior ‘sees’ only an integrated shelf effect, typically increasing shelf-edge amplitudes, retarding longshore Kelvin-wave propagation and increasing natural mode periods by 0 (10%). On the local shelf, the flow matches to the ocean interior and is nondivergent. Effects on shelf waves and slope currents depend subtly on the nature of the longshore variations. Curvature and contour convergence do not per se imply scaterring or generation of shelf waves. Indeed, any depth h(ξ) where ▽² ξ(x,y) = 0 (a condition approximating longshelf uniformity in the topography's convexity) supports essentially the same shelf waves as do straight depth contours (DAVIS, 1983), and slope currents follow depth contours. Scattering results rather from breaks in analyticity of the depth profile. Hence calculations for small isolated features (necessarily highly convex or concave) may overestimate scattering, and superposition for realistic topography may lead to much self-cancellation among scattered waves. Otherwise, examples show a strong preference for scattering into adjacent mode numbers and into any shelf wave mode near to its maximum frequency. A shelf sector, where the maximum shelf wave frequency maxω is less than the frequency ω of an incident shelf wave, causes substantial scattering unless maxω and ω are very close. Adjustment of slope currents to changed conditions takes place through (and over the decay distance of) scattered shelf waves.     

Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (S_max/H₀) on the basis of the following variables: relative water depth at the toe of the breakwater (h_toe/L₀), Shields parameter (θ), non-breaking wave steepness (H₀/L₀), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.     

Numerical simulation of time-dependent beach and dune erosion

A computational procedure is developed for predicting the time-dependent, two-dimensional beach and dune erosion during severe storms due to elevated water levels and waves. The model employs the equation of sediment continuity and a dynamic equation governing the cross-shore sediment transport due to a disequilibrium of wave energy dissipation levels. These equations are solved numerically by an implicit, double-sweep procedure to determine the change in position of elevation contours in the profile. Given sufficient time, the profile will evolve to a form where the depth, h, in the surf zone is related to the distance seaward of the waterline by the relationship: $\text{h = Ax}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$, which is consistent with many natural profiles and in which A depends on sediment characteristics.The model is verified qualitatively and quantitatively through application to several idealized cases and through a preliminary simulation of erosion during Hurricane Eloise. In general, the time scales for shoreline response were found to be quite long relative to natural storm systems and erosion in the early response stages was found to be sensitive to storm surge height, but much less sensitive to wave height. The model response characteristics for simulation of erosion due to time-varying storm conditions show a lag between the maximum storm surge elevation and maximum erosion with the maximum erosion rate occurring at the time of the peak surge. For the simulated erosion due to Hurricane Eloise, reasonable agreement was found between the post-hurricane dune profiles and those calculated. However, the eroded volumes were in better agreement than the profile forms as the steepening of the natural dune profiles was not reproduced in the model.     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.     

Prediction model for occurrence of impact wave force

This study investigates the applicability of neural networks to predict whether impact wave force will act on the upright section of a composite breakwater. We employ a three-layered neural network whose units of input layer are h/L, H/h, d/h and B_M/h (h: the total water depth; L: the wavelength; H: the wave height; d: the water depth above the mound; B_M: the horizontal distance from the shoulder of mound to the caisson). Teach signals are 0.99 and 0.01 according to the cases of occurrence and absence of impact wave force, respectively. The neural network whose parameters are determined through self-learning can accurately predict whether impact wave force occurs.     

Hydrodynamic efficiency of partially immersed caissons supported on piles

The efficiency of the breakwater, which consists of caissons supported on two or three rows of piles, was studied using physical models. The efficiency of the breakwater is presented as a function of the transmission, reflection and the wave energy dissipation coefficients. Regular waves with wide ranges of wave heights and periods and constant water depth were used. Different characteristics of the caisson structure and the supporting pile system were also tested. It was found that, the transmission coefficient (k_t) decreases with increasing the relative breakwater draft D/L, increasing the relative breakwater width B/h, and decreasing the piles gap-diameter ratio G/d. It is possible to achieve k_t values less than 0.25 when D/L≥0.1. The reflection coefficient takes the opposite trend especially when D/L≤0.15. The proposed breakwater dissipates about 10-25% of the incident wave energy. Also, simple empirical equations are developed for estimating the wave transmission and reflection. In addition, the proposed breakwater model is efficient compared with other floating breakwaters.     

Profiles of fully developed (Airy) waves in different water depths

Airy waves have a sinusoidal profile in deep water that can be modeled by a time series at any point x and time t, given by η(x,t) = (H_o/2) cos[2πx/L_o − 2πt/T_w], where H_o is the deepwater height, L_o is the deepwater wavelength, and T_w is the wave period. However, as these waves approach the shore they change in form and dimension so that this equation becomes invalid. A method is presented to reconstruct the wave profile showing the correct wavelength, wave height, wave shape, and displacement of the water surface with respect to the still water level for any water depth.     

Wave attenuation in mangroves: A quantitative approach to field observations

Coastal mangroves, dwelling at the interface between land and sea, provide an important contribution to reducing risk from coastal hazards by attenuating incident waves and by trapping and stabilizing sediments. This paper focusses on relations between vegetation densities, wave attenuation rates, sediment characteristics and sedimentation rates in mangroves. These processes were studied along two cross-shore transects through mangroves fringing estuaries in the southern Andaman region of Thailand. Volumetric vegetation densities in these mangroves were ranging up to 32‰, depending on the water depth. Generalized total wave attenuation rates increased from 0.002 m^− 1 in the sparsely vegetated forest fringes with Avicennia and Sonneratia species, up to 0.012 m^− 1 in the dense Rhizophora vegetation in the back of the forests. The total wave attenuation rates integrate effects of shoaling and energy losses due to various bio-physical interactions within the mangrove ecosystem. Wave attenuation in the mangroves is presumably dominated by energy losses due to vegetation drag, since wave attenuation due to bottom friction and viscous dissipation on the bare mudflats is significantly lower than those inside the mangrove vegetation.Additionally, wave attenuation in the mangroves was found to facilitate enhanced net sediment deposition and a gradual fining of the bed material. These findings corroborate the coastal defence function of mangroves by quantifying their contribution to wave attenuation and sediment trapping. The explicit linking of these properties to vegetation composition and structure facilitates modelling studies investigating the mechanisms determining the coastal defence capacities of mangroves.     

Shoreline response to multi-functional artificial surfing reefs: A numerical and physical modelling study

The results of a series of 2DH numerical and 3D scaled physical modelling tests indicate that processes governing shoreline response to submerged structures, such as artificial surfing reefs, are different from those associated with emergent offshore breakwaters. Unlike the case of emergent offshore breakwaters, where shoreline accretion (salient development) is expected under all structural/environmental conditions, the principal mode of shoreline response to submerged structures can vary between erosive and accretive, depending on the offshore distance to the structure. The predominant wave incidence angle and structure crest level also have important implications on the magnitude of shoreline response, but not on the mode of shoreline response (i.e. erosion vs. accretion). Based on the results obtained here, a predictive empirical relationship is proposed as a preliminary engineering tool to assess shoreline response to submerged structures.     

Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence

The wavelet-based bicoherence, which is a new and powerful tool in the analysis of nonlinear phase coupling, is used to study the nonlinear wave–wave interactions of breaking and non-breaking gravity waves propagating over a sill. Two cases of mechanically generated random waves based on Jonswap spectra are used for this purpose. Values of relative depth, k_ph (k_p is the wave number of the spectral peak and h is the water depth) for this study range between 0.38 and 1.22. The variations of wavelet-based total bicoherence for the test cases indicate that the degree of quadratic phase coupling increases in the shoaling region consistent with a wave profile that is pitched shoreward, relative to a vertical axis as seen in the experiments, but decreases in the de-shoaling region. For the non-breaking case, the degree of quadratic phase coupling continues to increase until waves reach the top of the sill. Breaking waves, however, achieve their highest level of quadratic phase coupling immediately before incipient breaking and the degree of phase coupling decreases sharply following breaking. In addition the wavelet-based bicoherence spectra provide evidence of the harmonics' growth which is reflected in the energy spectra. The bicoherence spectra also show that quadratic phase coupling between modes within the peak frequency as well as between modes of the peak frequency and its higher harmonics are dominant in the shoaling region, even though there are relatively high levels of quadratic phase coupling occurring between other frequencies. Furthermore, using the temporal resolution property of the wavelet-based bicoherence, we find that the quadratic wave interactions occur more readily during segments of time with large change of wave amplitude, rather than those segments having large wave amplitudes, but small gradients in amplitude.     

Composition,abundance, distribution and seasonality of larval fishes in the shallow nearshore of the proposed Greater Addo Marine Reserve,Algoa Bay,South Africa

The larval fish assemblage was investigated in the shallow, nearshore region of a proposed marine protected area in eastern Algoa Bay, temperate South Africa, prior to proclamation. Sampling was conducted at six sites along two different depth contours at ∼5 m and ∼15 m to assess shore association. Larvae were collected by means of stepped oblique bongo net tows deployed off a ski-boat, twice per season for 2 years between 2005 and 2007. In total, 6045 larval fishes were collected representing 32 families and 78 species. The Gobiidae, Cynoglossidae, Clupeidae, Engraulidae and Sparidae were the dominant fish families. Catches varied significantly among seasons peaking in spring with a mean of ∼200 larvae/100 m³. Mean overall larval density was higher along the deeper contour, at ∼15 m (40 larvae/100 m³). The preflexion stage of development dominated catches at the ∼5 m (80%) and ∼15 m (73%) depth contours. Body lengths of Argyrosomus thorpei, Caffrogobius gilchristi, Diplodus capensis, Heteromycteris capensis and Solea turbynei, all estuary associated species, were larger at the shallow sites nearer to shore. Larvae of coastal species that produce benthic eggs dominated catches (75%) in the shallow sites (∼5 m) but were less abundant (32%) farther from shore at the deeper (∼15 m) sites. All developmental stages of D. capensis, Engraulis capensis, H. capensis, Sardinops sagax and two Pomadasys species were found in the study area. It appears that some species use the shallow nearshore as a nursery area.     

Megacusps on rip channel bathymetry: Observations and modeling

The formation of beach megacusps along the shoreline of southern Monterey Bay, CA, is investigated using time-averaged video and simulated with XBeach, a recently developed coastal sediment transport model. Investigations focus on the hydrodynamic role played by the bay's ever-present rip channels. A review of four years of video and wave data from Sand City, CA, indicates that megacusps most often form shoreward of rip channels under larger waves (significant wave height (H_s) = 1.5–2.0 m). However, they also occasionally appear shoreward of shoals when waves are smaller (H_s ~ 1 m) and the mean water level is higher on the beach. After calibration to the Sand City site, XBeach is shown to hindcast measured shoreline change moderately well (skill = 0.41) but to overpredict the erosion of the swash region and beach face. Simulations with small to moderate waves (H_s = 0.5–1.2 m) suggest, similar to field data, that megacusps will form shoreward of either rip channels or shoals, depending on mean daily water level and pre-existing beach shape. A frequency-based analysis of sediment transport forcing is performed, decomposing transport processes to the mean, infragravity, and very-low-frequency (VLF) contributions for two highlighted cases. Results indicate that the mean flow plays the dominant role in both types of megacusp formation, but that VLF oscillations in sediment concentration and advective flow are also significant.     

The impact of sea level rise and climate change on inshore wave climate: A case study for East Anglia (UK)

In coastal areas, offshore wave propagation towards the shore is influenced by water depth variations, due to sea bed bathymetry, tides and surges. Considering implications of climate change both on atmospheric forcing and sea level rise, a simple methodology involving numerical modelling is implemented to compute inshore waves from 1960 to 2099. Simulations take into account five scenarios of linear sea level rise and one climatic scenario for storm surges and offshore waves. The methodology is applied to the East Anglia coast (UK). Extreme event analysis is performed to estimate climate change implication on inshore waves and the occurrence of extreme events. It is shown, for this coastal region, that wave statistics are sensitive to the trend in sea level rise, and that the climate change scenario leads to a significant increase of extreme wave heights in the northern part of the domain. For nearshore points, the increase of the mean sea level alters not only extreme wave heights but also the frequency of occurrence of extreme wave conditions.     

The effects of tropical storm Dennis on coastal phytoplankton

The effects of tropical storm Dennis were documented in the coastal waters of South Carolina during August 1981. Phytoplankton photosynthesis vs. irradiance curves showed initial depression of the parameter a followed by three- to five-fold increase of both a and the asymptotic maximum rate of photosynthesis P_m^B. Productivity rates were depressed in most samples immediately after the storm. Surface samples at the inshore stations were around 50 mg C m^?3 h^?1 at saturating light intensities, while the offshore station rates were around 10 mg C m^?3 h^?1. After a 10-day lag these rates had increased to about 200 mg C m^?3 h^?1 inshore and 75 mg C m^?3 h^?1 offshore. These changes are thought to be primarily caused by changes in species composition. Some of the dominant diatom species changed and dinoflagellate species were introduced. No significant changes in nutrient concentrations were observed. Transient depressions of water temperature, salinity and light intensity may have contributed to the observed changes.