Modeling undertow due to random waves

A numerical model of undertow due to random waves is developed. The model includes three sub-models: (i) a model for multi-directional and multi-frequency random wave transformation, (ii) a surface roller evolution model, and (iii) a model for calculating the vertical distribution and the mean value of the undertow velocity. The calculation of wave trough level is performed based on a theory for the wave asymmetry. The model was successfully validated against small- and large-scale laboratory experiments. Thus, the model is expected to provide reliable input for the modeling of sediment transport and morphological change due to waves and currents.     

Wave forces on, and water-surface fluctuations around a vertical cylinder encircled by a perforated square caisson

The wave forces and moments on and the water surface fluctuations around a vertical circular cylinder encircled by a perforated square caisson were experimentally investigated. The porosity of the outer square caisson was varied from 4.24 to 14.58%. The in-line wave forces on the inner vertical cylinder are influenced by changing the porosity of the outer caisson, whereas the variations in the water surface fluctuations are less influenced in this porosity range. The in-line moment on the vertical cylinder is relatively less sensitive when the porosity is increased from 4.24 to 8.75%, but varies substantially when it is increased from 8.75 to 14.58%. The force and moment ratio (i.e. the ratio of the force or moment on the vertical cylinder, when it is encircled by the perforated caisson to the force or moment on the cylinder without any protection around it) reduces with increased wave height, H, and wave length, L, whereas the wave height ratio (ratio of the wave height at a point in the vicinity of the structure to the incident wave height) is less sensitive for the varying H and L. A new non-dimensional parameter, p^1.5 (D/L)/(H/d), is introduced to predict the in-line force and moment on the inner vertical cylinder, where d is local water depth, D is the diameter of the inner cylinder and p is the porosity of the outer caisson in percentage. Simple predictive equations for forces, moments and water surface fluctuations are provided.     

Processes affecting the hydraulic stability of coastal revetments made of geotextile sand containers

Softer and flexible protection alternatives, such as structures made of geotextile sand containers (GSC) are often used instead of hard coastal structures made of concrete or rubble material.     

Core made of geotextile sand containers for rubble mound breakwaters and seawalls: Effect on armour stability and hydraulic performance

A systematic armour stability and the hydraulic performance, including wave reflection, wave transmission, experimental study in the twin-wave flumes of Leichtweiss-Institute (LWI) is performed on a geocore breakwater and a conventional rubble mound breakwater in order to comparatively determine the wave run-up and wave overtopping. The geocore breakwater consists of a core made of sand-filled geotextile containers (GSC) covered by an armour made of rock. The geocore is more than an order of magnitude less permeable than the quarry run core of a conventional breakwater. As expected, the core permeability substantially affects the armour stability on the seaside slope, the wave transmission and the wave overtopping performance. Surprisingly, however, wave reflection and hydraulic stability of the rear slope are less affected. Formulae for the armour stability and hydraulic performance of the geocore breakwater are proposed, including wave reflection, transmission, run-up and overtopping.     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

Model for prediction of sea dike breaching initiated by breaking wave impact

A computational model system is proposed for the prediction of sea dike breaching initiated from the seaward side by breaking wave impact with the focus on the application of the model system for the estimation failure probability of the defence structure. The described model system is built using a number of existing models for the calculation of grass, clay, and sand erosion. The parameters identified as those having the most significant influence on the estimation of the failure have been described stochastically. Monte Carlo simulations to account for uncertainties of the relevant input parameters and the model itself have been performed and the probabilities of the breach initiation and of the full dike breaching have been calculated. This will form the basis to assess the coastal flood risk due to dike breaching.     

Process based stability formulae for coastal structures made of geotextile sand containers

Geotextile Sand Containers (GSC) are increasingly used worldwide for shore protection structures such as seawalls, groins, breakwaters, revetments and artificial reefs. However, reliable design formulae for the hydraulic stability based on a good understanding of the processes involved in the wave-structure interactions are still needed.Although the effect of the deformations of the sand containers on the hydraulic stability is significant, no stability formula is available to account for those deformations and the associated processes leading to the observed failures. Therefore, based on the results of extensive experimental and numerical studies ([Recio J. 2008, Hydraulic Stability of Geotextile Sand Containers for Coastal Structures – Effect of Deformations and Stability Formulae – PhD Thesis, Leichtweiss Institute for Hydraulic Engineering and Water Resources, www.digibib.tu-bs.de/?docid=00021899]), analytical stability formulae are developed that account for the effect of the deformations of the individual GSCs for sliding and overturning stability. The required drag, inertia and lift coefficients are determined experimentally from hydraulic model experiments specially designed for this purpose. Several types of GSC configurations which are representative for a wide range of GSC-structure types are investigated under wave action. Moreover, deformation factors to account for the deformation of the containers on the stability are analytically derived and implemented in the stability formulae.Finally, Stability formulae for each type of coastal structures made of geotextile sand containers such as breakwaters, revetments, sea walls, dune reinforcement and scour protection systems are proposed and recommendations are given with respect to the practical application of the proposed hydraulic stability formula, including their limitations.     

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1). Zone 1 (0<z<d−H_i/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−H_i/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, H_i is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993) to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990) and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.     

The SWAN model used to study wave evolution in a flume

The SWAN numerical model is used to model the evolution of JONSWAP wave spectra and hence the significant wave height of waves in a tank. Comparison with experiment has shown that modelling triad interactions in the numerical model leads to too low predictions of spectra and significant wave height and should therefore be excluded. The modelling of the breaking constant was also investigated, by looking at the use of a constant breaking constant, Nelson formula, and Goda formula (added into SWAN for this study). Using a constant value of 0.78 within SWAN gave the best comparison between theory and experiment.