An experimental study on geometric characteristics of beach erosion profiles

The beach profile and sediment transport are very important factors in the design of coastal structures, and the beach profile is mainly affected by a number of parameters, such as wave height and period, beach slope, and the material properties of the bed. In this study, considering wave height (H₀=6.5, 11.5, 16, 20, 23, 26 and 30 cm), wave period (T=1.46 and 2.03 s), beach slope (m=1/10 and 1/15) and mean sediment diameter (d₅₀=0.18, 0.26, 0.33 and 0.40 mm), an experimental investigation of coastal erosion profile (storm profile) was carried out in a wave flume using regular waves, and geometric characteristics of erosion profile were determined by the resultant erosion profile. Dimensional and non-dimensional equations were obtained by using linear and non-linear regression methods through the experimental data and were compared with previously developed equations in the literature. The results have shown that the experimental data fitted well to the proposed equations with respect to the previously developed equations.     

A two-dimensional finite volume hydrodynamic model for coastal areas: Model development and validation

A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases.     

The phase difference effects on 3-D structure of wave pressure acting on a composite breakwater

In designing the coastal structures, the accurate estimation of the wave forces on them is of great importance. In this paper, the influences of the phase difference on wave pressure acting on a composite breakwater installed in the three-dimensional (3-D) wave field are studied numerically. We extend the earlier model [Hur, D.S., Mizutani, N., 2003. Coastal Engineering 47, 329–345] to simulate 3-D wave fields by introducing 3-D Navier–Stokes solver with the Smagorinsky's sub-grid scale (SGS) model. For the validation of the model, the wave field around a 3-D asymmetrical structure installed on a submerged breakwater, in which the complex wave deformations generate, is simulated, and the numerical solutions are compared to the experimental data reported by Hur, Mizutani, Kim [2004. Coastal Engineering (51, 407–420)]. The model is then adopted to investigate 3-D characteristics of wave pressure and force on a caisson of composite breakwater, and the numerical solutions were discussed with respect to the phase difference between harbor and seaward sides induced by the transmitted wave through the rubble mound or the diffraction. The numerical results reveal that wave forces acting on the composite breakwater are significantly different at each cross-section under influence of wave diffraction that is important parameter on 3-D wave interaction with coastal structures.     

Discussion of “A simple method to determine breaker height and depth for different deepwater wave height/length ratios and sea floor slopes”, by J.P. Le Roux [Coastal Engineering 54 (2007) 271–277]

In the recent paper by J.P. Le Roux [Coastal Engineering 54 (2007) 271–277], the author provides a simplified approach to calculating the depth, length, and height of waves at the onset of depth-induced breaking (i.e. at the breaker line). However, the proposed methodology and the comparisons to other methods suffer from a large number of inconsistencies and basic calculation errors. In addition, there are a number of erroneous physical interpretations and many of the conclusions are based on erroneous data. The remaining conclusions are either not new or based on circular logic, such as to render them moot. In the following, we will not attempt to point out all the errors or inconsistencies that we found, instead we focus on major points of contention.     

Effective fetch and non-linear four-wave interactions during wave growth in slanting fetch conditions

Wave growth in slanting fetch (with wind blowing obliquely off a coast) is investigated with 7 years worth of routine wave measurements in Lake IJssel in The Netherlands and with the SWAN wave model. Two aspects are considered in particular for this case: the validity of the concept of effective fetch and the role of the non-linear four-wave interactions. For slanting and parallel fetch conditions, we found some significant deviations from the effective fetch assumption, leading to 20–35% mismatch in either the peak period T_p or the significant wave height H_m0 respectively. However, the effect of discrepancies between various widely accepted wave growth formulas turned out to be even more important. The wave directions during slanting fetch are significantly ‘steered’ by the coastline, especially in the first kilometre(s) off the coast. The role of the non-linear four-wave interactions is investigated by running the SWAN (version 40.41) wave model with three different quadruplet formulations. Exact quadruplet methods (Xnl) yielded relatively strong wave steering, despite the four-wave interactions being relatively weak. Application of Xnl did not lead to better overall agreement with measurements — improvements for the mean wave period T_m01 were offset by some deterioration for the wave height H_m0.     

Large-scale dune erosion tests to study the influence of wave periods

Large-scale physical model tests were performed to quantify the effects of the wave period on dune erosion. Attention was focussed on 2D cross-shore effects in a situation with sandy dunes and extreme water levels and wave conditions. Besides profile measurements, detailed measurements in time and space of water pressure, flow velocities and sediment concentrations were performed in the near near-shore area. It was concluded that a longer wave period leads to a larger dune erosion volume and to a larger landward retreat of the dune face. Tests with double-peaked wave spectra showed that the influence of the spectral shape on dune erosion was best represented by the T_m − 1,0 spectral mean wave period, better than the peak wave period, T_p. The effect of the wave period on dune erosion was implemented in a dune erosion prediction method that estimates erosion volumes during normative storm conditions for the Dutch coast. More details of the measurements and additional analyses of physical processes are described in an accompanying paper by Van Thiel de Vries et al. [Van Thiel de Vries, J.S.M., van Gent, M.R.A., Reniers, A.J.H.M. and Walstra, D.J.R., submitted for publication. Analysis of dune erosion processes in large scale flume experiments, In this volume of Coastal Engineering.].     

Observations of wave pump efficiency

Currently available data on wave pump efficiency is reviewed. The obtainable efficiency is an important consideration in the design of practical devices for the extraction of wave energy and the analysis of natural systems (e.g., coral flats and rip currents). We find that the peak efficiency is 0.5 for very steep (∼ 40–45°) ramps where the waves break over the top of the ramp. For flatter (< 30°) ramps, the breaking process is more gradual and the peak efficiency is less than 0.1. We have identified natural atoll lagoon systems where the flushing is wave driven and successfully modeled it as driven by a wave pump. The same is the case for rip currents. For both of these natural systems, the pump efficiency is around 0.035. In addition a numerical swash model is used to estimate wave pump efficiency and is seen to match the experimental results for natural systems or breaking wave scenario.     

Hydrodynamic performance of a dual cylindrical caisson breakwater

The hydrodynamic performance of a dual cylindrical caisson breakwater (DCBW) formed by a row of caissons each of which consisting of a porous outer cylinder circumscribing an impermeable inner cylinder has been theoretically investigated. The theoretical formulation is based on the eigenfunction expansion method proposed by Spring and Monkmeyer (1974) which was further modified by Linton and Evans [Linton, C.M., Evans, D.V., 1990. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 215, 549–569] for an array of impermeable cylinders. The present formulation is an extension of the work of Wang and Ren [Wang, K.H., Ren, X., 1994. Wave interaction with a concentric porous cylinder system. Ocean Engineering 21(4), 343–360], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. In the present study, the formulation has been extended to the case of a group of porous dual cylinder system. Parametric studies are carried out to study the influence of porosity (G₀) on the outer caisson, width of the doughnut chamber (a/b) and the angle of wave incidence on the variation in the hydrodynamic loading, wave run-up, free-surface elevation in its vicinity as well as the transmission on its lee-side. The importance of the presence of the inner cylinder in achieving the required hydrodynamic performance in terms of either protection or providing tranquility on its lee side keeping higher stability for the breakwater system is highlighted.     

Discussion of “Wave setup and setdown generated by obliquely incident waves” by T.-W. Hsu et al., Coastal Engineering, 53, 865–877, 2006

In the recent paper by Tai-Wen Hsu, John R.-C. Hsu, Wen-Kai Weng, Swun-Kwang Wang, and Shan-Hwei Ou (Coastal Engineering, 53, 865–877, 2006), the authors derived theoretical formulations for calculating the wave setup and setdown induced by obliquely incident waves on a beach. The derivation of an expression for setdown contains errors which would lead to an imbalance in longshore momentum flux outside the surfzone. We correct their derivation and give results in terms of the radiation stress concept in a general case including an oblique wave incidence. We also point out that the correct form of wave setdown is important to describe the zero-net force in the momentum balance outside the surfzone.     

Reflected and transmitted waves in a channel with side porous mattresses

The problem of wave propagation and wave damping in a channel with side porous mattresses of arbitrary shape protruding from the walls is studied. The solution was achieved by applying 3-D boundary element method and was employed to study wave field in the channel and to analyze the effect of the geometry of the mattresses and physical and hydraulic properties of porous material on wave damping. The results show that wave damping in the channel strongly depends on wave parameters, especially, on the wave number. Wave reflection and transmission decrease with increasing the wave number. The results also show that the wave field in the channel strongly depends on the geometry of the mattresses as well as on physical and hydraulic properties of porous material used to build these wave dampers. The geometry of the mattresses and physical and hydraulic properties of porous material have a moderate effect on wave reflection and a significant effect on wave transmission. The results show that wave transmission down the channel decreases with increasing the length and thickness of the mattresses. Moreover, wave transmission decreases with increasing the porosity and damping properties of porous media used to build the mattresses. The analysis shows that porous mattresses protruding from the channel walls are very efficient in damping water waves propagating down the channel and may be built in channels to reduce high waves and achieve desired wave conditions. Theoretical results are in reasonable agreement with experimental data.