Breaking Wave Height Research Articles

Sea-Level Rise and Coastal Submergence along the South–East Coast of Nigeria

Coastal submergence and shoreline retreat constitute a serious threat to shoreline management in the Niger Delta. Short-term and long-term changes on the shoreline adjoining Qua-Iboe River estuary, south-east coast of Nigeria are analysed to assess the impact of sea-level rise and climate change on the shoreline. A comparison of the 2002 and 2013 editions of the maps of the shoreline indicates a landward retreat of the shoreline and a submergence of village of Itak Abasi in the Atlantic Ocean over an estimated area of 180000 m2 along the coastline. Analysis of shoreline changes over neap-spring tidal phase confirmed that the submerged area of the updrift shoreline was threatened by severe and chronic erosion in which the rate has reduced to 178 m3 per day. The downdrift experienced high rate of accretion at 1490 m3 per day with sediment gained from the updrift shoreline and the ebb tidal delta as well as input from fluvial discharge into the estuary. Near-shore wave climate was characterized by the wave breaker heights which fluctuated between 30 cm and 70 cm at a period which ranged between 5 to 8 seconds, the occurrence of edge waves during mid-flood tidal stage along the mid foreshore, predominantly eastward directed long-shore currents and storm surge events at the updrift shoreline are considered as the hydrodynamic processes which caused the shoreline retreat and submergence. The intensity and magnitude of the impact of the processes on the shoreline are attributed to sea-level rise and climate change. Sustainable shoreline management strategies including measures for mitigations and adaptations to climate change are recommended.

A quantitative sedimentary model for the modern lacustrine beach bar (Qinghai Lake, Northwest China)

Lake beach bar sandstone has been regarded as an important oil and gas reservoir in China. However, types and depositional mechanisms of the sandstone have not yet been fully studied. In this study, we analyzed modern beach bars in Qinghai Lake, the largest modern lake in China. The key factors controlling beach bar development in the lake were found to be wave length and height, lakeshore terrain, and material supply. Sedimentary models were established based on modern coastal dynamic theory. Beach bars were divided into breaking and surf bars. Breaking bars develop near the breaking zone where water depth is a function of wave height and length. Maximum breaking bar thickness is calculated from the difference between breaking point depth and breaking wave height. Surf bars develop in the surf zone where surf water depth equals breaking wave height. Maximum surf bar thickness is given by the breaking wave height. Wind waves play an important role in the location and construction of Qinghai Lake beach bars.

Research and Analysis on the Wave Transformation and Irregular Wave Breaking Criterion on the Shore

Within the surf zone which is the region extending from the seaward boundary of wave breaking to the limit of wave uprush, breaking waves are the dominant hydrodynamics acting as the key role for sediment transport and beach profile change. Breaking waves exhibit various patterns, principally depending on the incident wave steepness and the beach slope. Based on the equations of conservation of mass, momentum and energy, a theoretical model for wave transformation in and outside the surf zone was obtained, which is used to calculate the wave shoaling, wave set-up and set down and wave height distributions in and outside the surf zone. The analysis and comparison were made about the breaking point location and the wave height variation caused by the wave breaking and the bottom friction, and about the wave breaking criterion under regular and irregular breaking waves. Flume experiments relating to the regular and irregular breaking wave height distribution across the surf zone were conducted to verify the theoretical model. The agreement is good between the theoretical and experimental results.

Oil slicks on water surface: Breakup, coalescence, and droplet formation under breaking waves

The ability to calculate the oil droplet size distribution (DSD) and its dynamic behavior in the water column is important in oil spill modeling. Breaking waves disperse oil from a surface slick into the water column as droplets of varying sizes. Oil droplets undergo further breakup and coalescence in the water column due to the turbulence. Available models simulate oil DSD based on empirical/equilibrium equations. However, the oil DSD evolution due to subsequent droplet breakup and coalescence in the water column can be best represented by a dynamic population model. This paper develops a phenomenological model to calculate the oil DSD in wave breaking conditions and ocean turbulence and is based on droplet breakup and coalescence. Its results are compared with data from laboratory experiments that include different oil types, different weathering times, and different breaking wave heights. The model comparisons showed a good agreement with experimental data.

Theoretical and Observed Breaking Wave Height on a Barred Macrotidal Beach: Implications for the Estimation of Breaker Index on Beaches with Large Tidal Range

ABSTRACT Hequette, A. and Cartier, A., 2016. Theoretical and observed breaking wave height on a barred macrotidal beach: Implications for the estimation of breaker index on beaches with large tidal range. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 861–866. Coconut Creek (Florida), ISSN 0749-0208. Although a large number of studies were dedicated to the observation and prediction of wave height at breaking, field investigations were essentially carried out in micro- to mesotidal environments. Here we report the results of a study conducted on a barred macrotidal beach of northern France during which video observations of wave breaking were carried out simultaneously with measurements of wave data using a series of hydrodynamic instruments deployed across the intertidal and the nearshore zones and an offshore wave buoy. Our results show that wa...

On the distribution of wave height in shallow water

The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (Longuet-Higgins, 1952) and Weibull distributions (Forristall, 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth requires new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull–Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, HS, local wave-number, kL, and water depth, d), using data from both laboratory and field measurements from 4 offshore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche, 1944) and adopts HS as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is effectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

Prediction of Incipient Breaking Wave-Heights Using Artificial Neural Networks and Empirical Relationships

The accurate prediction of shallow water breaking heights is paramount to better understanding complex nonlinear near shore coastal processes. Over the past 150 years, numerous empirical relationships have been proposed based on scaled laboratory datasets. This study utilizes a newly available field collected full-scale dataset of breaking wave conditions to investigate the accuracy of published empirical models and a novel artificial neural networks (ANN) model in predicting the final breaking wave-height for laboratory-scaled and full-scaled ocean waves. Performance is measured by comparison against both the field datasets and 465 separate datasets from 11 independent laboratory studies. The relationship of Rattanapitikon and Shibayama [2000 “Verification and modification of breaker height formulas,” Coastal Eng. J. 42 (4), 389–406.] outperformed all available empirical models when tested against only laboratory datasets, but was superseded by the relationship of Robertson et al. [2015 “Remote sensing of irregular breaking wave parameters in field conditions,” J. Coastal Res. 31 (2), 348–363.] when tested against only field datasets. However, this study noted that models developed based on scaled laboratory tests tend to underestimate the ocean full-scale breaking wave-heights. The training and testing of the ANN model were accomplished using 75% and 25% of the combined field and laborartory datasets. The ANN models consistently outperformed predictive accuracy of empirical models. Sensitivity analysis of the trained ANN models quantified the relative impact of individual wave parameters on the final breaking wave-height.

Estimation of Shallow-Water Breaking-Wave Height From Synthetic Aperture Radar

The relationship between synthetic aperture radar (SAR) signatures of depth-limited breaking waves and wave height is studied. Wave height is estimated from SAR images using an empirically derived relationship that exploits the azimuthal shift in SAR images associated with moving scatterers. This relationship is derived from in situ measurements rather than from an idealized model of breaking waves as was done in a previous study. We find that the lengths of the SAR signatures are correlated with the observed significant wave height (the correlation coefficient is 0.78) for a range of wave conditions. The relationship between the wave heights and velocity bandwidths from the field data is similar to that between simulated (with a Boussinesq surface wave model) wave heights and velocity ranges (correlation $\mbox{coefficient}=0.82$ ).

Longshore Sediment Transport along the Coast of Kerala in Southwest India

Accurate estimation of longshore sediment transport (LST) along the entire coastal stretch of Kerala is challenging as the sediment transport pattern varies both spatially and temporally depending on the nearshore wave climate, nearshore bedslope, shoreline orientation, coastal morphology, presence of hard structures etc. While majority of the locations show a net northerly drift, there are certain stretches of the coast which are dominated by southerly transport. For the estimation of longshore sediment transport the three commonly used formulae viz. CERC (SPM (1984)), Van Rijn (1991) and Kamphuis (2002) were considered. After detailed analysis of the computed LST results for different sectors of the coast using these formulae, the formula of Kamphuis (2002) which considers all the important parameters like the nearshore bed slope, sediment grain size and peak wave period in addition to the usual input parameters like the wave breaker height and wave breaker angle was selected as the most appropriate one. To understand the spatial and temporal variation in the LST pattern along the Kerala coast, the LST rates for eight important locations - viz. Trivandrum, Quilon, Aleppey, Andhakaranazhi, Nattika, Calicut, Kannur and Kasargod spread along the Kerala coast were computed adopting the Kamphuis (2002) formula. For computation of the LST rates for the eight locations, the one year site specific nearshore wave data derived from numerical model studies was used. For validation, the results were compared with that of the earlier estimations available in literature. It was observed that even though the net magnitude was of the same range, there were deviations in the direction. However, when the results were compared with field observations (where morphological indicators were used) a reasonable agreement could also be established for the directions. The net annual longshore sediment transport was found to vary between 0.32 x 105 m3 and 2.3 x 105 m3 along the Kerala coast and the net transport direction was pre-dominantly northerly for almost all the locations selected for the study. The maximum gross sediment transport of 12.85 x 105 m3 was obtained for Trivandrum but the net transport for this station was much less, and therefore comparable with other locations.

REMOTE MEASUREMENT AND PREDICTION OF BREAKING WAVE PARAMETERS

The analysis of wave breaking in shallow water has been on-going for almost 150 years. Numerous research papers have been published that investigate methods to predict breaking conditions and the geometric characteristics of breaking waves. This study presents a novel, safe, and low cost method to extract breaking wave properties from irregular waves in the surf zone, using optical and in-situ measurement systems. Sensitivities studies on methods of measuring the breaking water depth are compared and the water depth at the wave trough depth, corrected for optical offsets using a still water correction of 1/3 wave height, is found to be exhibit the least variability. A new effective seafloor slope definition, based on individual breaking wavelength to depth ratios, was found to increase predictive ability over previously variable seafloor slope extraction methods. Collected field data is compared against established breaking wave height formulas with general exponential form consistently finding best correlation. An optimized breaking wave height predictor featured a root mean square relative error of only 1.672% against the measured dataset. Finally, the study of the geometric shape of the plunging wave vortex as a possible indicator for the breaking intensity of ocean waves has been ongoing for almost 50 years with limited success. The validity of using the vortex ratio and vortex angle as a method of predicting breaking intensity is examined. Through the first complete analysis of field collected irregular wave breaking vortex parameters it is illustrated that the vortex ratio and vortex angle cannot be accurately predicted using standard breaking wave characteristics and hence are not suggested as a possible indicator for breaking intensity

Observations and estimates of wave‐driven water level extremes at the Marshall Islands

AbstractWave‐driven extreme water levels are examined for coastlines protected by fringing reefs using field observations obtained in the Republic of the Marshall Islands. The 2% exceedence water level near the shoreline due to waves is estimated empirically for the study sites from breaking wave height at the outer reef and by combining separate contributions from setup, sea and swell, and infragravity waves, which are estimated based on breaking wave height and water level over the reef flat. Although each component exhibits a tidal dependence, they sum to yield a 2% exceedence level that does not. A hindcast based on the breaking wave height parameterization is used to assess factors leading to flooding at Roi‐Namur caused by an energetic swell event during December 2008. Extreme water levels similar to December 2008 are projected to increase significantly with rising sea level as more wave and tide events combine to exceed inundation threshold levels.

Application of a fuzzy inference system for the prediction of longshore sediment transport

A fuzzy inference system (FIS) and a hybrid adaptive network-based fuzzy inference system (ANFIS), which combines a fuzzy inference system and a neural network, are used to predict and model longshore sediment transport (LST). The measurement data (field and experimental data) obtained from Kamphuis [1] and Smith et al. [2] were used to develop the model. The FIS and ANFIS models employ five inputs (breaking wave height, breaking wave angle, slope at the breaking point, peak wave period and median grain size) and one output (longshore sediment transport rate). The criteria used to measure the performances of the models include the bias, the root mean square error, the scatter index and the coefficients of determination and correlation. The results indicate that the ANFIS model is superior to the FIS model for predicting LST rates. To verify the ANFIS model, the model was applied to the Karaburun coastal region, which is located along the southwestern coast of the Black Sea. The LST rates obtained from the ANFIS model were compared with the field measurements, the CERC [3] formula, the Kamphuis [1] formula and the numerical model (LITPACK). The percentages of error between the measured rates and the calculated LST rates based on the ANFIS method, the CERC formula (Ksig=0.39), the calibrated CERC formula (Ksig=0.08), the Kamphuis [1] formula and the numerical model (LITPACK) are 6.5%, 413.9%, 6.9%, 15.3% and 18.1%, respectively. The comparison of the results suggests that the ANFIS model is superior to the FIS model for predicting LST rates and performs significantly better than the tested empirical formulas and the numerical model.

Lagrangian description of gravity-capillary waves propagating on a sloping bottom

An asymptotic solution that describes a small amplitude gravity-capillary wave propagating on the surface of a gentle sloping beach is derived in the Lagrangian coordinates. The analytical solution in Lagrangian form satisfies the zero pressure at the free surface. In the Lagrangian approximation, the parametric expression of water particles can be obtained directly and explicitly as a function of the wave steepness, the bottom slope and surface tension. The analytical solution for wave asymmetry parameter up to the breaker line for an arbitrary bottom slope can also be derived. The Lagrangian solution enables the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile which leads to wave breaking. Furthermore, by comparing the theoretical values of wave asymmetry with experimental results, it is found that theoretical results of the present solution are in good agreement with the experimental data. It is also found that surface tension lower the breaking wave height, lengthen the wave length and increase the breaking water depth.

The Review of Studies on Formulas for Calculating Wave Breaking Height

Wave breaking is the most complex and intensified physical process in coastal zone. And as the maximum in this area, the breaking wave height has a major impact on ocean engineering and ship sailing. In this paper, the present calculation methods for breaking height are concluded and divided into two categories: one is directly computing models using deep wave elements; the other is indirectly calculation models based on the surf wave calculation model and the criterion of breaking.

Experimental and Lagrangian modeling of nonlinear water waves propagation on a sloping bottom

This paper presents an experimental and theoretical investigation of nonlinear water wave propagation over a sloping bed. Firstly, a series of monochromatic wave laboratory experiments were performed in order to measure the particle trajectories, evolution of wave profile, and wave phase velocity as wave propagates on a sloping bottom. The particle trajectories are quantified by means of images from a high speed camera, whereas the evolution of wave profile and variation of wave phase velocity are measured by a wave gauge array. Subsequently, the free-surface elevation, phase velocity, particle trajectories, and breaking wave height are estimated using a Lagrangian nonlinear wave transformation model. Model predictions show a reasonable agreement with experimental data.

Advective Diffusion of Contaminants in the Surf Zone

AbstractA theory on the horizontal spreading of contaminants in the surf zone is described in this paper. The surf zone is viewed as a narrow strip comparable to the characteristic wavelength, in which turbulence caused by wave breaking is strong. Flows inside the surf zone consist of both oscillatory motions and a steady current induced by breaking waves. The wave field in the shoaling zone is modeled by the linear theory for monochromatic waves, and it is assumed that the breaking wave height is proportional to the local depth in the surf zone. The simplest scenario of longshore current on a straight beach of constant slope is considered, for which the longshore current velocity is predicted by a slightly modified version of Longuet-Higgins' original theory developed in the 1970s. On the basis of the estimation that the time scale of horizontal diffusion is much longer than the wave period, the perturbation method of multiple scales is applied to derive the transport equation for the advective diffusion...

Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis

Khoury, A., Jarno-Druaux, A., and Marin, F., 2013. Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis Proceedings 12th International Coastal Symposium (Plymouth, England), Journal of Coastal Research, Special Issue No. 65, pp. 1791–1796, ISSN 0749-0208.-->Numerous studies have been carried out on sandy beach morphology; however, the physical processes which govern beach morphodynamic are still not well understood, despite the significance of this subject in view of the direct applications for coastal erosion. The present work brings a contribution to the study of these processes from well controlled tests carried out in a 10-m-long and 0.49-m-wide wave flume with macro – and mega-tidal regime simulations. The tests were carried out with very fine or fine sand of relative density s=2.65. The incident waves and the free surface in the shoaling zone were measured with resistive probes. The wave breaking height and the free surface in the swash zone were recorded with an optical method. The temporal evolution of bottom profiles was obtained using an acoustic method. Intertidal bars were generated; such bars were previously not observed in physical modeling to the authors' knowledge. Present experimental results are compared with field observations. Formation processes of intertidal bars are analyzed; we show in particular the significant effect of the relative tide range, of waves asymmetry, and of subtidal bars on these processes. Small local variations of the beach profile in the surf zone exhibit significant outcomes on the runup.

EFFECTS OF CROSS SHORE PROFILES ON THE SUSTAINABLE DESIGN OF COASTAL STRUCTURES

The performance of the existing coastal structures at different locations along Alexandria coastline, Egypt was re-examined. These coastal structures have been constructed (1998-2002) on Alexandria coastline during the phase of widening the coastal road. The constructions of these coastal structures, although protected the coastal road but didn’t maintain the sandy beaches. El-Sharnouby and Soliman (2011) studied the behaviour of these structures during a storm. This paper investigates the benefits of complementing the existing structures by adding limited modification. Three areas of different profiles and types of coastal protective works along Alexandria shoreline were selected to investigate their performance. The first area “Shatby” has a narrow sandy beach that is protected by a vertical seawall of 3-5 m above sea water level. The second area “Sporting” was protected by a revetment of 20-30 width with 10 ton concrete cubic blocks. In the third area “Loran”, revetment protected the shoreline against further erosion with beach profile completely covered by blocks, 
 Reeve et el. (2008) used a two dimensional Reynolds-Averaged Navier-Stokes (RANS) numerical model to obtain wave run-up and overtopping characteristics. This model was based on the work of Liu et al. (1999) and Lin and Xu, (2006). A proposed artificial offshore submerged breakwater was introduced to determine its impact on wave runup. Beach profile data were collected by Coastal Research Institute monitoring program for the Alexandria coastal area. Profiles‘surveying were carried out from a constructed land baseline to a water depth of 10.0 m below the M.W.L. The wave characteristics used at the three surveyed profiles are: significant wave height Hs = 1.00 m, dominant wave period = 6.0 sec with wave direction from N to NW. 
 
 Several coastal protection schemes were explored; submerged sills, T-groins,..etc. The objectives were to determine their effects on the reduction of wave breaking heights, wave run up as well as maintaining nourished sandy beaches. 
 
 The numerical model showed the reduction of wave runup (20%) by submerged reefs, however other design analyses would indicate that coupled systems could fulfil the sustainable design targets. However cost optimization as well as design risk level should play a rule in the final system selection. Detailed results are provided in the poster session as well as final paper.

APPLICATION OF AN AUTONOMOUS ROBOT FOR THE COLLECTION OF NEARSHORE TOPOGRAPHIC AND HYDRODYNAMIC MEASUREMENTS

Beach topographic and hydrodynamic measurements are essential for coastal geology and engineering studies as well as sustainable coastal management. Standard approaches involve either time-consuming manual data acquisition usually with limited coverage or remote sensing techniques which are usually characterized by low resolution or increased costs. The present contribution reports the results from the application of the autonomous robot RTS-Hanna with a calibrated sensor setup including 3D laser range scanners, a camera, a Differential GPS and an inertial measurement unit which significantly facilitates field data collection. RTS-Hanna was tested at the Wadden Sea Barrier Island Langeoog, Northern Germany, for two days and was proven capable of autonomously collecting topographic scans. 175 GB of dense topographic and water surface elevation data were collected, including RBG images, while RTS-Hanna covered a total of 21 km of coastline in approximately 3 hours. Scans of the surf/swash zone allowed continuous measurements of topographic changes at the beachface, wave propagation velocities and wave breaking heights.

Automated Detection of Breaking Wave Height Using an Optical Technique

Abstract SHAND, T.D.; BAILEY, D.G., and SHAND, R.D., 2012. Automated detection of breaking wave height using an optical technique. Obtaining accurate information of nearshore wave characteristics including the position and height of individual breaking waves is essential to understanding the drivers of coastal processes, for engineering design and hazard prediction. Demand for such information in real time for recreational planning and hazard assessment is also high. Remote optical techniques would offer considerable economic and spatial coverage advantages over conventional in situ instrumentation. However, optical methods for obtaining wave height information have been slow to develop and those available remain computationally expensive and require “favourable” environmental conditions. This paper presents a relatively simple yet robust approach to detecting and quantifying breaking wave position and height across a wide surf zone using a twin video camera configuration coupled with an image time-stack ...