Sandy shorelines exposed to very oblique wave incidence can be unstable and develop self-organized shoreline sand waves. Different types of models predict the formation of these sand waves with an initially dominant alongshore wavelength in the range 1–10 km, which is quite common in nature
Ribas, F.; Falques, A.; Van den Berg, N.; Caballería, M. International journal of sediment research Vol. 28, num. 3, p. 338-348 DOI: 10.1016/S1001-6279(13)60044-X Date of publication: 2013-09 Journal article
The southwestern (SW) coast of Africa (Namibia and Angola) features long sandy beaches and a wave climate dominated by energetic swells from the Southsouthwest (SSW), therefore approaching the coast with a very high obliquity. Satellite images reveal that along that coast there are many shoreline sand waves with wavelengths ranging from 2 to 8 km. A more detailed study, including a Fourier analysis of the shoreline position, yields the wavelengths (among this range) with the highest spectral density concentration. Also, it becomes apparent that at least some of the sand waves are dynamically active rather than being controlled by the geological setting. A morphodynamic model is used to test the hypothesis that these sand waves could emerge as free morphodynamic instabilities of the coastline due to the obliquity in wave incidence. It is found that the period of the incident water waves, Tp, is crucial to establish the tendency to stability or instability, instability increasing for decreasing period, whilst there is some discrepancy in the observed periods. Model results for Tp = 7-8 s clearly show the tendency for the coast to develop free sand waves at about 4 km wavelength within a few years, which migrate to the north at rates of 0.2-0.6 km yr-1. For larger Tp or steeper profiles, the coast is stable but sand waves originated by other mechanisms can propagate downdrift with little decay.
The beach of Calella, north of Barcelona, in the Catalan coast, features a series of shoreline sand waves with wavelengths ranging from 700 to 1400 m that match with similar undulations in the -5 m bathymetric line. Historical satellite images from 2002 till 2010 show that these undulations slightly change in time. The wave climate on that stretch of the Catalan coast has a large proportion of waves from the E-NE and from the SW, i.e., with high angles with respect to shore normal rending the shoreline potentially unstable. Here we show that those sand waves might be due to that instability. Model results, both Linear Stability Analysis and nonlinear time evolution, show that the shoreline is nearly at the threshold for instability and that the emergent wavelengths are roughly consistent with the observed ones.
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.
Shoreline sand waves are shoreline undulations with a length scale of several kilometres and a time scale of years to decades. They occur on many coasts, migrating in the direction of the dominant littoral drift and they introduce a variability into the shoreline position that can be greater than the long term coastal trend. The objective of this thesis is to provide more insight into the formation and dynamics of shoreline sand waves and, in particular, to explore the role of the so called high angle wave instability. Previous studies showed that the shoreline can be unstable under very oblique wave incidence. This high angle wave instability develops due to the feedback of shoreline changes and the associated changes in the bathymetry into the wave field. Wave propagation over this perturbed bathymetry leads to specific gradients in the alongshore transport that can cause the growth and migration of shoreline sand waves.
In this thesis a quasi 2D non-linear morphodynamical model is improved and used to explore high angle wave instability and predict the formation and evolution of shoreline sand waves. The model assumes that the large scale and long term shoreline dynamics is controlled by the wave driven alongshore transport so that the details of the surfzone morphodynamics are not resolved. It overcomes some of the limitations of previous modelling studies on high angle wave instability. The wave field is computed with a simple wave module over the evolving bathymetry and an empirical formula is used to compute the alongshore transport. Cross-shore dynamics is described in a parameterized way and the model is capable of describing shoreline perturbations with a finite and dynamic cross-shore extent. The conditions under which shoreline instability can lead to the formation of shoreline sand waves are refined. Generic simulations with constant wave conditions and random initial perturbations show that the shoreline becomes unstable when the wave incidence angle at the depth of closure (i.e., the most offshore extent of the shoreline perturbations) is larger than a critical angle of about 42 degrees and shoreline sand waves develop in unison. The cross-shore dynamics plays an essential role because it determines the offshore extent of the shoreline perturbations. Using default model parameters, wave conditions and cross-shore profile, the sand waves develop with wavelengths between 2 and 5 km, the time scale for their formation is between 5 and 10 years and they migrate downdrift at about 0.5 km/yr. Simulations with a localized large scale perturbation trigger the formation of a downdrift sand wave train. Larger wave obliquity, higher waves and shorter wave periods strengthen the shoreline instability. A more realistic wave climate, with alternating high and low angle wave incidence reduces the potential for shoreline instability. A percentage of about 80% of high angle waves is required for sand wave formation. It is demonstrated that the range of low wave angles that can occur on a coast is larger than the range of high wave angles, and that the stabilizing effect produced by low angle waves (causing diffusion) is bigger than the destabilizing effect produced by high angle waves (causing growth and migration). Even if high angle waves are not dominant, the instability mechanism might still play a role in the persistence and downdrift migration of large scale shoreline perturbations. The model results are in qualitative agreement with observations of shoreline sand waves.
The quasi 2D approach provides new insight into the physical mechanisms behind high angle wave instability and the occurrence of a minimal and optimal length scale for sand wave formation. Essential physical processes are wave energy dispersion due to wave refraction, wave energy focusing near the crest of a sand wave and the monotonic decrease of the gradients in alongshore transport for increasing length scales.
Les ones de sorra a la línia de costa són ondulacions de la línia de costa amb una escala espacial de kilòmetres i una escala temporal d’anys a dècades. Ocorren a moltes costes, migren en la direcció del transport litoral i introdueixen una variabilitat a la línia de costa que pot ser major que la seva tendència a llarg termini. L’objectiu d’aquesta tesi és estudiar amb més profunditat la formació i la dinàmica de les ones de sorra i, més concretament, explorar el rol de l’anomenada inestabilitat d’angle gran. Estudis previs van demostrar que la línia de costa pot ser inestable en cas d’onades obliqües que incideixen amb un angle gran. Aquesta inestabilitat d’angle gran es produeix degut a la retroalimentació entre els canvis a la línia de costa (i els que conseqüentment ocorren a la batimetria) i els canvis al camp d’onades. La propagació de les onades sobre la batimetria pertorbada crea gradients del transport de sediment longitudinal que causen el creixement i la migració de les ones de sorra.
En aquesta tesi s’ha millorat un model morfodinàmic quasi 2D i no lineal per usar-lo per explorar la inestabilitat d’angle gran i predir la formació i evolució de les ones de sorra. El model assumeix que la dinàmica a gran escala i llarg termini està dominada pel transport de sediment longitudinal produït per les onades de manera que la morfodinàmica de la zona de rompents no es detalla. S’han superat algunes de les limitacions dels estudis anteriors de modelat de la inestabilitat d’angle gran. El camp d’onades es calcula amb un mòdul senzill de propagació sobre la batimetria canviant i el transport longitudinal s’estima usant una fórmula empírica. La dinàmica transversal es parametritza per descriure pertorbacions de la línia de costa amb una extensió transversal finita i dinàmica.
S’han refinat les condicions sota les quals la inestabilitat d’angle gran produeix la formació d’ones de sorra. Les simulacions amb condicions constants d’onades i pertorbacions inicials aleatòries mostren que la línia de costa esdevé inestable quan l’angle d’incidència a la profunditat de tancament és major que un angle de 42 graus i les ones de sorra es desenvolupen a l’uníson. La dinàmica transversal té un rol essencial al determinar l’extensió transversal de les pertorbacions. Usant els valors per defecte dels paràmetres del model, les ones de sorra tenen espaiats d’entre 2 i 5 km i temps de creixement d’entre 5 i 10 anys, i migren en la direcció del transport a uns 0.5 km/any. Les simulacions també mostren que una pertorbació inicial localitzada desencadena la formació d’un tren d’ones de sorra. Com més obliqües i grans són les onades i com menor és el seu període major és la inestabilitat. Un clima d’onatge més realista, alternant onades d’angle d’incidència gran i petit, redueix el potencial de la inestabilitat d’angle gran. Calen almenys un 80% d’onades d’angle gran perquè es formin ones de sorra. El rang d’onades d’angle petit que poden succeir en una costa és major que el d’onades d’angle gran, i l’efecte estabilitzador de les onades d’angle petit (que produeix difusió) és més important que l’efecte desestabilitzador de les onades d’angle gran (que produeix creixement i migració). Fins i tot si les onades d’angle gran no dominen, el mecanisme d’inestabilitat pot tenir un paper important en la persistència i migració de pertorbacions de la línia de costa a gran escala. Els resultats s’assemblen qualitativament a les observacions d’ones de sorra.
L’enfocament quasi 2D permet estudiar més detalls del mecanisme físic que hi ha darrere de la inestabilitat d’angle gran i del fet que existeixin longituds d’ona mínima i òptima per la formació d’ones de sorra. Els processos físics essencials són la dispersió de l’energia de l’onatge degut a la refracció, la concentració d’energia de les onades a les crestes de les ones de sorra i el decreixement monòton del transport litoral quan augmenta l’escala espacial.
Previous research has shown that a very oblique wave incidence on a coast may render a rectilinear shoreline unstable.
Here, we present some further insight into the physics of such instability. The obliqueness of wave incidence has two
effects on the alongshore drift: (i) a direct effect on the relative angle between the wave fronts and the shoreline
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 selforganised
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.
The SW coast of Africa (Namibia and part of Angola) features very long sandy beaches and a wave climate dominated by energetic swells from the SSW, therefore approaching the coast with a very high obliquity. Satellite images reveal that along that coast there are many shoreline sand waves with wavelengths ranging from 2 to 8 km. A more detailed study, including a Fourier analysis of the shoreline position, confirms a high spectral density concentration at these lengths scales. Also, it becomes apparent that at least some of the sand waves are dynamically active rather than being controlled by the geological setting. A morphodynamic model is used to test the hypothesis that these sand waves could emerge as free morphodynamic instabilities of the coastline due to the obliquity in wave incidence. It is found that the wave period, Tp, is crucial to establish the tendency to stability or instability, instability increasing for decreasing period, whilst there is some discrepancy in the observed periods. Model results for Tp = 7 s clearly show the tendency for the coast to develop free sand waves at 2 km wavelength within a few years, which migrate to the north at rates of 0.6-0.7 km/yr. For Tp = 8 s, instability is weaker and rather sensitive to other factors as the underlying bathymetry. In this case, the coast seems to be nearly at neutral stability so that sand waves originated from other mechanisms can propagate downdrift with little decay.
The relatively long sandy beaches of El Maresme, and the bimodal wave climate of the Catalan coast, with dominant E-ENE and SSW waves that leads to high angle of incidence, propitiate good conditions for high angle of wave instability. Subtle undulations of the shoreline and the more intense undulations of the bathymetric contour line of 5 meters depth, with wavelengths of about 1300 m, can be found at that stretch of the coast. A morphodynamic model has been used to test if such undulations could be generated by high angle wave instability. Model results, for wave period of 4 s, show that at El Maresme coast high angle wave instability may develop with time rate of about 1 year and with dominant wavelength that ranges from 600 to 1400 m. For the wave climate of the Catalan coast, wave heights of 0.5 – 1 m and a mean peak period of 5.6 s, and at the steep beaches of El Mareme, it has been found that the wavelength of the instability is in good agreement with the observed undulations, and depends in a sensitive way of the mean slope of the bathymetric profile, and on the length of the bathymetric perturbation.
Falques, A.; Van den Berg, N.; Ribas, F.; Caballería, M. International Symposium Bifurcations and Instabilities in Fluid Dynamics p. 1 Presentation's date: 2011-07-19 Presentation of work at congresses
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.
A Design Study will be undertaken aimed at completing all technical preparatory work necessary for the construction of the European Virtual Observatory (Euro-VO). Euro-VO is a specifically European implementation of the Virtual Observatory (VObs) concep t, and will produce a world leading infrastructure providing a unified virtual data resource and the ability to peform complex data discovery and manipulation tasks across the whole range of astronomy. Access to data and tools will be equally good across Europe, regardless of location. This will require establishing an alliance of data centres, and a VObs facility centre in support of the community, but crucially requires the construction of an infrastructural glue of software components, in the context of rapidly evolving background developments in IT and the grid. The VO-TECH project aims specifically at feasibility studies and design work aimed at integrating such new technologies into the Euro-VO. Key IT advances to build on are in intelligent reso urce discovery (ontology and the semantic web), data mining, and visualisation capabilities. These will be integrated via global astronomical interoperability standards coupled with the latest distributed grid computing services. Additionally this projec t covers design and preparatory work to ensure that data from the major European telescopes and facilities (as represented by the Opticon and RadioNet networks) is fully accessible through the Euro-VO.
The aim of this study is to investigate the
effect of instability on beach nourishments. The main objective is finding out how the
nourishment of a particular beach must be designed to i) optimize its useful lifetime and ii) avoid damage on surrounding beaches.