Analysis of dune erosion processes in large-scale flume experiments

Large-scale physical model tests were conducted with different wave periods to examine the physical processes driving dune erosion. The model tests have been carried out in a flume (2DV) with a sandy dune exposed to extreme surge and wave conditions [Van Gent, M.R.A., Van Thiel de Vries, J.S.M., Coeveld, E.M., De Vroeg, J.H. and Van de Graaff, J., 2008. Large-scale dune erosion tests to study the effect of wave periods. Coastal Engineering. doi:10.1016/j.coastaleng.2008.04.003.]. Detailed measurements in time and space of water pressure, flow velocities and sediment concentrations were performed in the near shore area. The data revealed that both short- and long waves are important to inner surf hydrodynamics. Depth averaged flows are directed offshore and increase towards the shore line. The corresponding mean sediment concentrations rise sharply towards the dune face (up to 50 g/l near the bed). The strong increase in the mean sediment concentration towards the dune face correlates well with the maximum wave surface slope which in turn is coupled to both the pressure gradient and the near-bed wave-breaking induced turbulence. Analysis shows that the pressure gradient is only partially coupled to the flow acceleration suggesting that the latter cannot always be used as a proxy for the first. Weak correlation is obtained with the near-bed flows related to the bed shear stress. Tests with a larger wave period resulted in a larger dune erosion volume. During these tests more wave energy (combined incident and infragravity waves) reached the dune face, but more importantly, this wave energy is dissipated by fewer waves resulting in more intense wave breakers and steeper wave fronts. It is therefore expected that the wave-breaking induced near-bed turbulence increases resulting in significantly higher (O(100%)) mean sediment concentrations. In addition the mean flow velocities are comparable, yielding a substantially larger offshore directed sediment transport capacity. This increase in offshore directed transport is only partially compensated by a concurrent increase in the wave related onshore transport capacity associated with intrawave processes, resulting in a net increase in the dune erosion rate.     

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.     

The vertical structure of combined wave–current flow

A simple numerical model, based on the Reynolds stress equations and k–ε turbulence closure scheme, is developed for the coastal wave and current bottom boundary layer. The current friction velocity is introduced to account for the effect of currents on waves. The implicit Crank–Nicolson finite difference method discretizes the governing equations. Vertical changing step grids with the constant ratio for two adjacent spatial steps are used together with the equal time steps in the modeling. Vertical profiles of mean current velocity and wave velocity amplitude are obtained. These modeled results are compared with the laboratory experimental data of Van Doorn [1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. It has been shown that modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands) mean velocity profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands) wave velocity amplitude profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled wave velocity amplitudes are in good agreement with the laboratory experimental data of Van Doorn [1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands].     

Wave groupiness and spectral bandwidth as relevant parameters for the performance assessment of wave energy converters

To date the estimation of long-term wave energy production at a given deployment site has commonly been limited to a consideration of the significant wave height H_s and mean energy period T_e. This paper addresses the sensitivity of power production from wave energy converters to the wave groupiness and spectral bandwidth of sea states. Linear and non-linear systems are implemented to simulate the response of converters equipped with realistic power take-off devices in real sea states. It is shown in particular that, when the converters are not much sensitive to wave directionality, the bandwidth characteristic is appropriate to complete the set of overall wave parameters describing the sea state for the purpose of estimating wave energy production.     

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.     

A ten-year data set for fetch- and depth-limited wave growth

This paper presents the key results from a ten-year data set for Lake IJssel and Lake Sloten in The Netherlands, containing information on wind, storm surges and waves, supplemented with SWAN 40.51 wave model results. The wind speeds U₁₀, effective fetches x and water depths d for the data set ranged from 0–24 m s^− 1, 0.8–25 km and 1.2–6 m respectively. For locations with non-sloping bottoms, the range in non-dimensional fetch x? ( = gxU₁₀^− 2) was about 25–80,000, while the range in dimensionless depth d? ( = g d U₁₀^− 2) was about 0.03–1.7. Land–water wind speed differences were much smaller than the roughness differences would suggest. Part of this seems due to thermal stability effects, which even play a role during near-gale force winds. For storm surges, a spectral response analysis showed that Lake IJssel has several resonant peaks at time scales of order 1 h. As for the waves, wave steepnesses and dimensionless wave heights H? ( = gH_m0U₁₀^− 2) agreed reasonably well with parametric growth curves, although there is no single curve to which the present data fit best for all cases. For strongly depth-limited waves, the extreme values of d? (0.03) and H_m0 / d (0.44) at the 1.7 m deep Lake Sloten were very close to the extremes found in Lake George, Australia. For the 5 m deep Lake IJssel, values of H_m0 / d were higher than the depth-limited asymptotes of parametric wave growth curves. The wave model test cases of this study demonstrated that SWAN underestimates H_m0 for depth-limited waves and that spectral details (enhanced peak, secondary humps) were not well reproduced from H_m0 / d = 0.2–0.3 on. SWAN also underestimated the quick wave response (within 0.3–1 h) to sudden wind increases. For the remaining cases, the new [Van der Westhuysen, A.J., Zijlema, M., and Battjes, J.A., 2007. Nonlinear saturation-based whitecapping dissipation in SWAN for deep and shallow water, Coast. Eng., 54, 151–170] SWAN physics yielded better results than the standard physics of Komen, G.J., Hasselmann, S., Hasselmann, K., 1984. On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr. 14, 1271–1285, except for persistent overestimations that were found for short fetches. The present data set contains many interesting cases for detailed model validation and for further studies into the evolution of wind waves in shallow lakes.     

An analytical approach for the calculation of random wave forces on submerged tunnels

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [Arena F, Interaction between long-crested random waves and a submerged horizontal cylinder. Phys Fluids 2006;18(7):1–9 (paper 076602)] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [Ogilvie TF, First- and second-order forces on a cylinder submerged under a free surface. J Fluid Mech 1963;16:451–472; Arena F, Note on a paper by Ogilvie: The interaction between waves and a submerged horizontal cylinder. J Fluid Mech 1999;394:355–356] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [Sarpkaya T, Isaacson M, Mechanics of wave forces on offshore structures, Van Nostrand Reinhold Co.; 1981], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force C_do is equal to the C_dv of the vertical force. Finally, it is shown that, since a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude–Krylov force.     

Wave climate off northern Norway

The wave climate off northern Norway is considered and the investigation is based on wave measurements made at Tromsøflaket by means of a waverider buoy during the years 1977–1981. Data quality of waverider measurements is briefly commented upon; however, more emphasis is given to an evaluation of the long-term representativity of the actual measuring period and to a procedure accounting approximately for a lack of representativity. The wave climate is presented in terms of a smoothed joint probability density function of the significant wave height, H_s, and the spectral peak period, T_p. Based on this distribution a consistent design curve in the H_s, T_p space is established.     

Field measurements of wave overtopping at the rubble mound breakwater of Rome–Ostia yacht harbour

This paper describes a new station for full-scale measurement of wave overtopping at the Rome yacht harbour rubble mound breakwater in Ostia (Italy) and the results of the successful first measurement campaign carried out during the winter season 2003–2004. The equipment and the research activities were supported by the EU project CLASH, focusing on scale effects for wave overtopping at coastal structures. The site is characterized by a very small tidal range, a long shallow foreshore and depth-limited breaking waves which interact with a shallow sloping porous rock structure. Overtopping water is collected by a steel tank installed on the crown slab behind the parapet wall. The measurement of water level variation inside the tank by means of two pressure transducers allows the calculation of individual overtopping volumes. Incident waves, sea levels and wind are also measured. During seven independent storms, more than 400 individual overtopping events were recorded and about 86 h of valid data are available. This extensive dataset is presented, discussed and then used for comparison with two commonly used overtopping prediction formulae based on small-scale model tests showing their tendency to underestimate the prototype results. A strong correlation between the hourly mean overtopping discharge and corresponding maximum volume is also presented. The paper generally confirms the validity of the approach used in Troch et al. (2004) [Troch, P., Geeraets, J., Van de Walle, B., De Rouck, J., Van Damme, L., Allsop, W., Franco, L., 2004. Full-scale wave overtopping measurements on the Zeebrugge rubble mound breakwater. Coastal Engineering 51, 609–628] for field measurement of wave overtopping.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Neural network modelling of wave overtopping at coastal structures

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests (collected within the framework of the European project CLASH, see e.g. [Steendam, G.J., Van der Meer, J.W., Verhaeghe, H., Besley, P., Franco, L. and Van Gent, M.R.A. (2004). The international database on wave overtopping. World Scientific, Proc. 29th ICCE, vol. 4, pp. 4301–4313, Lisbon, Portugal.]). Moreover, a method was developed to obtain confidence intervals for the overtopping predictions of the neural network.     

Experimental study of irregular wave impact on structures in the splash zone

The experimental investigation of irregular wave slamming on structure members with large dimension in the splash zone is presented. The time-domain and frequency-domain analyses results of the irregular wave impact pressure on the subface of the structure under various case studies are presented. The influence of different incident wave parameters and relative clearance s/H_1/3 on the impact pressure is discussed. The empirical formula of the characteristic impact pressure P_c, P_t and the spectral moment of the impact pressure m₀ on the structure are proposed. The empirical expression of the characteristic peak impact pressure P_c and the spectral moment of the impact pressure m₀ on the structure is given.     

A model for wave growth in fetch-limited conditions

In this paper, it is held that the universal relationships of wave growth in fetch-limited conditions , i. e.,(f|~) p=A(x|~)-Band (m|~)0= C(x|~) Dshould satisfy the Toba 3/2 power law and the wave energy balance equation. In the ideal generation situation, theoretically it can be derived that the ideal fetch-limited wave growth relationship should have D=3B and D B =1, (i.e., B = 0.25, D = 0.75 ) and A3C=2. 1×l(T4C~(1/2)_d , where Cd is the drag coefficient. The 3/2 power law, the wave energy balance equation and the decrease of wave steepness with increasing fetch have became three requirements which should be satisfied by fetch-limited wave growth algorithms. A semi-empirical and semi-theoretical model for fetch-limited wave growth is presented. In the application to the slanting wind situation an un(?)ersal relationship of dimensionless wave energy vs dimensionless peak frequency is presented and the comparisons show that the model is in good agreement with observations.     

Wave parameters and functions in wavelet analysis

A preliminary study of wave parameters and functions in wavelet analysis is conducted in this paper. The Morlet wavelet transform is used to calculate the time–frequency wavelet energy density function, its volume (i.e. the total energy), its frequency-integral (i.e. the wavelet smoothed instantaneous wave energy history), its time-integral (i.e. the wavelet spectral density function), and two non-dimensional wave indices (NIF, NIT). The processing of the measured wave data obtained from the Chi-Gu coastal observation tower during the period August 2000 to July 2001 indicates that the inter-comparison of wavelet smoothed instantaneous wave energy history and smoothed instantaneous wave energy history (SIWEH) as defined by Funke and Mansard (Proc 17th Int Conf on Ocean Eng, 1980) can reveal the noise structure of the wave signal. The wave data with index NIF greater than 2 is always accompanied with noise, therefore NIF can be used as one of the data quality criteria. The index NIT is linearly correlated with the significant wave period and with the significant wave height, therefore NIT can be used to study the wave growth and decaying phenomena.     

The carbon dioxide system in the northwestern Indian Ocean during south–west monsoon

Data on the carbonate system of the Northwestern Indian Ocean obtained on a cruise of F.S. Meteor during SW monsoon in July/August 1995 were compared with those of George et al. [George, M.D., Kumar, M.D., Naqvi, S.W.A., Banerjee, S., Narvekar, P.V., de Sousa, S.N., Jayakumar, D.A., 1994. A study of the carbon dioxide system in the northern Indian Ocean during premonsoon. Mar. Chem. 47, 243–254] collected during intermonsoon. In general, deep water values agreed well between the two expeditions. Surface waters, however, showed a substantial increase in dissolved inorganic carbon (C_T) in the coastal regions due to strong upwelling in the SW monsoon. This was also accompanied by very high CO₂ partial pressures in surface waters. The north–south gradients in vertical profiles of the measured parameters in the Arabian Sea are discussed by comparing profiles from the oligotrophic equatorial region with those from the highly productive central Arabian Sea. The effect of denitrification on regenerated C_T and A_T is minor, with contributions of <9 and <8 μmol kg⁻¹, respectively, to the total amount regenerated also utilizing oxygen. The dissolution of biogenic carbonates is discussed; different approaches to define the depth, where the dissolution starts (lysocline(s), carbonate critical depth (CCrD)), are compared together with the calculation of saturation depth from carbonate concentrations. It is shown, that small differences in measured C_T and A_T (found between our data and those measured during GEOSECS) and different calculation approaches to the CO₂ system (different dissociation constants for species involved and taking into account phosphate and silicate concentrations) can produce pronounced differences in the calculated saturation depths. However, C_T and A_T data suggest substantial dissolution of biogenic carbonate in the water column even above the calcite lysocline, irrespective of the procedures followed to calculate this horizon.     

Calibration and modification of energy dissipation models for irregular wave breaking

This study is undertaken to recalibrate eight existing energy dissipation models and find out the suitable models, which can be used to compute H_rms for a wide range of experimental conditions. The examination shows that the coefficients in the existing models are not the optimal values for a wide range of experimental conditions. Using the new calibrated coefficients, all existing models can be used for computing H_rms and the model of Battjes, J.A., Stive, M.J.F. [1985. Calibration and verification of a dissipation model for random breaking waves. Journal of Geophysical Research 90 (C5), 9159–9167] gives the best predictions. The existing models are also modified by changing the breaker height formulas in the dissipation models. The accuracy of most existing models is improved significantly by using the suitable breaker height formula.     

A simple model of sediment initiation under waves

A simple model is developed to study the initial motion of sediment on a horizontal bed under non-breaking waves. The model is derived to be A=C(T−T₀) based on a wide range of experimental data collected in different flow regimes, where A is the nearbed semi-excursion of wave motion, T is the wave period, and C and T₀ are the coefficients dependent on sediment properties only. For a given sediment, the onset velocity of sediment motion derived from the model is shown to initially increase sharply with wave period T and then approach a constant. The flow Reynolds number Re corresponding to an initiated sediment is also calculated from the simple model and found to be a function of sediment properties and wave period. For the completeness of this study, the initial motion of light sediment under very short waves is also investigated. The present model agrees well with the available laboratory and field data.     

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.     

Predicting wave run-up on rubble-mound structures using M5 model tree

Prediction of run-up level is a key task in design of the coastal structures. For the design of the crest level of coastal structures, the wave run-up level with a 2% exceedance probability, R_u2%, is most commonly used. In this study, the performance of M5 model tree for prediction of the wave run-up on rubble-mound structures was investigated. The main advantage of model trees, unlike the other soft computing tools, is their easier use and more importantly their understandable mathematical rules. Experimental data set of Van der Meer and Stam was used for developing model trees. The conventional governing parameters were selected as the input variables and the obtained results were compared with Van der Meer and Stam’s formula, recommended by the Coastal Engineering Manual (CEM, 2006). The predictive accuracy of the model tree approach was found to be superior to that of Van der Meer and Stam’s empirical formula. Furthermore, to judge the generalization capability of the model tree method, the model developed based on laboratory data set was validated with the prototype run-up measurements on the Zeebrugge breakwater, Belgium. Results show that the model tree is more accurate than empirical formulas and TS Fuzzy approach in estimating the full-scale run-up.     

A generalized approach for long-term modelling of extreme crest-to-trough wave heights

This paper deals with the long-term modelling of high sea waves. The solution is given for the return period of sea storms during which an arbitrary chosen number of waves, with crest-to-trough heights exceeding a fixed threshold, occur. This return period is derived starting from the Equivalent Triangular Storm (ETS) model, which associates a triangle to each actual storm and thus represents a significant wave height time series at a fixed location by means of a sequence of triangular storms. The short-term statistics is then applied to investigate the occurrence of large crest-to-trough wave heights during a given storm. Finally, by combining the statistical distribution of significant wave heights, the ETS model and the short-term wave statistics, the solution is given for the return periods R_N and R_N of a sea storm in which N or at least N waves higher than a fixed threshold occur. The values of R_N are then calculated, starting from data of two buoys moored in the Pacific Ocean and in the Mediterranean Sea.