Surf Similarity Parameter Research Articles

SWASH ZONE BASED REFLECTION DURING ENERGETIC WAVE CONDITIONS AT A DISSIPATIVE BEACH: TOWARD A WAVE-BY-WAVE APPROACH

This paper presents a 11-day experiment conducted at the high-energy dissipative beach of Mataquito, Maule Region, Chile. During the experiment, offshore significant wave height ranged 1-4 m, with persistent long period up to 18 s and oblique incidence. Wave energy reflection value ranged from 1 to 4 %, and results show that it is highly linked to both incoming wave characteristics and swash zone beach slope, and is well correlated to a swash-slope based Iribarren number. The swash acting as a low-pass filter in the reflection mechanism, our results show that the cut-off period is better determined by swash slope rather than incoming wave's period. A new low cost technique for observing high-frequency swash hydro-morphodynamics is introduced and validated using LIDAR measurements. A good agreement is found. Separation of uprush and backswash components using the Radon Transform illustrates the low-frequency filtering effect. These results show the key role played by swash mechanism in the reflection rate and frequency selection. More investigation is needed to describe the reflection process and its link with shoreface evolution, moving toward a swash-by-swash approach.

Analysis of morphodynamic beach states along the South Brittany coast

This study presents a classification of morphodynamic beach states monitored along the South Brittany coast, on the western part of France. The investigated area faces the Atlantic Ocean and it is exposed to prevailing wind and waves mainly coming from the NW to SW and experience similar waves and wind climates as most beaches located on the French Atlantic coast. However, morphological settings of Brittany coast display more specific characteristics which contribute to make the morphodynamic beach behaviours more complex. To characterise the morphodynamic beach states, a beach survey programme was carried out from February 2008 to June 2009. Twenty five beaches were surveyed. Beach profiles were levelled from the toe of the dune to the water level line using a TRIMBLE electronic theodolite. Wave data were obtained from two offshore buoys, named l’Ile d’Yeu Nord (8503) and Le plateau du Four (04403), and owned by CETMEF (Centre d'Etudes Techniques Maritimes Et Fluviales). Wave characteristics used include significant wave height (Hs) and its associated period (Ts). Morphodynamic beach states were determined by the surf scaling and the surf similarity parameters using breaker wave’s height values derived from offshore wave height. Temporal changes of morphodynamic beach states were assessed in relation with beaches profiles and hydrodynamic factors variations. Six different morphodynamic beach behaviours were identified, mainly varying between reflective and intermediate states. Multivariate statistical analyses were then carried out to assess the main factors driving morphologic and morphodynamic beach disparities. Obtained results are related to both coastline orientation and nearshore bedrocks distribution, enhancing the role of these specific morphologic constraints in the complex behaviour of South Brittany coast.

Near shore waves, long-shore currents and sediment transport along micro-tidal beaches, central west coast of India

Coastlines are undergoing constant geomorphologic changes with respect to the incident wave climate. Based on waves measured at 9 m water depth, simulation of near shore wave transformation is done using REFDIF-1 numerical model and the near shore breaker parameters are estimated at two micro-tidal beaches along central west coast of India. Model results are validated with measured values. From the breaker parameters, long-shore current and long-shore sediment transport rates (LSTR) are computed by using semi-empirical equations. Estimated long-shore current and LSTR are showing dramatic variations with respect to seasons. Predominant direction of LSTR is observed towards north since the approach waves are from south-west direction during pre-monsoon and post monsoon. During monsoon season, waves are from west south-west and resulted in southerly transport. The estimated annual net and gross LSTR by Cambridge Environmental Research Consultants (CERC) at two locations are in the same order whereas LSTR estimated by Walton & Bruno and Kamphuis equations are showing different estimations because of difference in surf-zone width and foreshore slope between the two locations. For micro-tidal beaches with length less than 6 km, Kamphuis equation is giving agreeable estimation of LSTR. Sensitivity analysis of LSTR estimate shows that coastal inclination is the prominent factor in determining LSTR than incident wave angle.

Runup variability due to time dependence and stochasticity in the beach profiles: two extreme cases of the Spanish coast

ABSTRACT Diaz-Sanchez, R., Lopez-Gutierrez, J.S., Lechuga, A., Negro, V., 2013. Runup variability due to time dependency and stochasticity in beach profiles. In: Green, A.N. and Cooper, J.A.G. (eds.), Proceedings of the 13th International Coastal Symposium (Durban, South Africa), Journal of Coastal Research, Special Issue No. 70, pp. 001-006, ISSN 0749-0208. Equations for extreme runup worked out from several experimental studies are compared. Infragraviatory oscillations dominate the swash in a dissipative state but not in intermediate reflective states. Therefore two kinds of equation depending on either significant wave height, H0, or the Iribarren number, ξ0, should be used. Through a sand bed physical model with a uniform sand bed slope, equations are proposed for both beach states, and results are compared with precedent field and physical model experiments. Once the equations are chosen, the time-longshore variability in a medium long term time scale of the foreshore slope is evaluated in two extre...

Formation and development of a breaker bar under regular waves. Part 2: Sediment transport and morphology

In Part 2 of this work, the hydrodynamic model described in Part 1 is applied for the simulation of sediment transport and the associated morphological development of breaker bars. The sediment description is split into bed load and suspended load, and like the hydrodynamics the sediment transport is phase-resolved in order to get on- and offshore directed contributions to the sediment transport from phase lags between the suspended sediment and the hydrodynamics.First, the sediment transport over a morphologically fixed bed of a constant slope is considered, and the transport rates are discussed in terms of three dimensionless parameters: the surf similarity parameters (ζ0) and two variants of Dean's parameter (ΩD and ΩHK). These cover the ranges ζ0∈[0.08, 1.19], ΩD∈[1.1, 27.7] and ΩHK∈[0.01, 0.52].Secondly, the morphological development of the cross-shore profile is considered, where the initial condition is a profile of constant slope. One reference simulation is discussed in detail and the morphological development due to changes in the hydrodynamic forcing (wave period, wave height, wave irregularity and a net cross-shore current) and in other properties (sediment size and beach slope) is discussed relative to the reference simulation.The coupling between sediment transport rate and morphology is analysed and discussed.

Formation and development of a breaker bar under regular waves. Part 1: Model description and hydrodynamics

In this work a detailed hydrodynamic model is presented, which is used for the study of cross-shore sediment transport and morphodynamics in two dimensions. The model is described in the framework of the generally unstructured, finite volume method. Considerable emphasis is put on those subtleties in the morphological formulation, which are required to achieve mass conservation for the amount of sediment in the bed and in suspension.In this first part of two, the hydrodynamic description over the cross-shore profile is presented. The model is validated against an experiment with detailed measurements of the free surface and turbulence over a fixed breaker bar profile. A test matrix covering a large interval of the surf similarity parameter is simulated, and the phase lag between the breakpoint and the initiation of the setup is described. The relation of this phase lag to a cross-shore delay in dissipation of organised energy into turbulence is described. The relation of this phase lag to the distribution of the location of maxima in bed shear stresses and magnitude of the undertow is also described.Furthermore, processes in the hydrodynamics, which will have a smoothing effect on the mean cross-shore sediment transport and morphodynamic response are considered.All simulations are presented for regular waves and for values of the deep-water surf similarity parameter, ζ0, in the range from 0.08 to 1.19, i.e. covering both spilling and plunging breakers.

Seasonal morphodynamic classification of beaches in Necochea municipality, Buenos Aires Province, Argentina

The seasonal morphodynamic classification of Necochea and Quequén beaches (Buenos Aires Province, Argentina) was determined. Based on 102 seasonal beach profiles and sediment sampling between February 2006 and December 2009, variations in morphology and sediment budgets of five beaches were studied. According to the dimensionless fall parameter and the relative tide range, the beaches were classified depending on their modal morphodynamic state. In Quequén, beaches presented intermediate and reflective states, whereas in Necochea they presented dissipative states. The Iribarren number showed that plunging and spilling breakers predominated in Quequén and Necochea, respectively. In winter, the beaches became more dissipative, while in summer-autumn they were more reflective. This general behavior agrees with the erosion/accretion cycles. Beach profile variability was higher in Quequén. These results have been used to elaborate the coastal management program of the area.

Reduction of maximum tsunami run-up due to the interaction with beachfront development – application of single sinusoidal waves

Abstract. Experiments are presented that focus on the interaction of single sinusoidal long waves with beachfront development on the shore. A pump-driven methodology is applied to generate the tested waves in the wave flume. The approaching waves firstly propagate over a horizontal bottom, then climbing up a 1 in 40 beach slope. The experiments reported here are confined to the surf similarity parameter of the waves ranging from ξ =7.69–10.49. The maximum run-up of the tested waves under undisturbed conditions agrees well with analytical results of of Madsen and Schäffer (2010). Beachfront development is modelled with cubic concrete blocks (macro-roughness (MR) elements). The obstruction ratio, the number of element rows parallel to the shoreline as well as the way of arranging the MR elements influences the overall reduction of maximum run-up compared to the undisturbed run-up conditions. Staggered and aligned as well as rotated and non-rotated arrangements are tested. As a result, nomograms are finally compiled to depict the maximum run-up reduction over the surf similarity parameter. In addition, some guidance on practical application of the results to an example location is given.

Shoaling internal solitary waves

The evolution and breaking of internal solitary waves in a shallow upper layer as they approach a constant bottom slope is examined through laboratory experiments. The waves are launched in a two‐layer fluid through the standard lock‐release method. In most experiments, the wave amplitude is significantly larger than the depth of the shallow upper layer so that they are not well described by Korteweg‐de Vries theory. The dynamics of the shoaling waves are characterized by the Iribarren number, Ir, which measures the ratio of the topographic slope to the square root of the characteristic wave slope. This is used to classify breaking regimes as collapsing, plunging, surging, and nonbreaking for increasing values of Ir. For breaking waves, the maximum interface descent, , is predicted to depend upon the topographic slope, s, and the incident wave's amplitude and width, Asw and Lsw, respectively, as . This prediction is corroborated by our experiments. Likewise, we apply simple heuristics to estimate the speed of interface descent, and we characterize the speed and range of the consequent upslope flow of the lower layer after breaking has occurred.

사석방파제 위에 피복한 Rakuna-IV의 안정공식

In this study, a total of 51 cases of hydraulic model tests has been conducted for various wave conditions and slope angles of breakwater to develop a stability formula for Rakuna-IV armoring a rubble-mound breakwater. The stability number of the formula is expressed as a function of relative damage, number of waves, structural slope, and surf similarity parameter. The stability formula is derived separately for plunging and surging waves, the greater of which is used. The transitional surf similarity parameter from plunging waves to surging waves is also presented. Lastly, to explain the stability of Rakuna-IV to the engineers who are familiar with the stability coefficient in the Hudson formula, the required weight of Rakuna-IV is calculated for varying significant wave height for typical plunging and surging wave conditions, which is then compared with those of the Hudson formula using several different stability coefficients.

Experimental Investigation of Wave Structure Interactions

In the present work, physical models have been built to experimentally investigate the wave structure interactions. The paper is focusing on the effects of wave overtopping on wave reflection and wave forces at a seawall. The tests are implemented in the laboratory of the Coastal Engineering Research Center, the University of Queensland. The seawall model testing was performed in a wave flume using regular waves. Three types of waves that influence the relationship between wave overtopping and wave force on seawall are considered; non-breaking waves, waves breaking on the wall, and broken waves impacting on the wall. In order to approximate wave reflection from a vertical seawall fronted by a smooth impermeable slope, the Seelig method is adopted to estimate the wave reflection coefficients in cases of overtopping. The unknown coefficients of this approach have been estimated from fitting of the experimental data obtained in this study. The resulting formula is applicable for a range of the surf similarity parameter between 1.0 and 4.5 . The predicted reflection coefficients exhibit a good level of agreement with those measured. A power law type expression, written in terms of dimensionless parameters, is introduced to estimate the wave forces on a vertical seawall during wave overtopping. The regression shows good correlation to the data by using this form of equation.

Direct estimation wave setup as a medium level in swash

Díaz-Sánchez, R., López-Gutiérrez, J.S., Lechuga, A., Negro, V., Esteban, M.D., 2013. Direct estimation wave setup as a medium level in swash.The extreme runup is a key parameter for a shore risk analysis in which the accurate and quantitative estimation of the upper limit reached by waves is essential. Runup can be better approximated by splitting the setup and swash semi-amplitude contributions. In an experimental study recording setup becomes difficult due to infragravity motions within the surf zone, hence, it would be desirable to measure the setup with available methodologies and devices. In this research, an analysis is made of evaluated the convenience of direct estimation setup as the medium level in the swash zone for experimental runup analysis through a physical model. A physical mobile bed model was setup in a wave flume at the Laboratory for Maritime Experimentation of CEDEX. The wave flume is 36 metres long, 6.5 metres wide and 1.3 metres high. The physical model was designed to cover a reasonable range of parameters, three different slopes (1/50, 1/30 and 1/20), two sand grain sizes (D50 = 0.12 mm and 0.70 mm) and a range for the Iribarren number in deep water (ξ0) from 0.1 to 0.6. Best formulations were chosen for estimating a theoretical setup in the physical model application. Once theoretical setup had been obtained, a comparison was made with an estimation of the setup directly as a medium level of the oscillation in swash usually considered in extreme runup analyses. A good correlation was noted between both theoretical and time-averaging setup and a relation is proposed. Extreme runup is analysed through the sum of setup and semi-amplitude of swash. An equation is proposed that could be applied in strong foreshore slope-dependent reflective beaches.

長・短周期合成波における遡上域の範囲に関する実験的研究

Experiments on swash zone range by short waves, long waves and their combined waves respectively are conducted both on a steep and on a gentle slope. Long waves which form standing waves at the shoreline provide swash oscillation, and short waves which break and are partially reflected give both wave set-up and the small oscillation. Max run-up and max run-down height of the combined waves are evaluated by linear sum of those heights by component waves. In addition, the heights as well as the median of swash zone range of regular waves are expressed by functions of surf similarity parameter.

Nonlinear run-ups of regular waves on sloping structures

Abstract. For coastal risk mapping, it is extremely important to accurately predict wave run-ups since they influence overtopping calculations; however, nonlinear run-ups of regular waves on sloping structures are still not accurately modeled. We report the development of a high-order numerical model for regular waves based on the second-order nonlinear Boussinesq equations (BEs) derived by Wei et al. (1995). We calculated 160 cases of wave run-ups of nonlinear regular waves over various slope structures. Laboratory experiments were conducted in a wave flume for regular waves propagating over three plane slopes: tan α =1/5, 1/4, and 1/3. The numerical results, laboratory observations, as well as previous datasets were in good agreement. We have also proposed an empirical formula of the relative run-up in terms of two parameters: the Iribarren number ξ and sloping structures tan α. The prediction capability of the proposed formula was tested using previous data covering the range ξ ≤ 3 and 1/5 ≤ tan α ≤ 1/2 and found to be acceptable. Our study serves as a stepping stone to investigate run-up predictions for irregular waves and more complex geometries of coastal structures.

BONDED POROUS REVETMENTS – EFFECT OF POROSITY ON WAVE-INDUCED LOADS AND HYDRAULIC PERFORMANCE

The porosity and roughness of bonded revetments are both crucial for the hydraulic performance and the wave loading of the revetment and its foundation, and thus for the stability and durability of the entire structure. This is briefly shown by the selected results of a tentative comparative analysis of two large-scale test series performed in the Large Wave Flume (GWK) Hanover with two significantly different revetments: a highly porous and rough polyurethane bonded aggregate (PBA) revetment and an almost impermeable and relatively smooth interlocked pattern placed block (IPPB) revetment. These results motivated the initiation of the three years research project BoPoRe (Bonded Porous Revetments) which has the primary objective to investigate more systematically and separately the relative importance of both porosity and roughness for different slope steepnesses. This project is briefly introduced and the first results of preliminary scale model tests using 9 configurations for the porosity and roughness of the revetment subject to a wide range of wave conditions (surf similarity parameters 0.93-7.21) are briefly discussed.

Improvements in spectral wave modeling in tidal inlet seas

The performance of the spectral wind wave model SWAN in tidal inlet seas was assessed on the basis of extensive wave measurements conducted in the Amelander Zeegat tidal inlet and the Dutch Eastern Wadden Sea, as well as relevant data from other inlets, lakes, estuaries and beaches. We found that the 2006 default SWAN model (version 40.51), the starting point of the investigation, performed reasonably well for measured storm conditions, but three aspects required further attention. First, over the near‐horizontal tidal flats, the computed ratio of integral wave height over water depth showed an apparent upper limit using the default depth‐limited wave breaking formulation and breaker parameter, resulting in an underprediction of wave heights. This problem has been largely solved using a new breaker formulation. The second aspect concerns wave‐current interaction, specifically the wave age effect on waves generated in ambient current, and a proposed enhanced dissipation in negative current gradients. Third, the variance density of lower‐frequency wind waves from the North Sea penetrating through the inlets into the Wadden Sea was underpredicted. This was improved by reducing the bottom friction dissipation relative to that of the default model. After a combined calibration, these improvements have resulted in a relative bias reduction in Hm0 from −3% to −1%, in Tm−1,0 from −7% to −3%, and in Tm01 from −6% to −2%, and consistent reductions in scatter, compared to the 2006 default model.

Nearshore internal bores and turbulent mixing in southern Monterey Bay

We observed transient stratification and mixing events associated with nearshore internal bores in southern Monterey Bay using an array of instruments with high spatial and temporal resolution. The arrival of the bores is characterized by surging masses of dense (cold) water that tend to stratify the water column. The bore is followed by a gradual drop in the temperature throughout the water column over several hours (defined here as the bore period) until a sharp warm‐front relaxation, followed by high frequency temperature fluctuations, returns the column back to nearly its original state (defined here as the mixing period). Mixing periods revealed increased temperature variance at high frequencies (ω > ), as well as a greater percentage of events where dynamic instabilities may be present (Ri< 0.25), suggesting active mixing of the stratified water column. Turbulent dissipation rates in the stratified interior during the mixing period, estimated using the technique of isopycnal slope spectra, revealed mean values the same order of magnitude as near‐bed bottom‐generated turbulence. Observations indicate that local shear‐produced turbulent kinetic energy by the warm front relaxations dominates mixing in the stratified interior. The non‐canonical nature of these bore and relaxation events is also investigated with a numerical model, and the dynamics are shown to depend on the internal Iribarren number. Our results suggest that nearshore internal bores interacting with local bathymetry dramatically alter local dynamics and mixing in the nearshore with important ecological implications.

Free-stream velocity descriptions under waves with skewness and asymmetry

In shallow water, when waves shoal their orbital velocities exhibit skewness (velocity skewness) and asymmetry (acceleration skewness) in response to corresponding changes in the free surface. Near the bed, changes in the skewness and asymmetry of the time-varying velocities have important consequences for the residual velocities ‘spun up’ by the bottom friction and for sediment transport. In the wave boundary layer, where the largest sediment transport often occurs, there is a need to represent the free-stream velocity (the orbital velocity at the edge of the wave boundary layer) in a systematic way such that it can be mimicked in wave tunnel experiments and wave boundary layer models which usually do not represent the free surface. Since there is no readily accessible dynamical theory for shoaling waves that includes both skewness and asymmetry, it is necessary to synthesize the shoaling effect in a free-stream velocity description that is general enough to fit observed velocity time series. This paper reviews previous free-stream velocity descriptions, including the description of Abreu et al. (2010), and introduces a new description based on generalising a sawtooth wave shape. The paper quantifies all the relevant measures of skewness and asymmetry for each description. It then demonstrates that Abreu et al.'s (2010) description represents the most general one and improves upon their fitting techniques to observed free-stream velocities to further simplify it. When this description is used in conjunction with a characterisation of the velocity for irregular waves, such as that of Elfrink et al. (2006), it is possible to relate velocity skewness and asymmetry directly to the non-dimensional wave and beach parameters (wave height, surface wavelength and surf similarity parameter as a proxy for beach slope). MATLAB scripts are provided for the improved description of Abreu et al. (2010) and Elfrink et al.'s (2006) characterisation.

Toward reliable storm-hazard forecasts: XBeach calibration and its potential application in an operational early-warning system

The study aims to calibrate/validate and apply the dune-erosion model, XBeach, in order to predict morphological response to storm events along a meso-tidal, steeply sloping beach. More than 10,000 XBeach calibration runs, including different model parameters and erosion events, were compared with measurements of beach-profile response to storm conditions. Off-shore wave and tidal measurements were used as input for a SWAN wave model, which was used to provide wave conditions to XBeach. The results indicate that using XBeach to predict beach-profile morphodynamic response during storm events on steeply sloping intermediate-to-reflective beaches may be more demanding than for dissipative beaches and that the default model setup can overestimate dune/beach-face erosion. The performance of the model after calibration was satisfactory, with Brier Skill Scores from 0.2 to 0.72. XBeach was found to be more sensitive to input parameters such as the beach-face slope and the surf similarity parameter ξ (especially for values ξ > 0.6). The calibrated XBeach setup was used for simulations of storm scenarios with different return periods (5, 25, and 50 years), and the simulations highlighted the fragility of the dune field and the potential for storm-induced dune retreat, lowering, and overwash in the study area. Finally, the nested SWAN/XBeach models were forced by an existing operational wave-forecast WAVEWATCH-III/SWAN model, operated by the Portuguese Hydrographic Institute to generate daily forecasts of storm impact and serve as a prototype-case for an early warning system for storm hazard mitigation.

Suction Removal of Sediment from between Armor Blocks. III: Breaking Waves

When a sediment beach covered by stones or an armor layer is exposed to breaking waves, the turbulence generated by the breaking waves can cause mobilization and removal of the sediment underneath the stones. In two earlier studies by the Technical University of Denmark (DTU)-group, the suction removal of sediments from between armor blocks has dealt with the case of steady current and nonbreaking waves. The present study is an extension of these studies and the results will be presented in a similar way. The critical conditions for removal of sediment are determined. It is found that the onset of removal of sediment is governed by three parameters: (1) the sediment mobility (based on the sediment size, wave height, and wave period), (2) the ratio between the sediment size and the stone size, d/D, and (3) surf similarity parameter, ξ=tan(β)/(H0/L0)0.5. The variation of the critical mobility number for removal of sediment as function of d/D and ξ is determined for the range 0.001<d/D≤1.0 and 0.15<ξ<6.00. The experiments were made on 1∶2, 1∶14, and 1∶30 slopes. Spilling, plunging, and surging breakers were used in the experiments. Both one and two layers of armor stones and rectangular blocks were studied.