The instability mechanisms for self-organized kilometer-scale shoreline sand waves have been extensively explored by modeling. However, while the assumed bathymetric perturbation associated with the sand wave controls the feedback between morphology and waves, its effect on the instability onset has not been explored. In addition, no systematic investigation of the effect of the physical parameters has been done yet. Using a linear stability model, we investigate the effect of wave conditions, cross-shore profile, closure depth, and two perturbation shapes (P1: cross-shore bathymetric profile shift, and P2: bed level perturbation linearly decreasing offshore). For a P1 perturbation, no instability occurs below an absolute critical angle ¿c0˜ 40-50°. For a P2 perturbation, there is no absolute critical angle: sand waves can develop also for low-angle waves. In fact, the bathymetric perturbation shape plays a key role in low-angle wave instability: such instability only develops if the curvature of the depth contours offshore the breaking zone is larger than the shoreline one. This can occur for the P2 perturbation but not for P1. The analysis of bathymetric data suggests that both curvature configurations could exist in nature. For both perturbation types, large wave angle, small wave period, and large closure depth strongly favor instability. The cross-shore profile has almost no effect with a P1 perturbation, whereas large surf zone slope and gently sloping shoreface strongly enhance instability under low-angle waves for a P2 perturbation. Finally, predictive statistical models are set up to identify sites prone to exhibit either a critical angle close to ¿c0 or low-angle wave instability.
The role of the high-angle wave instability mechanism in the formation of shoreline undulations observed in the
northern flank of the Dungeness Cuspate Foreland (U.K.) is investigated with a linear stability model. The geographic site characteristics and the restrictions of the model require that waves are previously propagated from the wave buoy to 4 m depth, in front of the undulations. The wave climate is bimodal with oblique waves (which are supposed to be destabilizing) from the SW and nearly normal waves (which are supposed to be stabilizing) from the NE. Despite waves are propagated to a shallow depth, the incoming SW waves are still very oblique with respect to the local shoreline (above 70o) due to the shape of the cuspate foreland. The results of the stability analysis indicate that such highly-oblique waves can trigger the formation of undulations with wavelengths comparable to the observed one.
The feedbacks between morphology and waves through sediment transport are investigated as a source of kilometer-scale shoreline sand waves. In particular, the observed sand waves along Srd. Holmslands Tange, Denmark, are examined. We use a linear stability model based on the one-line approximation, linking the bathymetry to the perturbed shoreline. Previous models that consider the link by shifting the equilibrium profile and neglecting the curvature of the depth contours predict a positive feedback only if the offshore wave incidence angle (¿c) is above a threshold, ¿c¿42°. Considering curvilinear depth contours and using a linearly decaying perturbation in bed level, we find that ¿c can vary over the range 0–90° depending on the background bathymetric profile and the depth of closure, Dc. Associated to the perturbed wave refraction, there are two sources of instability: the alongshore gradients in wave angle, wave angle mechanism, and the alongshore gradients in wave energy induced by wave crest stretching, wave energy mechanism. The latter are usually destabilizing, but the former are destabilizing only for large enough Dc, steep foreshores, and gently sloping shorefaces. The critical angle comes out from the competition between both mechanisms, but when both are destabilizing, ¿c=0. In contrast with earlier studies, the model predicts instability for the Holmslands Tange coast so that the observed sand waves could have emerged from such instability. The key point is considering a larger Dc that is reasonably supported by both observations and wave climate, which brings the wave angle mechanism near the destabilizing threshold.
A morphodynamic model based on the wave-driven alongshore sediment transport, including cross-shore transport in a simplified way and neglecting tides, is presented and applied to the Zandniotor mega-nourishment on the Dutch Delfiand coast. The model is calibrated with the bathymetric data surveyed from January 2012 to March 2013 using measured offshore wave forcing. The calibrated model reproduces accurately the surveyed evolution of the shoreline and depth contours until March 2015. According to the long-term modeling using different wave climate scenarios based on historical data, for the next 30-yr period, the Zandmotor will display diffusive behavior, asymmetric feeding to the adjacent beaches, and slow Migration to the NE. Specifically, the Zandmotor amplitude will have decayed from 960 m to about 350 m with a scatter of only about 40 m associated to climate variability. The modeled coastline diffusivity during the 3-yr period is 0.0021 m(2)/s, close to the observed value of 0.0022 m(2)/s. In contrast, the coefficient of the classical one-line diffusion equation is 0.0052 m(2)/s. Thus, the lifetime prediction, here defined as the time needed to reduce the initial amplitude by a factor 5, would be 90 yr instead of the classical diffusivity prediction of 35 yr. The resulting asymmetric feeding to adjacent beaches prodtices 100 m seaward shift at the NE section and 80 m seaward shift at the SW section. Looking at the variability associated to the different wave climates, the migration rate and the slight shape asymmetry correlate with the wave power asymmetry (W vs N waves) while the coastline diffusivity correlates with the proportion of high-angle waves, suggesting that the Dutch coast is near the high-angle wave instability threshold.
The Sand Engine, ZM (Zandmotor), is a hook-shaped mega-nourishment (21.5 millions m³) located on the
Dutch coast with an alongshore length of 2.4 km and an offshore extension of 1 km. The mega-nourishment project was
initiated as a coastal protection measure on decadal time scales to maintain the coastline under predicted sea level rise.
It follows the philosophy of working in harmony with the forces of nature by taking advantage of the longshore
transport as the main distributor of sand along the adjacent coast (Stive et al., 2013).
In the present contribution we use the Q2Dmorfo model (van den Berg, et al., 2012) to predict the long-term
dynamics of the ZM.
The Sand Engine is a hook-shaped mega-nourishment (21.5 Mm³) located in the Dutch coast with
an alongshore length of 2.4 km and an offshore extension of 1 km. The mega-nourishment project
was initiated as a coastal protection measure on decadal time scales to maintain the coastline under
predicted sea level rise (Stive et al., 2013).
In the present work we use the Q2Dmorfo model (van den Berg, et al., 2012) to predict the
dynamics of idealized mega-nourishments, after validation of the model against the evolution of
the Sand Engine
KM-SCALE SHORELINE SAND WAVES AND NEW INSIGHTS INTO THE DEPTH OF CLOSURE
Albert Falqués, Technical University of Catalonia, email@example.com
Jaime Arriaga, Technical University of Catalonia, firstname.lastname@example.org
Daniel Calvete, Technical University of Catalonia, email@example.com
Déborah Idier, BRGM, D.Idier@brgm.fr
Km-scale shoreline sand waves are undulations of the shoreline with a wavelength in the range 1-10 km that extend offshore typically well beyond the surf zone (van den Berg et al., 2012). They are relevant to coastal engineering because they introduce variability into shoreline position and at the embayments the beach width is reduced, which increases coastal vulnerability (erosional hot spots). We here examine those sand waves that could be generated by the shoreline instability in case of very oblique wave incidence as a result of a positive feedback between shoreline undulations and gradients in littoral drift. This instability has been extensively explored by mathematical modelling (see, e.g., Falqués and Calvete, 2005; van den Berg et al., 2012; Kaergaard and Fredsoe, 2013). However, while modelling studies have been quite successful, direct experimental tests on such models are difficult (Kaergaard and Fredsoe, 2013b; Ribas et al., 2013; Idier and Falqués, 2013) and deserve further attention. In particular, it is very remarkable that for coastlines where the wave climate is dominated by high angle waves the models tend to predict shoreline stability even if these undulations are present. It is intriguing that strengthening the conditions favouring instability, e.g., increasing wave angle, decreasing wave periods or increasing the depth of closure, lead the models to predict instability with the observed wavelengths. For example this is so for the coast of Namibia where the depth of closure must be set to values much larger than those predicted by Hallermeier, 1978 (30-50 m, see Kaergaard and Fredsoe, 2013) to obtain the formation of sand waves with the correct wavelength.
We here explore a new simple formulation of the depth of closure. Morphodynamic models that work with variable conditions do not need a statistically defined Dc as in Hallermeier, 1978, but instantaneous values as a function of wave conditions at each time. Following this idea, the instantaneous Dc is here defined for given wave conditions as the depth where the bed shear stress induced by the wave orbital velocity first exceeds the critical bed shear stress for sediment motion.
We have first examined Holmsland Tange, along the west coast of Denmark (Kaergaard and Fredsoe, 2013), where coastline undulations with wavelength L ¿ 5-6 km, migrating to the south at V ¿ 0.37 km/yr are observed. The mean wave parameters are Hs=1.8 m, Tp=6 s, ¿=42o (at D=-25m). The grain size D50=0.2 mm. The new formulation then gives Dc=20 m. The linear stability model of Falqués and Calvete (2005) gives Lm=5.8 km and V=0.41 km/yr, thereby a remarkable agreement is found. A sensitivity analysis in terms of Dc is shown in Fig. 1. For Dc < 7 m sand waves do not grow anymore. It is also remarkable that there is instability for an angle at the threshold ¿=42o (van den Berg et al., 2012) and the instability mechanism related to wave refraction, which is active for low angle waves, might play a role (Idier et al, 2011). In contrast, Kaergaard and Fredsoe (2013) used Dc=5 m and needed to consider ¿=55-60o and Tp=4-5 s to obtain the growth of sand waves with the observed wavelength. We are now investigating i) the instability mechanism and ii) other coasts like the Netherlands and Namibia/Angola.
Arriaga, J.; Ribas, F.; Mariño-Tapia, I.; Falques, A. International Conference on Coastal Engineering p. 1-13 DOI: 10.9753/icce.v34.sediment.68 Data de presentació: 2014-06-16 Presentació treball a congrés
Km-scale shoreline sand waves have been studied with a quasi two dimensional model (Q2D-morfo model) and with
observations from a populated coastal zone in Yucatán (México) with frequent human interventions. The model was
modified to improve the physics in the case of large amplitude shoreline sand waves that develop due to the high angle
wave instability (HAWI). The modified version of the model can better reproduce the formation of large-amplitude
shoreline sand waves, compared with the original model. Shorelines of Yucatán, from 2004 to 2012, were digitized
and analyzed. Although undulations can be observed, they do not exhibit clear migration or growth, an indication of
being in the limit of instability, in accordance with the results of the model