High-angle Wave Research Articles

Modeling large scale shoreline sand waves under oblique wave incidence

The hypothesis that the formation and dynamics of large scale shoreline sand waves can be explained by a feedback mechanism between waves and nearshore morphology under very oblique wave incidence is explored with a quasi 2D nonlinear morphodynamic model. Using constant wave conditions it is found that if the wave incidence angle at the depth of closure is larger than about 45° the rectilinear coastline becomes unstable and a shoreline sand wavefield develops from small random perturbations. Shoreline sand waves develop with wavelengths between 2 and 5 km, they migrate downdrift at about 0.5 km/yr and they reach amplitudes up to 120 m within 13 years. Larger wave obliquity, higher waves and shorter wave periods strengthen the shoreline instability. Cross‐shore transport is essential for the instability and faster cross‐shore dynamics leads to a faster growth of the sand waves. Simulations with variable wave incidence angles (alternating between 60° and 30°) show that a large proportion of high angle waves is required for spontaneous sand wave formation (at least 80%). Insight is provided into the physical mechanism behind high angle wave instability and the occurrence of a optimal length scale for sand wave growth. The generic model results are consistent with existing observations of shoreline sand waves, in particular with those along the southwest coast of Africa.

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.

A multi-scale hybrid long-term morphodynamic model for wave-dominated coasts

Process-based modules based on conservative equations to solve the transport of waves, currents and sub-aqueous sediment, and behavior-oriented modules based on empirical descriptions of cliff erosion, bed-load and terrestrial aeolian sand transport are coupled with up-scaling measures and stability-maintaining approaches in a parallel code to simulate decadal-to millennial-scale morphological evolution of wave-dominated coasts. An application to the southern Baltic Sea for a hindcast of Holocene morphogenesis of the Darss–Zingst peninsula demonstrates the robustness of the model. The model is then used to investigate the morphogenesis and evolution of spits in an idealized fetch-limited sandy coastal environment. Evolution of the spit system can be categorized into three periods according to the simulation results. In the early period all initial coastline perturbations are amplified due to the high-angle wave effects. Size competition between adjacent spits starts afterwards. Interaction between adjacent spits dominates the middle period. Smaller spits tend to retrogress due to unbalanced sediment budget and this sediment loss feeds further growth of their larger neighbors. The retrograded spits are either smoothed or evolve into barrier-lagoons, and relatively stable large-scale spits originating from larger spits are developed in the late period. Low-frequency storms impinging from a regular high angle onto the coastline facilitate the development of spits in the early period, but become a hindering factor afterwards. Terrestrial aeolian transport not only plays a key role in stabilizing the spits, but is also revealed as an important factor for long-term coastline erosion.

Shoreline instability under low-angle wave incidence

[1] The growth of megacusps as shoreline instabilities is investigated by examining the coupling between wave transformation in the shoaling zone, longshore transport in the surf zone, cross-shore transport, and morphological evolution. This coupling is known to drive a potential positive feedback in case of very oblique wave incidence, leading to an unstable shoreline and the consequent formation of shoreline sand waves. Here, using a linear stability model based on the one-line concept, we demonstrate that such instabilities can also develop in cases of low-angle or shore normal incidence under certain conditions (small enough wave height and/or large enough beach slope). The wavelength and growth timescales are much smaller than those of high-angle wave instabilities and are nearly in the range of those of surf zone rhythmic bars, O(102–103 m) and O(1–10 days). The feedback mechanism is based on (1) wave refraction by a shoal (defined as a cross-shore extension of the shoreline perturbation) leading to wave convergence shoreward of it; (2) longshore sediment flux convergence between the shoal and the shoreline, resulting in megacusp formation; and (3) cross-shore sediment flux from the surf to the shoaling zone, feeding the shoal. Even though the present model is based on a crude representation of nearshore dynamics, a comparison of model results with existing depth-averaged two-dimensional model output and laboratory experiments suggests that the instability mechanism is plausible. Additional work is required to fully assess whether and under which conditions this mechanism exists in nature.

Long-term evolution of nourished beaches under high angle wave conditions

A nonlinear numerical model for large-scale dynamics of shoreline and nearshore bathymetry under wave action is applied to investigate the long-term evolution of a rectilinear coast dominated by high angle wave incidence, which is perturbed by a nourishment or an offshore borrow pit. Previous studies show that a coastline can be unstable due to high angle wave instability, which results from the feedback between shoreline changes and the wave field. In contrast to traditional one-line shoreline models, which always predict a diffusional behaviour, this instability can lead to the growth of shoreline perturbations. Model results suggest that due to high angle wave instability a nourishment or a borrow pit could trigger the formation of a shoreline sand wave train (alternating accretional and erosional zones). Its formation is a self-organised response of the morphodynamic system and can be seen as a spatial-temporal instability. New sand waves are formed downdrift while the old sand waves migrate downdrift and increase in amplitude and wavelength. Instability develops only if the bathymetric changes related to shoreline perturbations extend to a depth where the wave angle is greater than the critical angle of 42°. The potential for coastline instability is therefore limited by the wave incidence angle at the depth of closure and not the angle at deep water as suggested in previous studies. Including a fraction of low angle waves to the wave climate causes saturation of the amplitudes of the sand waves and limits the formation of the sand wave train. Even on a stable coast dominated by low angle waves, the feedback between morphology and the wave field can be crucial for the prediction of nourishment evolution. This feedback leads to relatively slow diffusion of shoreline perturbations and it can lead to downdrift migration. While some existing observations describe downdrift advection, no satisfactory explanation had been provided previously.

SHORELINE SAND WAVES AND BEACH NOURISHMENTS

The effects of the feedback between the changing coastal morphology and the wavefield on the generation and propagation of large scale (O(1-10 km)) shoreline sand waves is examined with a quasi-2D morphodynamic model. Traditional shoreline change models do not include this feedback and are only able to describe diffusion of shoreline sand waves and furthermore they are unable to describe migration. It is found with the present model that if there is a dominant littoral drift, the feedback causes downdrift migration of coastline features no matter if they grow or decay. Consistently with previous studies, simulations show that a rectilinear coastline becomes unstable and sand waves tend to grow spontaneously from random perturbations, if the wave incidence angle is larger then about 42o (θc) at the depth of closure (high angle wave instability). The initial wavelengths at which the sand waves develop are 2-3 km and this is similar to previous linear stability analysis. The implications of high angle wave instability for beach nourishments are investigated. The nourished shoreline retreats initially due to cross-shore transport because the nourished profile is steeper than the equilibrium profile. When a dominant littoral drift is present, the nourishment also migrates downdrift. If the wave angle at the depth of closure is below θc the alongshore transport contributes to the diffusion of the nourishment. However, if the angle is above θc (constant high angle wave conditions) the diffusion is reversed and the nourishment can trigger the formation of a shoreline sand wave train. Numerical experiments changing the proportion of 'high angle waves' and 'low angle waves' in the wave climate show that relatively small proportions of low angle waves slow down the growth of sand waves. These simulations with more realistic wave climates show shoreline sand waves that migrate downdrift maintaining more or less the same amplitude for years.

Prediction of Development of Sand Spits and Cuspate Forelands of Rhythmic Shapes as Shoreline Instability using BG model

The high-angle wave instability problem defined by Ashton et al. was numerically solved using the BG model proposed by Serizawa et al. The development of sand spits was predicted under the oblique wave incidence that the angle between the direction normal to the shoreline and wave direction becomes larger than 45°, given an infinitesimal perturbation to the initial topography. In this model, not only the shoreline configuration but also three-dimensional topographic changes around the sand spits can be predicted.

Reply to comment by M. Ortega‐Sánchez et al. on “High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes”

[1] We would like to thank Ortega-Sanchez et al. for highlighting Carchuna beach (southern Spain) [OrtegaSanchez et al., 2003] as another natural example where large-scale cuspate shoreline features are coincident with a wave climate dominated by high-angle waves, providing an independent test of the hypothesis presented by Ashton et al. [2001] and Ashton and Murray [2006a, 2006b]. OrtegaSanchez et al. discuss a series of large-scale cuspate shoreline features and also demonstrate the apparent formation of smaller-scale shoreline undulations along a relatively straight portion of the coast, suggesting that a straight coast in this subregion may also be responding to the high-anglewave instability. In model simulations, cuspate features are not completely regular, with variations in the spatial wavelength of up to a factor of two, and some portions of the coast can temporarily attain fairly straight configurations between cuspate features (see Figure 9 and auxiliary material in the work of Ashton and Murray [2006a]). The selforganization mechanism can explain both variation in wavelength and the appearance of different quasi-rhythmic features at distinctly different scales—both observed at Carchuna beach. [2] As discussed in detail by Ashton and Murray [2006a] and investigated by others [Falques and Calvete, 2005], we agree that the assumptions underlying our numerical model become less appropriate at spatial scales much less than a kilometer (for an open-ocean coast). When the scale of shoreline features is not much greater than the storm surf zone [Ortega-Sanchez et al., 2004], breaking-wave dynamics, local hydrodynamics, and deviations from shore-parallel contours, factors not captured by the exploratory model, become increasingly important in morphologic evolution. Many other factors not included in this simple model will influence the specific evolution and shape of a natural coast, including the geologic framework, preexisting coastline configurations, and the external supply of sediment. Direct comparison between the model results and a natural example should be performed with care, as the objective of the described exploratory model [Murray, 2003] is to investigate the range of shoreline behaviors resulting from the simple interactions considered, and not to reproduce in detail the evolution of any particular coastline. [3] We also urge caution in the interpretation of the figures demonstrating how model behaviors change with variation in the model parameters A, the fraction of waves approaching from the right (the asymmetry), and U, the fraction of unstable, high-angle waves [Ashton and Murray, 2006a, Figure 9a]. A and U are model-specific parameters used to determine the wave climate in the numerical experiments [e.g., Ashton and Murray, 2006a, Figure 8], and should not be directly related to a natural wave climate with the expectation of a quantitatively accurate comparison. Ashton and Murray [2006b] present a methodology for more rigorously analyzing and characterizing a wave climate, introducing a stability parameter, G. Approximate values of this stability parameter can be computed using wave energy roses such as those presented in the comment by Ortega-Sanchez et al. [2008], and its computation should be more straightforward than approximations of the model parameter H.

Wave driven alongshore sediment transport and stability of the Dutch coastline

The wave-driven alongshore sediment transport is commonly supposed to smooth out the irregularities on the coastline. However, it has been shown that waves approaching the coast with a high angle with respect the shore-normal can reverse that tendency and cause the rectilinear coast to be unstable [Ashton, A., Murray, A.B., Arnault, O., 2001. Formation of coastline features by large-scale instabilities induced by high-angle waves. Nature 414, 296–300; Falqués, A., Calvete, D., 2005. Large scale dynamics of sandy coastlines. Diffusivity and instability. J. Geophys. Res. 110, doi:10.1029/2004JC002587]. The extended one-line coastline model presented in the latter paper is here applied to investigate the stability of the Dutch coast. The main aim is testing the hypothesis that the shoreline sand waves observed along this coast could be generated by such an instability. It is found that the Dutch coast has potential for instability. This is most prominent on the Holland coast, followed by the Delta coast and is very weak on the Wadden coast. Whether the instability actually occurs or not depends on the cross-shore bathymetric profile of the shoreline waves. Under the sensible assumption that the bathymetric perturbation is just a shift of the equilibrium beach profile, the Dutch coast is stable. In this case, the mean annual coastline diffusivity is evaluated and it is found to be typically about 0.010–0.015 m 2 s − 1 , that is, roughly smaller by a factor 2 than that predicted by the traditional one-line model. However, the Dutch coast may be unstable with respect to coastline waves with a maximum bathymetric signal at a few hundred meters from the coast. This is shown in one case where the shoals associated with the sand wave are inside the surf zone during moderate storm waves. Thus the sand waves could result from the cross-shore redistribution of the sand associated with an alongshore series of shoals and bed depressions generated by the alongshore transport in the surf zone. While the generation or not of such shoreline waves by this instability strongly depends on their profile, its propagation once they have been created is less sensitive and is well reproduced by the present model. It is explained why the propagation is to the NE along the Delta and Wadden coasts, why it is faster on the latter and why on the Holland coast there is no clear propagation direction.

Erratum: Formation of coastline features by large-scale instabilities induced by high-angle waves

Erratum: Formation of coastline features by large-scale instabilities induced by high-angle waves

Formation of coastline features by large-scale instabilities induced by high-angle waves.

Along shore sediment transport that is driven by waves is generally assumed to smooth a coastline. This assumption is valid for small angles between the wave crest lines and the shore, as has been demonstrated in shoreline models. But when the angle between the waves and the shoreline is sufficiently large, small perturbations to a straight shoreline will grow. Here we use a numerical model to investigate the implications of this instability mechanism for large-scale morphology over long timescales. Our simulations show growth of coastline perturbations that interact with each other to produce large-scale features that resemble various kinds of natural landforms, including the capes and cuspate forelands observed along the Carolina coast of southeastern North America. Wind and wave data from this area support our hypothesis that such an instability mechanism could be responsible for the formation of shoreline features at spatial scales up to hundreds of kilometres and temporal scales up to millennia.