Longshore Sediment Drift Research Articles

Longshore sediment transport rate in Formosa Bay, Rio de Janeiro State - Southeast Brazil

An approach involving data on wave-induced sediment transport estimates is essential for managing coastal environments. Numerical models are powerful tools to understand and investigate many processes responsible for longshore sediment transport (LST) in a systematic way, since direct measurement of LST is a difficult task. This paper presents estimates of longshore sediment transport through numerical modeling of wave-induced sediment dispersion patterns in the Formosa Bay, State of Rio de Janeiro - Southeast Brazil. The analysis was conducted using the computational package Coastal Modeling System/SMC-Brazil and mathematical formulations proposed by Cerc (1984). The results suggest average residual solid discharge (Qsravg) in the order of 131,442.745 m3/yr in northern sector, −151,908.32 m3/yr in central sector, and 71,987.69 m3/yr in southern sector of investigated area. In addition, it is important to highlight that minor variations in the wave incidence angle may cause changes in the longshore sediment drift, promoting the convergence and divergence zones throughout the investigated area. The results presented contribute to the advancement of knowledge on the topic addressed here and will be useful in future engineering projects related to beach nourishment and the management of coastal areas subject to erosion processes.

The formation and spatio-temporal variations of a new sand spit in Vaan Island, India—An influence of the multipurpose artificial reefs deployed to restore the sinking island

Sand spits constitute one of the depositional landforms that occur along the coast. This study (conducted from December 2015 to December 2020) investigated the spatio-temporal changes of the newly formed sand spit of Vaan Island in Gulf of Mannar, Southeast India. The investigation was based on morphological variations, bathymetry variations, wave climate, sediment nature and rate of deposition. Morphological variations were monitored using handheld Garmin GPS, and bathymetry variations were studied with low-cost bathymetry survey technique using Garmin echo-sounders. The freely available ECMWF wave data were used to obtain information on wave climate that approaches the study area. Satellite sun glitter imagery interpretation method was used to obtain information on wave direction around the Vaan Island for different time periods. Sand spit sediment characters and sedimentation rate were also estimated. The results indicate that the artificial reef modules, deployed on the windward side of the island for the purpose of restoring it from sinking, hinder the wave action, which has led to the formation of sand spit on the northwest by the long-shore sediment drift. Seasonal variations and morphological changes undergone by the sand spit are associated with the local wave climate. Bathymetry variation and shoreline configuration are also related. On shifting into deep contour the spit breaches into two or more pieces, whereas on shifting into shallow flat contour the area of exposure above sea level increases during the regular seasonal oscillation. The changes that this highly dynamic spit undergoes are cyclic, which indicates that the spit is undisturbed. Higher sediment supply from the nearby reef area will further increase the area of spit and island in future.

An overview of longshore sediment transport on the Brazilian coast

The present study investigates the wave behavior and the longshore sediment transport rate on the Brazilian continental shelf, using a computational model and four different formulations, for the period between 1979–2015. The average significant wave height is substantially variable along the study region, with the largest values occurring in southern Brazil, whereas the smaller values occur in northern Brazil. The longshore sediment transport rates are well within the range of values presented in previous works and indicate which method performs best in estimating annual mean rates of sediment transport. The highest sediment transport rates were found in the sector situated within the northern coast of the Bahia state and the Alagoas state, reaching 460000 m3 year−1. On the other hand, the opposite was found between the Rio de Janeiro and southern Bahia coast, where the smallest transport rates occurred with a global average of 109000 m3 year−1. Additionally, it is important to emphasize that small variations in the wave incidence angle may cause significant changes in the longshore drift of sediments, favoring the occurrence of zones of convergence and divergence along the coast. The novel results presented for the entire Brazilian shore contribute to the literature related to wave and sediment transport along the Brazilian coast and can be useful for future engineering projects that consider the sustainable management of the coastal zone.

Coastal dynamics in the Narva bay of the Baltic sea: present-day state and development tendencies

Central part of Narva bay is characterized by accretive coast, which is formed due to the presence of significant volumes of sand deposits. In the paper, the current state of coastal relief was analyzed and the forecast of its evolution under the prevailing wave climate was performed. The problem of the equilibrium of the coastal morphosystem for a given sediment budget and the probable trend of relative sea level was considered. Morphodynamic forecast for the period of the next decades was justified for designing the crossing of the coastal zone by the main pipeline route. Increasing of the role of accumulation processes from the south to the north has been identified through the field survey and analysis of satellite images, and has been shown by the nature of the beach relief and the underwater coastal slope. The calculation of the longshore sediment drift revealed the existence of a convergence zone for two differently directed sediment flows. Convergence of the sediment flows leads to accumulation of sand deposits at the rate of 19.0 m3 per one running meter per year. Estimates of the sediment budget resulted in the estimation of the accumulation rate at 8 m3 per one running meter per year in the coastal zone of area of the pipeline route. Sand accumulation leads to coastal accretion at the rate of 1 m per year. The obtained results lead to the conclusion on the stability of the coast in the coming decades unless the change of the sources of sand sediments and tendencies of its transport.

Model Hipotetikal Kesetimbangan Sedimen sebagai Indikator Awal Adanya Penurunan Muka Tanah Di Pantai Utara Pulau Jawa

North Coast of Java Island continues to experience coastal dynamics which resulted significant coastline erosion problems. According to the Ministry of Marine and Fisheries data (KKP), from 100 locations of coastline erosion in 17 provinces of Indonesia, North Coast of Java Island suffered the worst erosion, reaching 745 km or 44 percent of total coastline length. The shoreline retreat can be caused by three factors: sea level rise, erosion and land subsidence. The aim of this research was to determine the correlation between sediment equilibrium in coastal cells and the initial hypothesis of land subsidence which caused a coastline retreat. The method to calculate sediment equilibrium uses hypothetical sediment budget model. Modeling itself is done along the North Coast of Java. LITDRIFT model of Longshore Sediment Drift is employed to assess the coastline profile. The result of the research shows that there is anomalous model that is the condition of sediment is surplus but the condition of the field is backward. Several locations experienced a sediment surplus but experienced a coastline retreat, and after comparison with field observations and secondary data there was evidence of land subsidence: Pondok Bali Beach, Randusongo Beach, Muara Reja Beach, Depok Beach, Slamaran Beach, Jeruksari-Mulyorejo Beach and Sriwulan Beach. Furthermore this result can be used as an initial indicator of the land subsidence causing the coastline to retreat. In order to solve the erosion and sedimentation problem, the detail study with more comprehensive parameter needs to be conducted.

Erosional features identification along a recently prograding coastal barrier by ground penetrating radar facies analysis: Paradeep, Odisha, India

Coastal barrier dynamics is a complicated system which mainly involves shoreline changes due to accretion and erosion of the coast. Erosional activity in the coastal area of Paradeep, Odisha is risking the lives of the people and the community/factory infrastructures of this major port city, adjoining to the Bay of Bengal. So, understanding of the complex barrier dynamics is more important in this study area. The purpose of this study was to identify several erosional features within sedimentary beddings by Ground Penetrating Radar (GPR) survey and to understand the processes involved in this microtidal barrier from obtained GPR facies/radar facies. GPR reflection survey, with 200 MHz antenna, along (17 profiles) and across (21 profiles) the barrier was done to delineate shapes and sizes of the sedimentary features, erosional surfaces, channels, scour-and-fill structures, progradational beddings and internal geometry of the beach ridge deposits. GPR facies analyses of the beach ridge have established the longshore drift of sediments from nearby river mouths e.g. Mahanadi and Devi river mouths. This interpretation technique has also characterized the palaeo-tidal channels of the study area into two types – (a) larger channels which are perpendicular to the shoreline having channel width of about 400 m with maximum depth of 3.4 m from the surface and (b) smaller channels (width up to 60 m) flow parallel to the shoreline. Here, seaward-dipping beach progradational facies is positioned within oblique erosional surfaces below the facies boundary. This describes the cyclicity of erosion and accretion activity at Paradeep coastal barrier.

Genesis and morphological evolution of coastal talus-platforms (fajãs) with lagoons: The case study of the newly-formed Fajã dos Milagres (Corvo Island, Azores)

Supratidal talus-platforms are low-relief subaerial accumulations of debris produced by mass wasting along high coastal cliffs, being particularly abundant at reefless volcanic islands subjected to high wave energy. Known as “fajãs” across the Portuguese-speaking Atlantic archipelagos, these coastal features, on rare occasions, may exhibit lagoons, constituting sites of high geological, biological, landscape, and social value. Whilst the origin of fajãs is firmly established as being the product of coastal landslides, little is known about the processes that shape fajãs with lagoons. In particular, doubts still remain concerning whether fajãs featuring lagoons are a fortuitous product of mass wasting, or result from marine reworking (by waves and currents) after emplacement. On October 30, 2012, a coastal landslide (~0.001 km3) occurred on Corvo Island, Azores Archipelago, forming a nearshore gravel islet that later migrated to the island's coast, resulting in a fajã with an ephemeral lagoon (Fajã dos Milagres). This event provided a unique opportunity to study the generation and development of fajãs with lagoons, and therefore a 3-year survey was carried out to record its evolution. This GIS-based study used aerial oblique photography and satellite optical imagery, complemented with a land survey for a more precise topographic reconstruction. Analysis of data concerning bathymetry, precipitation, and wave regime was also employed to investigate the driving forces behind the morphodynamic evolution of the deposit. “Fajã dos Milagres” evolved very rapidly, through an evolutionary pattern with five main stages: 1) “islet stage”; 2) “gravel spit stage”; 3) “early lagoon stage”; 4) “mature lagoon stage”; and 5) “fajã (without lagoon) stage”. Our reconstructions show that, for fajãs with lagoons to be formed, several factors should converge: a) presence of high coastal cliffs, made up of composite volcanic sequences, capable of producing large landslides that supply sufficient mobile sediment to the shelf; b) presence of a shallow, wide insular shelf where the sediments can be transported without significant loss to the submarine slopes; and c) a wave-dominated, high-energy regime, capable of significant cross-shore and longshore sediment drift. These observations allowed us to propose a preliminary conceptual evolutionary model for the generation of fajãs with lagoons, where marine reworking plays a fundamental role. Finally, this study documents the generation and very rapid subsequent evolution of a clastic coastal morphology solely driven by the action of waves and currents, and without interference from relative sea level and/or external sediment replenishment, with possible implications to other settings.

SEDIMENTATION, TRANSPORT UND EROSION AN DER NORDKÜSTE KOLUMBIENS ZWISCHEN BARRANQUILLA UND DER SIERRA NEVADA DE SANTA MARTA

The coast of Northern Colombia between Barranquilla and the Sierra Nevada de Santa Marta has been subject to swift morphological alterations in the near geological past. The Magdalena River mouth into the Caribbean Sea is actually in the western end of the region and has formed deltas in three phases during the recent Quaternary. The two older ones were destroyed by erosion ad can only be detected by submarine morphology. The second phase is represented by a delta, that reached its widest dimensions approximately 2.400 years ago. The then starting destruction continues untill today and is not yet finished. The recent mouth foresets the youngest delta of the Magdalena River. A westbound longshore current along the not always even shoreline is produced by north-eastern tradewinds. This current transports the eroded sediments of the second oldest delta to the mouth of the Magdalena River. Part of them helps to build its new delta, and part of them glides through submarine cañons to the deep sea. Besides the morphological evidence, sedimentary analysis of the shore sands shows: 1. a longshore drift of sediments from east to west. 2. a change in the balance of energy: sedimentation in the east; erosion in the west (placers of heavy minerals). The very important highway from Barranquilla to Santa Marta ist thus endangered by erosion in the near future. 3. the sources of the upper sedimentlayers in the shore area: in the oldest delta their provenance is the Sierra Nevada de Santa Marta; in the younger deltas the area of affluents of the Magdalena River.

Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part1: Wave climate variability and impacts on the longshore sediment transport

The short, medium and long-term evolution of the sandy coastline of the Bight of Benin in the Gulf of Guinea, West Africa, has become a major regional focal point due to the rapid socio-economic development that is occurring in the region, including rapid urbanization and a sharp increase in harbor-based trade. Harbors have a significant impact on the present evolution of this coast, notably by affecting longshore sediment transport. However, little is known of the environmental drivers, notably the wave climate, that governs longshore sediment transport and the ensuing pattern of shoreline evolution of this coastal zone. This article aims to address this important knowledge gap by providing a general overview of coastal evolution in the Bight of Benin and the physical processes that control this evolution.Here, the 1979–2012 ERA-Interim hindcast is used to understand the temporal dynamics of longshore sediment transport. Oblique waves (annual average Hs=1.36m, Tp=9.6s, S-SW incidence) drive an eastward drift of approximately 500,000m3/yr. The waves driving this large longshore transport can be separated into two components with distinct origins and behavior: wind waves generated locally in the Gulf of Guinea and swell waves generated in the southern hemisphere sub- (30–35°S), and extra-tropics (45–60°S). The analysis undertaken here shows that the contribution to the gross annual longshore transport from swell wave-driven longshore currents is an order of magnitude larger than the local wind wave-driven longshore currents. Swell waves are dominantly generated by westerlies in the 40–60°S zone and to a lesser extent by trade winds at 30–35°S. The longshore sediment drift decay (−5% over 1979–2012) is found to be linked with a decrease in the intensity of westerly winds associated with their southward shift, in addition to a strengthening of the trade winds, which reduces the eastward sediment transport potential. The equatorial fluctuation of the Inter-Tropical Convergence Zone (ITCZ) is found to explain most of the variability in transport induced by wind waves, while the Southern Annular Mode (SAM), an extra-tropical mode, has a predominant influence on transport induced by swell waves. The ITCZ and SAM have, respectively, a negative and positive trend over the period 1979–2012 that explains the decrease in both wind- and swell-wave-induced transport. For future scenarii, General Circulation Models (GCMs) predict a stabilization of the SAM, and, thus, a non-substantial or weak change in longshore sediment transport can be expected on the coast of the Bight of Benin.

Long-term evolution of a sand spit, physical forcing and links to coastal flooding

Aerial photographs, topographic field data and environmental forcing agents were used to assess historic and annual sand spit changes at Ginst Spit, Pendine Sands, West Wales. Aerial photographs highlighted that the spit shoreline facing the dominant wave direction had accreted steadily throughout the assessment timeframe (1947–2010). Stabilisation works in the form of rubble mounds aided recovery of the dune system thought to have been damaged due to training exercises carried out during the Second World War. Annual topographic surveys (1995–2010) showed a terminal end eastward migration extending into the channel of the 3 estuary complex. Dominant waves emanate from south southwest, and wave models suggest that longshore sediment drift is from west toward east. Sub-dominant southeast waves create a counter drift back toward the west forming the customary northward hook. Model results showed significant wave transformation from offshore model boundaries to the nearshore zone for both wave height and direction, which found agreement with qualitative assessment. Annually averaged wave components showed varying correlations with sand spit rates of shoreline change. Precipitation and spit growth were associated with flood events, which suggested that a combination of fluvial and coastal processes contribute to lowland inundation. By showing the major role the spit plays in protecting the town in its lee, this work provides a new understanding of sand spit evolution to inform coastal management.

Relationships between sand spit evolution, environmental forcing and inland inundation

ABSTRACT Thomas, T., Lynch, S.K., Phillips, M.R., Williams, A.T., Duck, R.W. 2014. Relationships between sand spit evolution, environmental forcing and inland inundation.In: Green, A.N. and Cooper, J.A.G. (eds.), Proceedings 13th International Coastal Symposium(Durban, South Africa),Journal of Coastal Research, Special Issue No. 70, pp. 072–077, ISSN 0749-0208. Topographic field data and environmental forcing agents were used to assess morphological changes (1995–2010) at Ginst Spit, Pendine Sands, West Wales and flood potential at Laugharne, a town in the lee of the spit. Areal change between annual surveys showed variable distal end migration eastward extending into the channel of the Towy, Taf and Gwendreath estuaries. Dominant waves emanate from south toward southwest and suggest that the longshore sediment drift is from west toward east. However, sub-dominant waves from southeast are limited by fetch but engender a counter drift back toward the west at the distal end forming the customary northward h...

20th century sediment budget trends on the Western Gulf of Lions shoreface (France): An application of an integrated method for the study of sediment coastal reservoirs

This paper presents a shoreface sediment budget established for the 20th century (1895–1984–2009) along the microtidal wave-dominated coast of the western Gulf of Lions (Languedoc-Roussillon, Mediterranean Sea, SE France). The implementation of a diachronic bathymetric approach, coupled with the definition of sand reservoirs (upper sand unit — USU) by very high-resolution seismic surveys and the results of LiDAR investigations, offers a new means of defining precisely the magnitude and change trends of the sediment budget. The aim of this study is to link the Large Scale Coastal Behaviour (LSCB) of the littoral prism (expressed in terms of shoreface sediment budget, shoreface sediment volume and spatial distribution pattern of cells) to climatic change, river sediment input to the coast, longshore sediment transport distribution, impact of hard coastal defence structures and artificial beach nourishment. The results show a significant reduction of the volume of the western Gulf of Lions littoral prism over 114years (−26.1±4.6×106m3). From 1895 to 1984, the overall budget is slightly positive, with a volume estimated at 4.1±3.5×106m3. For 1984–2009, however, the estimated sediment budgets clearly indicate that erosion is dominant over the last 25years, with a volume loss of −30.2±4.2×106m3. In relation to the long-term sediment budget and longshore drift pattern, the long-term trend of the USU volume distribution displays strong spatio-temporal contrasts linked to longshore sediment drift, spatial distribution of fluvial sediment inputs and hard engineering structures. Locally, the sedimentary reservoir is significantly eroded within a century (−80% of USU), since the initial amount present was low and not sustainable. The emphasis is on the importance of considering the volume changes of available sediment reservoirs rather than their losses and gains. Erosion of the Languedoc-Roussillon shoreface is likely to continue in the future due to the “natural” decrease of river sediment input and the sand removal for human purposes. Consequently the littoral sand prism results in sedimentary reservoirs that are gradually being used up.

Origin and evolution of interdistributary delta plains; insights from Mekong River delta

The geometry of river deltas is considered to refl ect the interplay of coastal processes, river discharge, and sediment supply. As ~25% of the world’s population lives on deltaic lowlands, prediction of delta growth is critical. Knowledge of processes responsible for delta geometries is not well established, although such knowledge is critical for the risk management of land use and settlements on deltas. The Mekong River delta of southern Vietnam is one of the largest deltas in the world and offers a unique opportunity to understand the sedimentary evolution of mixed tide- and wave-dominated large river deltas. We constrained the three-dimensional sedimentary evolution of the delta plains, based on optically stimulated luminescence dating of beach ridges coupled with radiocarbon-dated sediment cores. Results show that the beach shoreline in the lower delta plain initiated ca. 3.5 ka by aggradation on basement shoals. The delta plain propagated laterally during the late Holocene, evolving from bars that resulted in asymmetric bifurcation of the river mouth. Asymmetry was caused by the southwestward longshore sediment drift enhanced by the winter monsoon. Bars were successively formed on the wider side of the bifurcated river mouths, and subsequently accreted seaward, being stabilized by tide effects to result in shore-perpendicular elongate delta plains. Our work, based on the Mekong delta, demonstrates for the fi rst time that bar emergence is a key process in the long-term evolution of mixed tide- and wave-dominated deltas.

A diachronic view of the net longshore sediment drift during the Late Holocene at the Jequitinhonha River delta, Brazil, using numerical modeling

Using numerical modeling, this work estimates sediment dispersion patterns caused by the incidence of waves in five distinct coastline contours of the Jequitinhonha River delta plain during the Late Holocene. For this study, a wave cliate odel based on the construction of ave refraction diagras relative to the current boundary conditions as defined and assumed to be valid for the five coastlines. Numerical modeling from the refraction diagrams was carried out considering the angle of incidence and wave height along the coastline. This work has allowed us to reproduce past and current patterns of net longshore sediment drift defined by a conceptual model developed from the integration of sediment cores, aerial photograph interpretation, C14 datings and geomorphic indicators of longshore drift. These results show that, on average, current wave conditions in the east-northeastern Brazilian region seem to have remained characteristically the same from approximately 5100 years BP until the present time. This type of information can be important when attempting to simulate possible future situations in terms of the long-term general behavior of the east-northeastern Brazilian coastal region.

Past and current sediment dispersion pattern estimates through numerical modeling of wave climate: an example of the Holocene delta of the Doce River, Espírito Santo, Brazil

This paper presents a numerical modeling estimation of the sediment dispersion patterns caused by waves inciding through four distinct coastline contours of the delta plain of the Doce River during the Late Holocene. For this, a wave climate model based on the construction of wave refraction diagrams, as a function of current boundary conditions, was defined and was assumed to be valid for the four coastlines. The numerical modeling was carried out on basis of the refraction diagrams, taking into account the angle of approximation and the wave height along the coastline. The results are shown to be comparable with existing data regarding the directions of net longshore drift of sediments estimated from the integration of sediment cores, interpretation of aerial photographs and C14 datings. This fact apparently suggests that, on average, current boundary conditions appear to have remained with the same general characteristics since 5600 cal yr BP to the present. The used approach may prove useful to evaluate the sediment dispersion patterns during the Late Holocene in the Brazilian east-northeast coastal region.

Field measurement and quantification of longshore sediment transport: an unattainable goal?

Abstract Longshore sediment transport (LST) is an important component of many coastal systems. This common term is frequently expressed as an annual volume, either net or gross, passing a particular point. In spite of its importance as a factor in coastal morphodynamics it has received relatively little attention as a process. We review the mechanisms of longshore sediment transport and current approaches to its assessment using field measurement and geoindicators. We conclude that approaches to date have never succeeded in quantifying longshore sediment drift rates in an adequate way. This shortcoming is attributed to the spatial and temporal variability of contributing processes coupled with a technical inability to quantify simultaneously longshore sediment transport in all its modes. We also conclude that research involving the measurement of longshore transport can enhance our understanding of the processes of transport and rates of transport under certain conditions. However, the accurate quantification of drift rates as annual volumes is an unattainable goal. We propose that such quantifications be replaced by qualitative values (small, medium, large) or measures of the relative importance of longshore transport in effecting morphological change (e.g. drift-dominated, cross-shore dominated, mixed processes).

A significant longshore transport divergence zone at the Northeastern Brazilian coast: implications on coastal Quaternary evolution

By using the mean directions of the wave-fronts approaching the Brazilian northeastern coastal stretch comprised between the localities of Real river (Sergipe State) and Galinhos (Rio Grande do Norte State) - coincident with those of the main winds occurring in the area - and their periods, we have defined a wave climate model based on the construction of refraction diagrams. The resulting model of sediment transport, as obtained by numerical modelling from the refraction diagrams, taking into consideration the angle of approach and waves heights along the 10-m isobath, was capable of reproducing the patterns of sediment dispersion provided by geomorphic indicators of the longshore drift. All this coastal region, approximately 900 km in length, is characterized by a significant divergence zone in the direction of net longshore drift of sediments, the potential intensity of which increases considerably in value, in almost its entire length, continuously toward downdrift, which might explain the greater or lesser long term susceptibility to erosion, during the Quaternary, along the coastal stretch studied.

Longshore Sediment Transport on Mediterranean Coast of Israel

A modified version of the CERC formula, which relates longshore sediment drift to deep water wave height and direction, has been used to define the equivalent wave height. The directional distribution of these wave heights and corresponding sediment transport rates and their analytical approximations are found using statistical analysis of high quality directional wave data measured simultaneously at two sites, Ashdod and Haifa. The directional distributions enable one to determine the directional shift between the average wave directions at both sites and to find the necessary corrections of wave directions at any location along the coast. The results emphasize the importance of accounting for wave directional shift in sediment transport calculations even when the locations are close. A detailed computation of directional shift for different ranges of wave heights is performed using correlation analysis of data sets. The corrections of wave directions at various locations along the coast are found by interpolation, and an excellent agreement between sediment fluxes at each location has been obtained when using the LITPACK package for littoral transport simulations with each data set.

Recent coastal evolution of the Caspian sea as a natural model for coastal responses to the possible acceleration of global sea-level rise

The Caspian Sea serves as an excellent natural laboratory for studies of coastal response patterns, as it is highly variable in its water level over decadal and secular time scales. Coastal morphology, presumably nearshore bottom slope and profiles of depositional coastal bodies or erosional scarps, as well as rates and amplitudes of water-level changes, appear to be the most important factors of coastal response rates and patterns. Nearshore bottom slope determines not only shoreline retreat values, according to the Bruun Rule, but also the very patterns of coastal evolution for various morphological types of depositional coasts including deltaic coasts. Strict analytical prediction of coastal response to the accelerated sea-level rise is yet to be solved. Analysis of every response pattern of depositional coasts to sea-level changes requires a specific modification of the Bruun Rule. However, these equations should be regarded only as the means to estimate an order of magnitude of shoreline retreat or advance. In many cases, equations based on the Bruun Rule cannot be applied at all. Boundary conditions for each quantitative model should be thoroughly studied. Where possible, longshore sediment drift, sediment washover on to the landward slope of depositional coastal features, and possible onshore or offshore aeolian sediment movement should be taken into account. Moreover, applicability of the Bruun-Rule based equilibrium approach will possibly diminish under the possible future acceleration of sea-level rise.

Hydrons and Alongshore Migrating Undulating Beach Forms

A beach undulation (rhythmic topography) is an equilibrium beach form. The water wave energy flux depends upon the refraction of the hydrons (water wave packets), and the angle of the breaking waves is determined by the refraction of the wavelets within a hydron. The refraction of the hydrons and wavelets work together to provide a constant longshore drift of sediments.