Shoreline Undulations Research Articles

Long‐Term Morphodynamics of a Coupled Shelf‐Shoreline System Forced by Waves and Tides, a Model Approach

AbstractSand ridges, with length scales of several km, are prominent features of the seafloor landscape of many sandy continental shelves. Knowledge about the extent to which these ridges influence the large‐scale (i.e., decadal and kilometer scales) morphodynamic evolution of the adjacent shoreline and vice versa (shelf‐shoreline morphodynamic coupling) is limited. The present work aims at quantifying this coupling by using a coupled nonlinear shelf‐shoreline model forced by tides and different wave conditions. Model results show that the presence of sand ridges on the shelf creates longshore non‐uniform wave patterns, which act as a forcing template for the morphodynamic development of the shoreline. The shelf‐shoreline coupling primarily works one way, meaning that the morphodynamic evolution of the shelf affects the evolution of the shoreline. When wave propagation is predominantly aligned with the long axis of the shelf ridges, the forced shoreline undulations are so prominent, that they affect the shelf morphology (significant two‐way coupling). Moreover, for those waves, the longshore spacing of the ridges is strongly imprinted on the shoreline morphology. Weaker shoreline undulations develop for waves that propagate more across the ridges and the weakest for time‐varying wave conditions with large variability in their angles of propagation. Model results compare fairly well with observations. Physical mechanisms underlying the different morphodynamic responses of the coupled shelf‐shoreline system to different wave conditions are also given.

Recent Shoreline Changes Due to High-Angle Wave Instability along the East Coast of Lingayen Gulf in the Philippines

A small perturbation on the shoreline may develop under high-angle wave conditions, resulting in the formation of sand spits along the shoreline. Serizawa et al. explained the development of sand spits caused by the instability mechanism using the BG model (a model for predicting 3-D beach changes based on Bagnold’s concept). However, examples of the development of sand spits caused by this mechanism in the field are limited in number. Lingayen Gulf in the Philippines has a large aspect ratio, so shoreline instability occurs along the coastline, significantly affecting the shore protection along the coast. In this study, the shoreline instability along the river delta coasts around the Balili and Aringay Rivers flowing into Lingayen Gulf and a sand spit were investigated using satellite images together with field observation. The shoreline changes observed south of the Aringay River mouth were compared with those observed in a previous study on the development of a sand spit by San-nami et al. The rate of longshore sand transport to form a sand spit at Santo Tomas in Lingayen Gulf was estimated to be approximately 1.3 × 105 m3/yr, which is in good agreement with the value measured on the Shimizu coast in Suruga Bay, with a comparable aspect ratio of 1.2 relative to 1.3 in Lingayen Gulf. It was concluded that shoreline undulations have evolved downcoast of two river deltas owing to high-angle wave instability along the east coast of Lingayen Gulf and the formation of a sand spit has occurred. A soft measure, such as sand bypassing, would be better to be adopted along the coasts in Lingayen Gulf instead of hard measures against erosion, to prevent rapid expansion of an artificial, protected coastline.

Efficient Modeling of Complex Sandy Coastal Evolution at Monthly to Century Time Scales

With large-scale human interventions and climate change unfolding as they are now, coastal changes at decadal timescales are not limited to incremental modifications of systems that are fixed in their general geometry, but often show significant changes in layout that may be catastrophic for populations living in previously safe areas. This poses severe challenges that are difficult to meet for existing models. A new free-form coastline model, ShorelineS, is presented that is able to describe large coastal transformations based on relatively simple principles of (1) alongshore transport gradient driven changes as a result of coastline curvature and (2) spit formation at high-angle wave incidence. An arbitrary number of coast sections is supported, which can be open or closed and can interact with each other through relatively straightforward merging and splitting mechanisms. Rocky parts or structures may block wave energy and/or longshore sediment transport. These features allow for a rich behavior including shoreline undulations and formation of spits, migrating islands, merging of coastal shapes, salients and tombolos. The main formulations of the (open-source) model are presented. Test cases show the capabilities of the flexible, vector-based model approach, while field validation cases for a large-scale sand nourishment (the Sand Engine; 21 million m3) and an accreting groyne scheme at Al-Gamil (Egypt) show the model’s capability of computing realistic rates of coastline change as well as a good representation of the shoreline shape for real situations.

Rhythmic patterns of shoreline contour in the gulf of Terpenya of Sakhalin Island

The results are discussed of the long-term observations of the system of mega-cusps (large-scale shoreline cusps) revealed on the coast of the Gulf of Terpenya of Sakhalin Island. Typical spatial step of the rhythmic forms is about 800 m and the amplitude of shoreline undulations is of tens of meters. Despite of significant changes in temporal scales of the seasons, years and decades the main morphological features of mega-cusps are kept over the period of more than 60 years. The model is suggested explaining creation of rhythmic shoreline patterns by self-organization of bottom relief under the wave impact. Development of mega-cusps is shown to be connected with generation of nearshore circulation cells. Due to flows within the cells a small initial perturbation of shoreline contour can increase in time. A positive feedback between the coastal morphology and the hydrodynamics arises when a certain relation is established between the length of perturbation, the width of surf zone and the velocities of nearshore currents. It is concluded that the system of mega-cusps in the Gulf of Terpenya is mainly supported by the moderate waves of significant wave height about 1.6 m.

Rhythmic Patterns in the Shoreline Contour of the Gulf of Terpenya, Sakhalin Island

The paper considers the results of long-term observations of megacusp (large-scale shoreline cusps) on the coast of the Gulf of Terpenya (Gulf of Patience), Sakhalin Island. The typical spatial step of the rhythmic forms is about 800 m, and the amplitude of shoreline undulations is 40–50 m. Despite significant changes on time scales of seasons, years, and decades, the main morphological features of the megacusps are preserved for more than 60 years. A model is proposed that explains the evolution of rhythmic shoreline patterns by self-organization of the bottom relief under wave impact. Development of megacusps is shown to be related to the generation of nearshore circulation cells; due to flows within the cells, a small initial perturbation to the shoreline contour can increase over time. A positive feedback between the coastal morphology and hydrodynamics arises when a certain relation is established between the length of the perturbation, the width of the surf zone, and the speeds of nearshore currents. It is concluded that the megacusp system in the Gulf of Terpenya is mainly supported by moderate waves with a significant wave height of ~1.6 m.

Rhythmic morphology in a microtidal low-energy beach

Observations of rythmic features along the inner side of the Trabucador barrier beach are coupled to two numerical models to unravel the mechanisms of its formation. The Trabucador is a long (6 Km) narrow (125 m) barrier and microtidal beach at the SW side of the Ebro delta (Catalonia). Its inner side is a low energy beach with a sandy shallow terrace featuring an intricate alongshore rhythmic morphology. Sixteen aerial orthophotos from 1946 to 2014 have been analyzed and complemented with field observations from 1986 to present. This morphology is dynamic but it is usually characterized by: a) long finger transverse bars (LFTB) and b) large scale shoreline undulations (LSSU). The LFTB are thin and elongated with a length of the order of their spacing. They are intertidal and typically attach to the shoreline by a megacusp, commonly opening an anti-clockwise angle of 10°–40° with the shore normal. There can be many, up to 90, with both the mean and the most frequent alongshore spacing in the range 15–25 m. Spectral analysis always shows peaks in this range and sometimes additional peaks in the range 30–65 m that correspond to the spacing between the largest bars with smaller bars in between. The LSSU typically have wavelengths in the range 150–250 m. Their apexes sometimes coincide with the shore attachment of the largest bars but not always. Numerical modelling shows that both features could emerge out of feedbacks between hydrodynamics and morphology during the SW wind events involving a) deflection of the longshore current by the bars combined with the refractive wave focusing and b) gradients in total alongshore sediment transport rate triggering the high-angle wave instability.

Large-Scale Shoreline Undulations and Role of Self-Organization Processes

Large-Scale Shoreline Undulations and Role of Self-Organization Processes

Formation events of shoreline sand waves on a gravel beach

Kilometric-scale shoreline sand waves (KSSW) have been observed in the north-east flank of the Dungeness Cuspate Foreland (southeastern coast of the UK). They consist of two bumps separated by embayments with a 350–450-m spacing. We have analysed 36 shoreline surveys of 2-km length using the Discrete Fourier Transformation (DFT), from 2005 to 2016, and seven topographic surveys encompassing the intertidal zone, from 2010 to 2016. The data set shows two clear formation events. In order to test the role of high-angle waves on the KSSW formation, the 10-year wave series is propagated from the wave buoy located at 43 m depth up to a location in front of the undulations at 4 m depth using the SWAN wave model. The dominating SW waves arrive with a very high incidence angle (∼ 80°) while the NE waves arrive almost shore normal. The ratio R, which measures the degree of dominance of high-angle waves with respect to low-angle waves, correlates well with the shoreline DFT magnitude values of the observed wavelength undulations. In particular, the highest R values coincide with the formation events. Finally, a linear stability model based on the one-line approximation is applied to the Dungeness profile and the 10-year propagated wave series. It predicts accurately the formation moments, with positive growth rates in the correct order of magnitude for wavelengths similar to the observed ones. All these results confirm that the shoreline undulations in Dungeness are self-organized and that the underlying formation mechanism is the high-angle wave instability. The two detected formation events provide a unique opportunity to validate the existing morphodynamic models that include such instability.

How Observed Kilometric Sandy Shoreline Undulations depend on Wave Climate

Idier, D.; Falques, A.; Garcin, M., and Rohmer, J., 2018. How observed kilometric sandy shoreline undulations depend on wave climate. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 191–195. Coconut Creek (Florida), ISSN 0749-0208.Coastlines sometimes exhibit km-scale undulations, also called shoreline sandwaves. This work focuses on self-organized undulations and investigates how frequent they are, on which parameters they depend and whether existing theories of morphodynamic instabilities can explain them. We perform a wavelet analysis on shoreline data from areas appearing free of human or geological constraints and representing totally 1268 km around the world. It is found that 61% of cases exhibit undulations with wavelengths in the range 1–10 km. The wave parameter that correlates the best with their existence is the incidence angle with respect to shore normal and, to a lesser extent, the closure depth. The shoreline undulation probability increases with the angle, from 50% for low angles to almost 100% for large angles, suggesting that the High-Angle Wave Instability mechanism (HAWI) would be their primary cause, but that Low-Angle Wave Instability (LAWI) may also play a role. These results are consistent with recent theoretical investigations.

Persistent Shoreline Shape Induced From Offshore Geologic Framework: Effects of Shoreface Connected Ridges

AbstractMechanisms relating offshore geologic framework to shoreline evolution are determined through geologic investigations, oceanographic deployments, and numerical modeling. Analysis of shoreline positions from the past 50 years along Fire Island, New York, a 50 km long barrier island, demonstrates a persistent undulating shape along the western half of the island. The shelf offshore of these persistent undulations is characterized with shoreface‐connected sand ridges (SFCR) of a similar alongshore length scale, leading to a hypothesis that the ridges control the shoreline shape through the modification of flow. To evaluate this, a hydrodynamic model was configured to start with the US East Coast and scale down to resolve the Fire Island nearshore. The model was validated using observations along western Fire Island and buoy data, and used to compute waves, currents and sediment fluxes. To isolate the influence of the SFCR on the generation of the persistent shoreline shape, simulations were performed with a linearized nearshore bathymetry to remove alongshore transport gradients associated with shoreline shape. The model accurately predicts the scale and variation of the alongshore transport that would generate the persistent shoreline undulations. In one location, however, the ridge crest connects to the nearshore and leads to an offshore‐directed transport that produces a difference in the shoreline shape. This qualitatively supports the hypothesized effect of cross‐shore fluxes on coastal evolution. Alongshore flows in the nearshore during a representative storm are driven by wave breaking, vortex force, advection and pressure gradient, all of which are affected by the SFCR.

Spatial and temporal scales of shoreline morphodynamics derived from video camera observations for the island of Sylt, German Wadden Sea

Spatial and temporal scales of beach morphodynamics were assessed for the island of Sylt, German Wadden Sea, based on continuous video camera monitoring data from 2011 to 2014 along a 1.3 km stretch of sandy beach. They served to quantify, at this location, the amount of shoreline variability covered by beach monitoring schemes, depending on the time interval and alongshore resolution of the surveys. Correlation methods, used to quantify the alongshore spatial scales of shoreline undulations, were combined with semi-empirical modelling and spectral analyses of shoreline temporal fluctuations. The data demonstrate that an alongshore resolution of 150 m and a monthly survey time interval capture 70% of the kilometre-scale shoreline variability over the 2011–2014 study period. An alongshore spacing of 10 m and a survey time interval of 5 days would be required to monitor 95% variance of the shoreline temporal fluctuations with steps of 5% changes in variance over space. Although monitoring strategies such as land or airborne surveying are reliable methods of data collection, video camera deployment remains the cheapest technique providing the high spatiotemporal resolution required to monitor subkilometre-scale morphodynamic processes involving, for example, small- to middle-sized beach nourishment.

A public, open Western Europe database of shoreline undulations based on imagery

Beaches around the world frequently exhibit a wide variety of shoreline morphological features of different dimensions, and increasing attention has been focused on shoreline undulations in recent years. Shoreline undulations (SUs) are medium to large spatial-scale features with longshore dimensions ranging from hundreds to thousands of meters and cross-shore widths ranging from tens to hundreds of meters. This work presents a public, open database with a total of 294 sites showing SUs identified using Google Earth Imagery along 50,000 km of Western European and Northwestern African coasts. Insights from regional, geometrical and hydrodynamic analyses are also presented to explore the potential of using the methodology for geographic studies occupying large extensions. The database contains information on 17 fields and is shared in a suitable and open format. Denmark exhibits the most features, followed by Spain and Italy. SUs ranging from 50 to 100 m in length and below 25 m in width are predominant, whereas SUs larger than 1000 m in length and 50 m in width are of minor importance. A total of 223 (76%) sites exhibit a series of one, two or three individual undulations, whereas the rest show more than three. The existence of SUs greatly depends on the tidal range, with lower (higher) tidal ranges indicating a higher (lower) number of undulations. A detailed analysis for the Spanish case was performed focusing on the relation between the presence of SUs and climate variables. The results show that SUs are more frequent where the wave energy is lower and the wave periods are shorter. An additional data mining analysis with association rules was conducted to corroborate the relationships between variables.

How kilometric sandy shoreline undulations correlate with wave and morphology characteristics: preliminary analysis on the Atlantic coast of Africa

Abstract. Sandy coasts are characterized by a number of rhythmic patterns like, amongst others, shoreline undulations or sandwaves at a kilometric scale. One hypothesis for their formation is that high angle waves (large incidence angle with respect to shore normal) could induce an instability of the shoreline (Ashton et al., 2001). More recently, a scaling for their wavelength has also been proposed (van den Berg et al., 2014). The existing studies rely mainly on modelling but quantitative field tests are lacking. We aim at investigating how both the formation hypothesis of these shoreline undulations and the theoretical scaling do fit with nature at a global scale. The first step, which is the goal of this paper, is to set up the methodology by analyzing the Atlantic African coast as test site. First, based on global databases, shoreline wavelength LS, wave characteristics (obliquity θW and wavelength λW) and mean shoreface slope β are determined. Then the wave obliquity is confronted with the presence of shoreline undulations. Finally the values of the ratio β LS / λW are estimated and discussed in comparison with the estimate of van den Berg et al. (2014). It is found that the correlation between shoreline sandwave occurrence and wave obliquity is very good, allowing the identification of 5 new potential unstable shoreline stretches, whereas the results on the scaling are not conclusive and deserve further investigations.

A note on alongshore sediment transport on weakly curvilinear coasts and its implications

This paper presents a simple approximation for assessment of the alongshore sediment transport rate on dissipative weakly curvilinear coasts. The approximation considers spatial variations in the wave angle and energy, sediment size, beach slope and type of wave breaking inside the surf zone. Similar approaches were employed in the past for coasts forced by high oblique waves where shoreline undulations frequently develop. With our approach, we can analyze more realistic situations, i.e., alongshore relations between the sediment size and the beach slope. The general expression for alongshore sediment transport is made explicit using a simple model for wave propagation. The solution is used to examine the implications of the behavior of alongshore sediment transport on shoreline evolution. After the analysis of the effects of variations in the wave conditions, the alongshore beach slope distribution and the shoreline geometry, three different shoreline tendencies were obtained for undulating shorelines: migration for changes in deep-water wave angle; amplitude growth for increases in wave height or period and changes in shoreline geometry; and wavelength changes and asymmetries for coasts with alongshore changes in beach slope. Our results also indicate that wave setup may enhance the formation of undulating shoreline features.

Numerical modeling of shoreline undulations part 1: Constant wave climate

This paper presents a numerical study of the non-linear development of alongshore undulations up to fully developed quasi-steady equilibrium. A numerical model which describes the longshore sediment transport along arbitrarily shaped shorelines is applied, based on a spectral wave model, a depth integrated flow model, a wave-phase resolving sediment transport description and a one-line shoreline model.First the length of the shoreline undulations is determined in the linear regime using a stability analysis. Next the further evolution from the linear to the fully non-linear regime is described. In the fully non-linear regime down-drift spits and migrating shoreline undulations are described.Three different shoreline shapes are found depending on the wave conditions: undulations with no spits, undulations with shore parallel spit and undulations with reconnecting spits.

WHAT DETERMINES THE WAVELENGTH OF SELF-ORGANIZED SHORELINE SAND WAVES?

Shoreline undulations extending into the bathymetric contours with a length scale larger than that of the rhythmic surf zone bars are referred to as shoreline sand waves. Many observed undulations along sandy coasts display a wavelength in the order 1-7 km. Several models that are based on the hypothesis that sand waves emerge from a morphodynamic instability in case of very oblique wave incidence predict this range of wavelengths. Here we investigate the physical reasons for the wavelength selection and the main parametric trends of the wavelength in case of sand waves arising from such instability. It is shown that the existence of a minimum wavelength depends on an interplay between three factors affecting littoral drift: (A) the angle of wave fronts relative to local shoreline, which tends to cause maximum transport at the downdrift flank of the sand wave, (B) the refractive energy spreading which tends to cause maximum transport at the updrift flank and (C) wave focusing (de-focusing) by the capes (bays), which tends to cause maximum transport at the crest or slightly downdrift of it. Processes A and C cause decay of the sand waves while process B causes their growth. For low incidence angles, B is very weak so that a rectilinear shoreline is stable. For large angles and long sand waves, B is dominant and causes the growth of sand waves. For large angles and short sand waves C is dominant and the sand waves decay. Thus, wavelength selection depends on process C, which essentially depends on shoreline curvature. The growth rate of very long sand waves is weak because the alongshore gradients in sediment transport decrease with the wavelength. This is why there is an optimum or dominant wavelength. It is found that sand wave wavelength scales with λ0/β where λ0 is the water wave wavelength in deep water and β is the mean bed slope from shore to the wave base.

Numerical modeling of shoreline undulations part 2: Varying wave climate and comparison with observations

The present work applies the shoreline model from part 1 to a real environment. In part 1, a numerical shoreline model which could handle the development of arbitrarily shaped shorelines was applied to consider the development of shoreline undulations on an unstable shoreline exposed to incoming waves with a directional spreading. In this paper, these findings are extended to firstly include the effect of a varying wave climate on the shoreline morphology and secondly, to tune the model to two naturally occurring shorelines. It is found that the effect of a variable wave climate is to slow down the development of the morphology and in some cases to inhibit the formation of shore-parallel spits at the crest of the undulations. On one of the natural shorelines, the west coast of Namibia, the shore is exposed to very obliquely waves from one main direction. Here, the shoreline model is able to describe the observed shoreline features qualitatively and quantitatively. The model slightly over-predicts the scale of the feature and, associated with this, slightly under-predicts the migration speeds of the features. On the second shoreline, the west coast of Denmark, the shore is exposed to waves with an angle close to the critical around 45°, and here the existence of undulations is discussed in detail.

NONUNIFORM ALONGSHORE SEDIMENT TRANSPORT INDUCED BY COASTLINE CURVATURE

This work proposes an expression for the alongshore sediment transport and a one-line type model to analyze the importance that the curvature of the shoreline and the bathymetric contours, and the associated alongshore wave energy gradients have in the evolution of the coastline and in the development of shoreline undulations. This model characterizes the alongshore wave energy gradients by means of the surf zone width variations and does not make any restriction on the shoreline curvature. The shoreline undulations of two different types of coast are investigated: a curvilinear coast in a prograding spit front, and an erosional stretch of coast adjacent to a river mouth. The results for the first one are in good agreement with observations. For the erosional coast good qualitative results are obtained, although a more intensive study is required.

Short and medium-term evolution of shoreline undulations on curvilinear coasts

This article proposes a one-line type model to explain the formation and evolution of shoreline undulations on circular or elliptic curvilinear coasts, such as littoral spits. The model takes into account the variation of the surf zone width stemming from the convergence and divergence of the waves propagating over a conical bathymetry with a small radius of curvature. The alongshore sediment transport varies with the angle formed by the wave crests and the coastline, as well as with surf zone width and sediment grain size. This model was applied to the shoreline undulations observed at the mouth of the River Guadalquivir (Gulf of Cádiz, Spain) and those at El Puntal Spit (Cantabrian Sea, Spain). In the first case, the model was forced with several sets of five-year wave climate simulations. At the El Puntal Spit, three different wave conditions, corresponding to the growth, saturation, and decay stages of the undulations, were simulated. In both cases, a net longitudinal growth of the spits was observed. Despite simplifications, the amplitude and wavelength of the shoreline undulations agree with the observations. Furthermore, both the zone and development time of the shoreline undulations can be estimated. The mechanism proposed for their generation and evolution may be complementary to other mechanisms, such as the instability mechanism of the coastline associated with high-angle waves.

Coastline undulations on the West Coast of Denmark: Offshore extent, relation to breaker bars and transported sediment volume

This paper deals with field measurements of undulations of the bottom bathymetry along an otherwise straight coast at the Danish West Coast. Two bathymetric datasets and two time series of wave measurements are used in order to determine the following properties: the offshore extent of shoreline undulations, the amount of sediment transported alongshore in the shoreline undulations, the relationship between the shoreline undulations and longshore bars and the relationship between the morphology and the hydrodynamics. In one of the data sets the shoreline undulations are well correlated with undulations on the depth contours between −5m and +2m relative to mean sea level. In the other data set, only undulations on the depth contours between −1m and +1m are well correlated with the shoreline undulations. The main difference in the wave climate between the two locations is the orientation of the shoreline such that the wave incidence angle is more oblique on the section of shoreline with well correlated depth contours, suggesting that the well correlated depth contours are a result of the oblique wave incidence.