Equilibrium Beach Research Articles

Experimental investigation of flow and sediment transport on an equilibrium beach formed by surging breaker

Flow patterns and sediment transport induced by breaking waves on a beach profile have been studied in a laboratory wave flume. Two parallel experiments were conducted on the same profiled rigid bed and sediment (mobile) bed, each subjected to identical wave forcing. The rigid bed experiments include measurements of bed shear stress and water-surface elevation, while the sediment bed experiments involve the measurement of pore-water pressures. The beach profile features a beach step leading to the generation of a hydraulic jump at the end of the rundown phase and accordingly forms a backwash vortex. The bed shear stress measurements revealed that the maximum onshore directed mean bed shear stress occurs after the wave breaking whereas the offshore directed one occurs during rundown at the same section. The increase of the bed shear stress with respect to that in the approaching wave boundary layer during the wave breaking and hydraulic jump processes can be by as much as a factor of 13 and 4, respectively. The effect of the wave breaking on turbulence is also more pronounced by a factor of 2.2 than the hydraulic jump in terms of r.m.s values of the fluctuating component of the bed shear stress. The pore pressure measurements showed that the vortex generated during the wave breaking creates an impulsive, upward-directed pressure gradient force that can be up to 1.2 times the submerged weight of the sediment. The sediment transport occurs in the sheet flow regime in a large part of the beach profile. The turbulence generated by the backwash vortex and the hydraulic jump at the beach step directly impacts the local sediment suspension which serves as the source for the advected sediment in the swash zone. The results are compared with a previous study that used the same methodology but involved plunging waves and the initial bed profile.

Simulation of the Evolution of Cross-Shore Beach Profiles using SBEACH Modelling

Coastal erosion significantly threatens sandy beaches worldwide, impacting coastal communities and ecosystems. This research investigates the application of SBEACH (Storm-induced BEAch Change), a numerical beach modelling computer programme, as a tool for coastal engineers to predict beach profile evolution in response to wave and tidal actions. The study used SBEACH simulations to explore the equilibrium beach profiles under varying conditions, including wave height, wave period, sediment grain size, and beach slope. This study also examined the effects of storm tides on equilibrium profiles and proposed protective sand dunes' dimensions to safeguard against storm surges. This research highlights SBEACH's potential as a valuable tool for assessing and planning coastal erosion mitigation strategies. While SBEACH provides insights into cross-shore beach profile dynamics, combining it with GENESIS offers a more comprehensive approach to coastal management. However, it is crucial to consider real-world engineering experience and safety factors when deciding on beach stabilisation and protection measures. Coastal countries can benefit from such modelling approaches to better manage and protect their sandy beaches, which play a crucial role in coastal defence and maintaining ecosystem integrity.

Experimental Analysis of the Changes in Coral Sand Beach Profiles under Regular Wave Conditions

This study utilized 50 laboratory experiments to document the evolution of coral beaches under varying regular wave conditions, including five distinct wave periods and ten wave heights. Both the type of equilibrium beach and the shape of sand bars were used to represent beach evolution. The evolution of coral sand beaches was then compared to quartz sand beaches. The experimental results show that the predicted (modeled) equilibrium profile of a quartz sand beach was not applicable to coral sand beaches. Compared to sand bars on quartz sand beaches, the distance from bar crests to the beach berm in coral sand beaches was greater, whereas the erosional depth of sand troughs was deeper. However, the grain size distribution of sand associated with the coral sand beach under wave action was consistent with Celikoglu’s law. Both an equilibrium beach profile classification model and a sand bar shape prediction model for coral sand beaches were developed based on the experimental data.

Shoreline response to sea-level rise according to equilibrium beach profiles

Shoreline position is a key parameter of a beach state, often used as a descriptor of the response of the system to changes in external forcing, such as sea-level rise. Changes in shoreline position are the result of coupled hydrodynamic and morphodynamic processes happening in the nearshore and acting at different temporal scales. Due to this complexity, methodologies aimed at reproducing shoreline evolution at decadal time scale require many simplifications. Simpler methods usually consider an equilibrium beach profile whose shape depends only on beach morphology, and whose location varies depending on incoming forcing. Here, we derive a general equation for shoreline evolution using equilibrium beach profiles. We particularize it based on several common assumptions, and evaluate changes on shoreline position caused by sea-level rise, combined with simultaneous wave and high-frequency sea-level forcing. We compare our model against other analytical equilibrium beach profile-based models and with a dynamic model explicitly computing sediment transport. Results indicate that: (i) it is necessary to consider the area of the emerged beach subject to marine forcing rather than focusing only on the submerged part, (ii) the rates of shoreline recession may change for narrow beaches, defined as those for which marine forcings act onto all of their aerial surface, and (iii) Bruun’s Rule can describe beach shoreline evolution, but the uncertainty in selecting the landward boundary of the active profile entails a huge uncertainty in the magnitude of shoreline evolution. This problematic uncertainty can be drastically reduced if instantaneous forcing conditions are used instead of the arbitrary emerged/submerged active profile boundaries typically defined by only one statistic parameter of extreme conditions.

NEW PROCESS BASED EQUATION FOR A STATIC EQUILIBRIUM BEACH PLANFORM

Equilibrium planform formulations of beaches are engineering tools for providing solutions for beach erosion problems. They aim at defining the final orientation of the beach on a scale of years and thus they are used for evaluating the shoreline response due to human interference (ports, breakwaters, protection works…etc). These formulations create engineering solution to numerous coastal stability problems. The Parabolic Bay Shape Equation (PBSE) proposed by Hsu and Evans (1989) is the most used equation and allow to solve problems. However, these shape equations are valid under certain simplifications. Therefore, they are unable to determine the beach planform when the bathymetry is complex, with rocky areas or/and islands. The aim of this study is to present a new equilibrium beach planform equation (Gainza et al. 2018) that overcomes the problem previously mentioned. What is more, an extension of the model is presented in order to modeled the shape of a shoreline on a given day.

Influence of the Initial Beach Profile on the Sediment Transport Processes During Post‐Storm Onshore Bar Migration

AbstractOnshore bar migration is a characteristic bar behavior during post‐storm beach recovery. The present large‐scale experiments, feature bichromatic wave groups over an initially steep (1:15), fully‐evolving beach. The same accretive wave condition is applied on two different post‐storm beach profiles featuring outer and inner bars. They are characterized by a larger (smaller) shoreline erosion and a larger (smaller) outer breaker bar located farther away from (closer to) the shoreline depending on the larger (smaller) energy of the storm condition. After a considerable post‐storm recovery time, similar equilibrium profiles are obtained, stressing the link between wave condition and equilibrium beach configuration. However, the evolution toward the equilibrium is different and depends on the initial morphological condition (post‐storm beach profile). After the larger storm, the morphological evolution is termed accretive merging (AM) and characterized by merging of the two bars (outer bar dissipation). After the smaller storm, the morphological evolution denoted as accretive non‐merging (AN) is characterized by onshore migration of the two bars with constant distance between them (bar maintenance). This study focuses on processes around the outer bar. During AN it features wave breaking, causing large suspended net offshore transport. AM, in contrast, mainly features bedload related to short wave asymmetries and low decomposed net transport rate magnitudes. High suspended net offshore transport occurs solely onshore of the outer bar trough. This causes filling of the bar trough and bar dissipation during migration. Additionally, processes around the outer bars are linked to accretion onshore of the bars and at the shoreline.

Impacts of soil properties on bluff recession under combined waves and surge actions: An experimental study with uncertainty quantification

Soil mixtures with five fines contents, two water contents, and two relative densities underwent soil mechanics tests to quantify their strength indices. Then small-scale steep beaches and bluff models were built with those soil mixtures in a small wave flume and subjected to varying water levels and waves. The equilibrium beach profile of the model containing a higher fines content, higher relative density, and the optimum water content, followed a concave down profile, while that of the models with the lower density and/or lower fines content, was concave up. The bluffs composed of the materials with the optimum water content exhibited a reduced crest recession compared to those with the constituent materials dry of optimum. The recession rate of the bluff crest decreased with the increase of the effective cohesion. For a given effective cohesion, the recession rate was significantly influenced by the relative density. The impact of the effective cohesion on the recession rate for the bluff composed of the looser soil was significantly greater than that of the bluffs with the denser constituent material. Furthermore, uncertainties associated with the impacts of the variations in the fines content, relative density, and water content on the recession rate were quantified.

Prediction of Long-Term Beach Profile Evolution Due to Episodic Wave Incidence Under Tidal Environment

Recently, studies have been conducted that long-term changes in shoreline position can be sufficiently interpreted using an ordinary differential equation that includes only erosion and recovery processes. Here, the erosion process term is given as a function of the breaking wave energy, which causes the shoreline to retreat to the ultimate erosion position by the incoming wave energy. The recovery process term is given as a function of the concentration of suspended sediment and allows it to recover to its shoreline position. Therefore, in this study, we propose a numerical technique that simulates long-term changes in the beach profile by extending the ordinary differential equation to be applied to the change in seabed constituting the beach profile by applying the parabolic equation of the equilibrium beach profile of the surf zone. This model also consists of a term that allows the beach profile to converge to the equilibrium beach profile due to the breaking wave energy and another term that allows it to converge back to the linear shoaling profile when the wave is extinguished. Therefore, it is possible to simulate the repeated formation and disappearance of scarp and berm whenever a storm wave passes, and it can also be applied to the morphological change at the beach with a large tidal range. The validity of the proposed methodology was verified by comparing the long-term shoreline observation data of Tairua Beach, New Zealand, where the tidal difference is about 2 m, with the results of the long-term beach section convergence model of this study. In addition, short-term observation data were also compared and analyzed to investigate the ability to simulate morphological changes due to episodic erosion and recovery processes. The results of this study are expected to be applied not only to the beach profile but also to the three-dimensional morphology change of the beach, and it is expected that it will serve as a cornerstone for a more detailed topographic change prediction study due to sea level rise.

MeePaSoL: A MATLAB-based GUI software tool for shoreline management

Headland-bay beaches (HBBs) are ubiquitous on Earth and many coastal scientists and engineers have attempted to define their planform since the 1940s, by employing laboratory tests, analytical tools, numerical models, and empirical equations. One of the latest attempts in numerical modeling is the development of a MATLAB-based GUI software called “MeePaSoL” to facilitate the application of the empirical parabolic model for HBBs. This visualization package can be applied to determine the predominant wave direction to the shoreline planform of a HBB in static equilibrium, and to minimize the uncertainty in locating downdrift control point while using other software. The background concepts (e.g., parabolic model, equilibrium beach and wave orthogonality hypothesis) are introduced, and the operation procedure with stepwise guides for applying MeePaSoL are given to assist the users. The reliability of MeePaSoL is validated by comparing the wave direction given by this package with that by the wave energy flux approach derived from field data. Examples of engineering applications are then demonstrated, covering local to regional wave direction, the effect of jetty/breakwater length and direction, harbor siltation in a macro-tidal environment, and devising engineering works for shoreline management in Korea. Sensitivity and uncertainty are also discussed.

Surf and Swash Dynamics on Low Tide Terrace Beaches

Low tide terrace (LLT) beaches are characterised by a moderately steep beach face and a flat shallow terrace influencing the local hydro-morphodynamics during low tide. The upper beachface slope (β) and the terrace width (Lt) are the main morphological parameters that define the shape of LTT cross-shore beach profiles. This work aims at better understanding the behaviour of β and Lt and their link with the incoming wave forcing. For this purpose, our results are based on 3.5 years times series of daily beach profiles and wave conditions surveys at two different microtidal LTT beaches with similar sediments size but different wave climate, one at Nha Trang (Vietnam) and the other one at Grand Popo (Benin). While they look similar, two contrasting behaviour were linked to two sub-types of LTT regimes: the first one is surf regulated beaches (SRB) where the swash zone is highly regulated by the surf zone wave energy dissipation on the terrace, and the second is swash regulated beaches (SwRB) acting in more reflective regime where the terrace is not active and the energy dissipation is mainly produced in the swash zone, the terrace becomes a consequences of the high dynamics in the swash zone. Finally, extending the common view of an equilibrium beach profile as a power law of the cross-shore distance, the ability of a simple parametrized cubic function model with the Dean number as unique control parameters is proposed and discussed. This simple model can be used for the understanding of LLT environments but it can not be extended to the whole beach spectrum.

Flooding of Sandy Beaches in a Changing Climate. The Case of the Balearic Islands (NW Mediterranean)

The fate of the beaches around the world has paramount importance as they are one of the main assets for touristic activities and act as a natural barrier for coastal protection in front of marine storms. Climate change could put them at risk as sea levels rise and changes in the wave characteristics may dramatically modify their shape. In this work, a new methodology has been developed to determine the flooding of sandy beaches due to changes in sea level and waves. The methodology allows a cost-effective and yet accurate estimation of the wave runup for a wide range of beach equilibrium profiles and for different seagrass coverage. This, combined with regional projections of sea level and wave evolution, has allowed a quantification of the future total water level and coastline retreat for 869 beaches across the Balearic Islands for the next decades as a function of greenhouse gases emission scenario. The most pessimistic scenario (RCP8.5) at the end of the century yields an averaged percentage of flooded area of 66% under mean conditions which increases up to 86% under extreme conditions. Moreover, 72 of the 869 beaches of the region would permanently disappear while 314 would be completely flooded during storm episodes. Under a moderate scenario of emissions (RCP4.5), 37 beaches would permanently disappear while 254 would disappear only during storm episodes. In both cases, the average permanent loss of beach surface at the end of the century would be larger than 50%, rising over 80% during storm conditions. The results obtained for the Balearic Islands can be extrapolated to the rest of the Mediterranean as the beaches in all the regions have similar characteristics and will be affected by similar changes in sea level and wave climate. These projections indicate that adaptation plans for beach areas should be put in place as soon as possible.

Analytical solution for time-dependent shoreline position response to the tectonic recovery process in the Sendai Plain, Japan, after the 2011 Great East Japan Earthquake

The 2011 Great East Japan Earthquake on March 11, 2011 triggered not only giant tsunami waves, but also caused significant land subsidence followed by land rise in the Sendai Coastal Plain areas. These impacts resulted in severe damages to the coastal infrastructure and induced coastal morphology changes along Japan's northeast coast. It was observed that the maximum downward deformation in the Sendai Coastal Plain was initially about - 0.3 m. Immediately after the earthquake, the land started to rise and it has already recovered back to its original position at some locations after 10 years. Thus, the high-quality measured beach profile data sets after the 2011 Tohoku Earthquake are valuable for exploring the impact of sea level rise (SLR) on shoreline position evolution, since the bed level change is inversely related to the sea level rise process. The data also provide a unique opportunity to evaluate the Equilibrium Beach Profile (EBP) theory and validate the Bruun concept. In the present study, a new simple analytical solution for time-dependent shoreline position response to the tectonic recovery process is developed based on the convolution method. The model results are able to predict the time-dependent shoreline evolution, including the maximum potential response and the characteristic erosion time scale at which the profile evolves towards a new equilibrium state.

The solution of the long-wave equation for various nonlinear depth and breadth profiles in the power-law form

Long waves bring many important challenges in the ocean and coastal engineering, including but are not limited to harbor resonance and run-up. Therefore, understanding and modeling their dynamics is crucially important. Although their dynamics over various types of geometries are well-studied in the literature, the study of the geometries with power-law variations remains an open problem in this setting. With this motivation, in this paper, we derive the exact analytical solutions of the long-wave equation over nonlinear depth and breadth profiles having power-law forms given by h(x)=c1xa and b(x)=c2xc, where the parameters c1,c2,a,c are some constants. We show that for these types of power-law forms of depth and breadth profiles, the long-wave equation admits solutions in terms of Bessel functions and Cauchy–Euler series. We also derive the seiching periods and resonance conditions for these forms of depth and breadth variations. Our results can be used to investigate the long-wave dynamics and their envelope characteristics over equilibrium beach profiles, the effects of nonlinear harbor entrances and angled nonlinear seawall breadth variations in the power-law forms on these dynamics, and the effects of reconstruction, geomorphological changes, sedimentation, and dredging to harbor resonance, to the shift in resonance periods and to the seiching characteristics in lakes and barrages.

Reinterpreting the Bruun Rule in the Context of Equilibrium Shoreline Models

Long-term (>decades) coastal recession due to sea-level rise (SLR) has been estimated using the Bruun Rule for nearly six decades. Equilibrium-based shoreline models have been shown to skillfully predict short-term wave-driven shoreline change on time scales of hours to decades. Both the Bruun Rule and equilibrium shoreline models rely on the equilibrium beach theory, which states that the beach profile shape equilibrates with its local wave and sea-level conditions. Integrating these two models into a unified framework can improve our understanding and predictive skill of future shoreline behavior. However, given that both models account for wave action, but over different time scales, a critical re-examination of the SLR-driven recession process is needed. We present a novel physical interpretation of the beach response to sea-level rise, identifying two main contributing processes: passive flooding and increased wave-driven erosion efficiency. Using this new concept, we analyze the integration of SLR-driven recession into equilibrium shoreline models and, with an idealized test case, show that the physical mechanisms underpinning the Bruun Rule are explicitly described within our integrated model. Finally, we discuss the possible advantages of integrating SLR-driven recession models within equilibrium-based models with dynamic feedbacks and the broader implications for coupling with hybrid shoreline models.

Study of shelly shore ridge formation using wave flume experiments: Morphological evolution and depositional patterns

Coarse shore/berm ridges comprising mollusk shells are peculiar morphological features occurring in some beaches globally, generally wave-built, generated during storms and high tides. Studies regarding the formation of these shelly shore ridges using wave flume experiments (physical modeling) do not provide a detailed analysis of their morphological evolution and depositional features. A bioclastic beach profile with a constant dip, formed by mollusk shells (whole and fragmented ones, DSV-50 = 4.5 mm) of bivalves and gastropods, was subjected to a storm wave condition simulated in a two-dimensional flume with a scale reduction factor of 1/20. A decimeter-scale shelly shore ridge was successfully formed by swash bar emergence. The seaward surface was steeper than the landward slope. The bar was progressively built by swash currents that accumulated shells along the shoreline. According to Dean's function, the equilibrium beach profile displays a good fit for coefficient A, as related to the settling velocity of the bioclasts. The power of m is lesser in the equilibrium beach than that in beaches composed of siliciclastic sand. Three patterns of shell organization and pore framework represent the back, top, and frontal sectors of the ridge. The ridge front includes poorly organized shell particles of dense packing. The crest comprises bioclast beds of uniformly obliquely oriented, densely packed particles. Back ridge sediments exhibit loosely packed moderate shell organization. The morphological evolution of the bioclastic ridge formed in the flume closely resembled bioclastic beach sediments. The depositional pattern in the flume ridge was directly related to the energy of breaking waves and associated swash-current energy.

A Coupled Hydrodynamic-Equilibrium Type Beach Profile Evolution Model

An equilibrium beach profile model is developed and coupled with a parametric hydrodynamic model to provide feedback between the evolving morphology and the hydrodynamics. The model is compared to laboratory beach profiles evolving toward equilibrium conditions under constant forcing. The equilibrium model follows the classical approach but uses the bulk sediment transport as the governing model parameter. This approach is coupled with empirically derived and normalised sediment transport functions and a parametric surf zone wave transformation model. The dissipation predicted by the surf zone model controls the cross-shore position of the maxima in the sediment transport functions and hence the cross-shore evolution of the beach profile. Realistic beach profile shapes are generated for both erosive (barred) and accretive (bermed) beach profiles, and predictions of bar and berm position are satisfactory. With more complex normalised sediment transport functions, the model can be applied to conditions with a cyclical wave climate. However, the model concept is better associated with erosive wave conditions and further work is required to improve the link between the modelled dissipation and local transport for accretive conditions.

The Equilibrium Concept, or…(Mis)concept in Beaches

Beaches, as deposits of unconsolidated material at the land/water interface, are open systems where input and output items constitute the sediment budget. Beach evolution depends on the difference between the input/output to the system; if positive the beach advances, if negative the beach retreats. Is it possible that this difference is zero and the beach is stable? The various processes responsible for sediment input and output in any beach system are here considered by taking examples from the literature. Results show that this can involve movement of a volume of sediments ranging from few, to over a million cubic meters per year, with figures continuously changing so that the statistical possibility for the budget being equal can be considered zero. This can be attributed to the fact that very few processes are feedback-regulated, which is the only possibility for a natural system to be in equilibrium. Usage of the term “beach equilibrium” must be reconsidered and used with great caution.

Equilibrium beach profile on sandy beach of the Mehdya coast of Morocco

The world’s coastlines are shaped by mean sea level, wave conditions and storm surge. Climate change driven variations in these environmental forcing’s will inevitably have a profound effect on the coastal zone. They will result in unprecedented coastal recession, threatening billions of dollars worth of coastal developments and infrastructure. Coastal erosion is observed in some locations along Atlantic alluvial plain (Kenitra coastal (Morocco)) and is an important factor to consider for the coastal zone management. Therefore, for coastal recession estimates are obtained via the simple, deterministic method (Bruun rule) especially, that has been widely used over the last 50 years. It is in widespread contemporary use at a global scale both as a management tool and as a scientific concept. We investigated the potential erosion at the site and the result was very important. The result shows a severe erosion of the 21st century.

EQUILIBRIUM MODELING OF CURRENT AND FUTURE BEACH EVOLUTION: VOUGOT BEACH, FRANCE

The impacts of climate change, including sea level and wave climate changes, may increase future erosion risks. Thus, it is important to improve knowledge of the dominant physical processes controlling medium- to long-term shoreline evolution, as well as the performance of beach evolution models reproducing past observations and predicting future changes. Empirical equilibrium beach change models may be an optimal choice at these spatial and temporal scales. Here, morphological changes at Vougot Beach (Brittany, France) are analyzed by evaluating the cross-shore evolution of contour elevations (-1 to 6m) along six intertidal beach profiles using observations and an equilibrium beach change model, and then three methods for estimating the impacts of climate change are applied and compared.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/p70KuzjR1kU

Modelling of embayed beach equilibrium planform and rotation signal

Embayed beaches are highly attractive sandy beaches bounded laterally by rigid boundaries, which deeply affect equilibrium beach planform and shoreline dynamics. We use LX-Shore, a state-of-the-art shoreline change model coupled with a spectral wave model to address embayed beach shoreline dynamics driven by longshore sediment transport processes. The model is applied to different idealized embayed beach configurations including variations in headland lengths. The model simulates a large range of equilibrium embayed beach planforms and associated spatial and temporal modes of shoreline variability. For short headlands enabling occasional headland sand bypassing, both embayed beach curvature and maximum erosion at the upwave side of the embayment increases with increasing headland length. Beach curvature also increases with increasing headland length for headlands long enough to prevent any headland sand bypassing. In contrast, at the same time, embayed beach becomes increasingly curved and symmetric, with maximum localised erosion within the embayment decreasing in intensity. When there is no headland sand bypassing, rotation signal decreases in amplitude and becomes increasingly symmetric with increasing headland length. The modal (time-invariant) directional spreading of incident waves is critical to embayed beach behaviour, with the envelope and variance of cross-shore shoreline change and time-averaged shoreline curvature all increasing with decreasing modal directional spreading. Embayed beach rotation characteristic timescale increases with increasing embayed beach length, while the narrower the embayment the smaller the cross-shore amplitude of shoreline variability. Our simulations provide new insight into the influence of embayment characteristics and incident wave conditions on equilibrium planform and shoreline dynamics of embayed beaches. This work also implies that the degree of potential headland sand bypassing should be taken into account for modelling of beach rotational dynamics and embayed beach dynamic planform configuration.